Journal articles: 'Two Dimensional Discrete Wavelet Transform'

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SUN, YANKUI, YONG CHEN, and HAO FENG. "TWO-DIMENSIONAL STATIONARY DYADIC WAVELET TRANSFORM, DECIMATED DYADIC DISCRETE WAVELET TRANSFORM AND THE FACE RECOGNITION APPLICATION." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 03 (2011): 397–416. http://dx.doi.org/10.1142/s0219691311004110.

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Currently, two-dimensional dyadic wavelet transform (2D-DWT) is habitually considered as the one presented by Mallat, which is defined by an approximation component, two detail components in horizontal and vertical directions. This paper is to introduce a new type of two-dimensional dyadic wavelet transform and its application so that dyadic wavelet can be studied and used widely furthermore. (1) Two-dimensional stationary dyadic wavelet transform (2D-SDWT) is proposed, it is defined by approximation coefficients, detail coefficients in horizontal, vertical and diagonal directions, which is essentially the extension of two-dimensional stationary wavelet transform for orthogonal/biorthogonal wavelet filters. (2) ε-decimated dyadic discrete wavelet transform (DDWT) is introduced and its relation with 2D-SDWT is given, where ε is a sequence of 0's and 1's. (3) Mallat decomposition algorithm based on dyadic wavelet is introduced as a special case of ε-decimated DDWT, and so a face recognition algorithm based on dyadic wavelet is proposed, and experimental results are given to show its effectiveness.

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Kimura, Motoaki, Masahiro Takei, Chih-Ming Ho, Yoshifuru Saito, and Kiyoshi Horii. "Visualization of Shear Stress With Micro Imaging Chip and Discrete Wavelet Transform." Journal of Fluids Engineering 124, no. 4 (2002): 1018–24. http://dx.doi.org/10.1115/1.1516599.

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The two-dimensional low-speed structure of a turbulent boundary layer has been clearly visualized by a combination of a shear stress sensor using micro electro mechanical systems and the discrete wavelet transform. The application of two-dimensional discrete wavelet transforms to the visualization of wall shear stress data obtained using the micro shear stress imaging chip is described. The experiment was carried out under various Reynolds number conditions. It is shown that it is possible to visualize the low-speed streak structure as contours of two-dimensional wavelet level corresponding to spanwise wave number as a function of Reynolds number.

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Asamoah, F. "Discrete Wavelet Analysis of Two-Dimensional Signals." International Journal of Electrical Engineering & Education 39, no. 2 (2002): 162–74. http://dx.doi.org/10.7227/ijeee.39.2.8.

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Discrete wavelet transform using Daubechies coefficients is applied to decompose a two-dimensional signal into levels. Examples are given using BMP images of a sheep and a thumbprint. The size of the two- dimensional signal is 2N by M. It is shown that it is not necessary for M to be a power of 2. A MATLAB program is written for the computations involved.

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Nahar, A. K. "A Compression Original Image Based On The DDWT Technique And Enhancement SNR." International Journal of Engineering Technology and Sciences 5, no. 3 (2018): 73–89. http://dx.doi.org/10.15282/ijets.v5i3.1132.

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Generally, Discrete wavelet transform (DWT) are good perform a when little to no simple mathematical operations in the wavelet basis, in many applications, wavelet transforms can be severely truncated compressed and retain useful information Image compression. Though, DWT and the divided wavelet transform, still suffering from Poor directionality Lack of phase information, and Shift- sensitivity, which is a major drawback in most the communications systems. The Double-Density Discrete Wavelet Transform (DDDWT) achieves great results compared to previous conventional methods less complexity. Credited with this good result, so due to a simplified account that deal with two-dimensional and three-dimensional images by the way and transformation matrices as if through a matrix multiplication between the picture and the conversion of number DDWT. Moreover, the form of repeated goal is achieved with the optimization process for the appropriate application.

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Po-Cheng Wu and Liang-Gee Chen. "An efficient architecture for two-dimensional discrete wavelet transform." IEEE Transactions on Circuits and Systems for Video Technology 11, no. 4 (2001): 536–45. http://dx.doi.org/10.1109/76.915359.

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Shama, Kumara, and Rohan Pinto. "An efficient VLSI architecture for two-dimensional discrete wavelet transform." International Journal of High Performance Systems Architecture 8, no. 3 (2018): 179. http://dx.doi.org/10.1504/ijhpsa.2018.10022496.

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Wang, Ning, and Chungu Lu. "Two-Dimensional Continuous Wavelet Analysis and Its Application to Meteorological Data." Journal of Atmospheric and Oceanic Technology 27, no. 4 (2010): 652–66. http://dx.doi.org/10.1175/2009jtecha1338.1.

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Abstract The two-dimensional continuous wavelet transform (2D CWT) has become an important tool to examine and diagnose nonstationary datasets on the plane. Compared with traditional spectral analysis methods, the 2D CWT provides localized spectral information of the analyzed dataset. It also has the advantage over the 2D discrete wavelet transform (DWT) in that it covers the domain of the analyzed data with a continuous analysis from which detailed, shift-invariant spectral information of different positions and orientations can be obtained. In this paper, a brief introduction of the 2D CWT and some of the most common wavelet mother functions are given, and some practical issues arising from the implementation and applications of the 2D CWT are discussed. The 2D CWT is applied to several test functions to illustrate the effects of the transforms. To demonstrate its practical application, the 2D CWT is used to analyze a set of meteorological data obtained from a numerical model stimulation.

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Pang, Qilong, Liangjie Kuang, Youlin Xu, and Xiang Dai. "Study on the extraction and reconstruction of arbitrary frequency topography from precision machined surfaces." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 233, no. 7 (2018): 1772–80. http://dx.doi.org/10.1177/0954405418802307.

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This article presents an extraction and reconstruction method for arbitrary two-dimensional and three-dimensional frequency features in precision machined surfaces. A combination of power spectrum density and continuous wavelet transform is used to analyze the potassium dihydrogen phosphate crystal surface topography. All frequencies involved in sampling area of measuring instrument are distinguished by power spectrum density method. Compared to discrete wavelet transform used to decompose frequency features, continuous wavelet transform method can extract and reconstruct two-dimensional profile and three-dimensional topography of arbitrary frequency features from original precision machined surfaces. Analysis results show that amplitude and distribution of different frequency features in two-dimensional profile or three-dimensional surface topography are fully restored by continuous wavelet transform. The effects of different factors in machining process on precision machined surface topography may be discovered. Furthermore, the extraction and reconstruction method is generally applicable for the analysis of all precision machined surfaces.

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Ďuriš, Viliam, Vladimir I. Semenov, and Sergey G. Chumarov. "Wavelets and digital filters designed and synthesized in the time and frequency domains." Mathematical Biosciences and Engineering 19, no. 3 (2022): 3056–68. http://dx.doi.org/10.3934/mbe.2022141.

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<abstract> <p>The relevance of the problem under study is due to the fact that the comparison is made for wavelets constructed in the time and frequency domains. The wavelets constructed in the time domain include all discrete wavelets, as well as continuous wavelets based on derivatives of the Gaussian function. This article discusses the possibility of implementing algorithms for multiscale analysis of one-dimensional and two-dimensional signals with the above-mentioned wavelets and wavelets constructed in the frequency domain. In contrast to the discrete wavelet transform (Mallat algorithm), the authors propose a multiscale analysis of images with a multiplicity of less than two in the frequency domain, that is, the scale change factor is less than 2. Despite the fact that the multiplicity of the analysis is less than 2, the signal can be represented as successive approximations, as with the use of discrete wavelet transform. Reducing the multiplicity allows you to increase the depth of decomposition, thereby increasing the accuracy of signal analysis and synthesis. At the same time, the number of decomposition levels is an order of magnitude higher compared to traditional multi-scale analysis, which is achieved by progressive scanning of the image, that is, the image is processed not by rows and columns, but by progressive scanning as a whole. The use of the fast Fourier transform reduces the conversion time by four orders of magnitude compared to direct numerical integration, and due to this, the decomposition and reconstruction time does not increase compared to the time of multiscale analysis using discrete wavelets.</p> </abstract>

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Zhao, Di. "Mobile GPU Computing Based Filter Bank Convolution for Three-Dimensional Wavelet Transform." International Journal of Mobile Computing and Multimedia Communications 7, no. 2 (2016): 22–35. http://dx.doi.org/10.4018/ijmcmc.2016040102.

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Mobile GPU computing, or System on Chip with embedded GPU (SoC GPU), becomes in great demand recently. Since these SoCs are designed for mobile devices with real-time applications such as image processing and video processing, high-efficient implementations of wavelet transform are essential for these chips. In this paper, the author develops two SoC GPU based DWT: signal based parallelization for discrete wavelet transform (sDWT) and coefficient based parallelization for discrete wavelet transform (cDWT), and the author evaluates the performance of three-dimensional wavelet transform on SoC GPU Tegra K1. Computational results show that, SoC GPU based DWT is significantly faster than SoC CPU based DWT. Computational results also show that, sDWT can generally satisfy the requirement of real-time processing (30 frames per second) with the image sizes of 352×288, 480×320, 720×480 and 1280×720, while cDWT can only obtain read-time processing with small image sizes of 352×288 and 480×320.

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Hsieh, Chin Fa, and Tsung Han Tsai. "FPGA Implementation of a High-Speed Two Dimensional Discrete Wavelet Transform." Applied Mechanics and Materials 479-480 (December 2013): 508–12. http://dx.doi.org/10.4028/www.scientific.net/amm.479-480.508.

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This paper proposes high-speed VLSI architecture for implementing a forward two-dimensional discrete wavelet transform (2D DWT). The architecture is based on 2D DWT mathematical formulae. A pipelined scheme is used to increase the clock rate, which allows its critical path to take only one adder delay. The proposed design enables 100% hardware use and faster computing than other 2D DWT architecture. It is easily extended to multilevel decomposition because of its regular structure. It requires N/2 by N/2 clock cycles for k-level analysis of an N by N image. The proposed architecture was coded in VerilogHDL and verified on a real time platform which uses a CMOS image sensor, a field-programmable gate array (FPGA) and a TFT-LCD panel. In the simulation, the design worked with a clock period of 132.38MHz. It can be used as an independent IP core for various real-time applications.

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King-Chu Hung, Yao-Shan Hung, and Yu-Jung Huang. "A nonseparable VLSI architecture for two-dimensional discrete periodized wavelet transform." IEEE Transactions on Very Large Scale Integration (VLSI) Systems 9, no. 5 (2001): 565–76. http://dx.doi.org/10.1109/92.953491.

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Xiong, Chengyi, Jinwen Tian, and Jian Liu. "Efficient Architectures for Two-Dimensional Discrete Wavelet Transform Using Lifting Scheme." IEEE Transactions on Image Processing 16, no. 3 (2007): 607–14. http://dx.doi.org/10.1109/tip.2007.891069.

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Yang, Lina, Yuan Yan Tang, and Qi Sun. "Implementation of 2D Discrete Wavelet Transform by Number Theoretic Transform and 2D Overlap-Save Method." Mathematical Problems in Engineering 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/532979.

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To reduce the computation complexity of wavelet transform, this paper presents a novel approach to be implemented. It consists of two key techniques: (1) fast number theoretic transform(FNTT) In the FNTT, linear convolution is replaced by the circular one. It can speed up the computation of 2D discrete wavelet transform. (2) In two-dimensional overlap-save method directly calculating the FNTT to the whole input sequence may meet two difficulties; namely, a big modulo obstructs the effective implementation of the FNTT and a long input sequence slows the computation of the FNTT down. To fight with such deficiencies, a new technique which is referred to as 2D overlap-save method is developed. Experiments have been conducted. The fast number theoretic transform and 2D overlap-method have been used to implement the dyadic wavelet transform and applied to contour extraction in pattern recognition.

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Upadhyaya, Prashant, Omar Farooq, M. R. Abidi, and Priyanka Varshney. "Comparative Study of Visual Feature for Bimodal Hindi Speech Recognition." Archives of Acoustics 40, no. 4 (2015): 609–19. http://dx.doi.org/10.1515/aoa-2015-0061.

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Abstract In building speech recognition based applications, robustness to different noisy background condition is an important challenge. In this paper bimodal approach is proposed to improve the robustness of Hindi speech recognition system. Also an importance of different types of visual features is studied for audio visual automatic speech recognition (AVASR) system under diverse noisy audio conditions. Four sets of visual feature based on Two-Dimensional Discrete Cosine Transform feature (2D-DCT), Principal Component Analysis (PCA), Two-Dimensional Discrete Wavelet Transform followed by DCT (2D-DWT- DCT) and Two-Dimensional Discrete Wavelet Transform followed by PCA (2D-DWT-PCA) are reported. The audio features are extracted using Mel Frequency Cepstral coefficients (MFCC) followed by static and dynamic feature. Overall, 48 features, i.e. 39 audio features and 9 visual features are used for measuring the performance of the AVASR system. Also, the performance of the AVASR using noisy speech signal generated by using NOISEX database is evaluated for different Signal to Noise ratio (SNR: 30 dB to −10 dB) using Aligarh Muslim University Audio Visual (AMUAV) Hindi corpus. AMUAV corpus is Hindi continuous speech high quality audio visual databases of Hindi sentences spoken by different subjects.

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KATO, TAKESHI, ZHONG ZHANG, HIROSHI TODA, TAKASHI IMAMURA, and TETSUO MIYAKE. "A NOVEL DESIGN METHOD FOR DIRECTIONAL SELECTION BASED ON 2-DIMENSIONAL COMPLEX WAVELET PACKET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (2013): 1360010. http://dx.doi.org/10.1142/s0219691313600102.

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In this paper, we propose a design method for directional selection in the two-dimensional complex wavelet packet transform (2D-CWPT). Current two-dimensional complex discrete wavelet transforms (2D-CDWT) can extract directional components from images, but the number of directions is small, and the directions and resolutions are fixed. Thus the current 2D-CDWTs are not flexible enough. In this study, we propose a new design method of the directional filters that can detect desirable direction components. Additionally flexible directional selection is achieved because the directional filters are added to the 2D-CWPT. Finally, the proposed method is applied to defect detection in semiconductor wafer circuits and an encouraging result is obtained.

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Zazulyak, P. M., and V. I. Nikulishin. "Application of two-dimensional discrete wavelet transform for mapping of the Moon." Astronomical School’s Report 10, no. 2 (2014): 145–46. http://dx.doi.org/10.18372/2411-6602.10.2145.

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YOSHIDA, Taichi, Taizo SUZUKI, Seisuke KYOCHI, and Masaaki IKEHARA. "Two Dimensional Non-separable Adaptive Directional Lifting Structure of Discrete Wavelet Transform." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A, no. 10 (2011): 1920–27. http://dx.doi.org/10.1587/transfun.e94.a.1920.

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Li, H. "5. Visualization of the turbulent jet with two-dimensional discrete wavelet transform." Journal of Visualization 1, no. 2 (1998): 131. http://dx.doi.org/10.1007/bf03182505.

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Meher, P. K., B. K. Mohanty, and J. C. Patra. "Hardware-Efficient Systolic-Like Modular Design for Two-Dimensional Discrete Wavelet Transform." IEEE Transactions on Circuits and Systems II: Express Briefs 55, no. 2 (2008): 151–55. http://dx.doi.org/10.1109/tcsii.2007.911801.

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Darji, Anand, Arun R., Shabbir Noman Merchant, and Arun Chandorkar. "Multiplier‐less pipeline architecture for lifting‐based two‐dimensional discrete wavelet transform." IET Computers & Digital Techniques 9, no. 2 (2015): 113–23. http://dx.doi.org/10.1049/iet-cdt.2013.0167.

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Nourani, Vahid, Armin Farshbaf, and S. Adarsh. "Spatial downscaling of radar-derived rainfall field by two-dimensional wavelet transform." Hydrology Research 51, no. 3 (2020): 456–69. http://dx.doi.org/10.2166/nh.2020.165.

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Abstract Downscaling of rainfall fields, either as images or products of global circulation models, have been the motive of many hydrologists and hydro-meteorologists. The main concern in downscaling is to transform high-resolution properties of the rainfall field to lower resolution without introducing erroneous information. In this paper, rainfall fields obtained from Next Generation Weather Surveillance Radar (NEXRAD) Level III were examined in the wavelet domain which revealed sparsity for wavelet coefficients. The proposed methodology in this work employs a concept named Standardized Rainfall Fluctuation (SRF) to overcome the sparsity of rainfall fields in wavelet domain which also exhibited scaling behaviors in a range of scales. SRFs utilizes such scaling behaviors where upscaled versions of the rainfall fields are downscaled to their actual size, using a two-dimensional discrete wavelet transform, to examine the reproduction of the rainfall fields. Furthermore, model modifications were employed to enhance the accuracy. These modifications include removing the negative values while conserving the mean and applying a non-overlapping kernel to restore high-gradient clusters of rainfall fields. The calculated correlation coefficient, statistical moments, determination coefficient and spatial pattern display a good agreement between the outputs of the downscaling method and the observed rainfall fields.

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Deng, Ming Hui, Jian Xin Kang, and Yan Jun Li. "The Fusion Algorithm of Infrared and Visible Images Based on Computer Vision." Advanced Materials Research 945-949 (June 2014): 1851–55. http://dx.doi.org/10.4028/www.scientific.net/amr.945-949.1851.

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Directionlet transform is a lattice-based skewed discrete wavelet transform. It has advantages of multi-directional and anisotropy compared with standard two-dimensional wavelet transform, thus, it is better at describing the characteristics of images. For the research focus of different-source image fusion, a novel fusion algorithm based on Directionlet transform was proposed, and the fusion speed was improved efficiently by combing the transform with a lifting scheme. Firstly, between transform direction and alignment direction, two registered source images were decomposed by using lifting Directionlet transform respectively in different times, thus anisotropic sub images were obtained. Then, the low frequency components were combined averagely and the selection principle of high frequency sub images were based on which has stronger anisotropic edge information. Finally, the fused image was obtained by using inverse Directionlet transform. Experimental results show that the fusion effect and speed are both better than standard wavelet transform and other second generation wavelet transform.

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Kerimov, Azer. "An algorithm of the sequence of artificial symmetric signals for comparing and creating a new convolution method." Problems of Information Society 15, no. 2 (2024): 24–29. http://dx.doi.org/10.25045/jpis.v15.i2.03.

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The objective of this article is to create an algorithm of the sequence of artificial signals that can be used to compare and create methods for processing one- and two-dimensional signals. It will then be implemented to compare feature extraction methods that rely on discrete wavelet transforms. The discrete wavelet transform is superior to other signal processing techniques in several ways. Developing a feature set is a crucial step in using the discrete wavelet transform. Mean value and standard deviation are suggested as feature extraction techniques in this study. The mean value is the only option selected for the first feature extraction method; the mean value and standard deviation are selected for the second feature extraction method. To build any number of artificial signal sequences from a single, several conditions are taken into account, for example, their symmetry, they are supposed to be located at the same distance from each other, that is, with an equal step. Symmetrical signal sequences constructed in this way differ from common wellknown signal sequences, such as Fourier series, in that they converge to a given signal in equal steps.

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PourArian, Mohammad Rasoul, and Ali Hanani. "Blind Steganography in Color Images by Double Wavelet Transform and Improved Arnold Transform." Indonesian Journal of Electrical Engineering and Computer Science 3, no. 3 (2016): 586. http://dx.doi.org/10.11591/ijeecs.v3.i3.pp586-600.

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<p>Steganography is a method which can put data into a media without a tangible impact on the cover media. In addition, the hidden data can be extracted with minimal differences. In this paper, two-dimensional discrete wavelet transform is used for steganography in 24-bit color images. This steganography is of blind type that has no need for original images to extract the secret image. In this algorithm, by the help of a structural similarity (SSIM) and a two-dimensional correlation coefficient, it is tried to select part of sub-band cover image instead of embedding location. These sub-bands are obtained by 3-levels of applying the DWT. Also to increase the steganography resistance against cropping or insert visible watermark, two channels of color image is used simultaneously. In order to raise the security, an encryption algorithm based on Arnold transform was also added to the steganography operation. </p>

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Abdul-Jabbar, Jassim, Zahraa Abede, and Akram Dawood. "A Multiplier-less Implementation of Two-Dimensional Circular-Support Wavelet Transform on FPGA." Iraqi Journal for Electrical and Electronic Engineering 9, no. 1 (2013): 16–28. http://dx.doi.org/10.37917/ijeee.9.1.2.

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In this paper, a two-dimensional (2-D) circular-support wavelet transform (2-D CSWT) is presented. 2-D CSWT is a new geometrical image transform, which can efficiently represent images using 2-D circular spectral split schemes (circularlydecomposed frequency subspaces). 2-D all-pass functions and lattice structure are used to produce 1-level circular symmetric 2-D discrete wavelet transform with approximate linear phase 2-D filters. The classical one-dimensional (1-D) analysis Haar filter bank branches H0(z) and H1(z) which work as low-pass and high-pass filters, respectively are transformed into their 2-D counterparts H0(z1,z2) and H1(z1,z2) by applying a circular-support version of the digital spectral transformation (DST). The designed 2-D wavelet filter bank is realized in a separable architecture. The proposed architecture is simulated using Matlab program to measure the deflection ratio (DR) of the high frequency coefficient to evaluate its performance and compare it with the performance of the classical 2-D wavelet architecture. The correlation factor between the input and reconstructed images is also calculated for both architectures. The FPGA (Spartan-3E) Kit is used to implement the resulting architecture in a multiplier-less manner and to calculate the die area and the critical path or maximum frequency of operation. The achieved multiplier-less implementation takes a very small area from FPGA Kit (the die area in 3-level wavelet decomposition takes 300 slices with 7% occupation ratio only at a maximum frequency of 198.447 MHz).

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Palmer, Stuart, and Xungai Wang. "Objective Classification of Fabric Pilling Based on the Two-Dimensional Discrete Wavelet Transform." Textile Research Journal 73, no. 8 (2003): 713–20. http://dx.doi.org/10.1177/004051750307300809.

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Ponce de León, Jesús, José Ramón Beltrán, and Fernando Beltrán. "Instantaneous frequency estimation and representation of the audio signal through Complex Wavelet Additive Synthesis." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 03 (2014): 1450030. http://dx.doi.org/10.1142/s0219691314500301.

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In this work, an improvement of the Complex Wavelet Additive Synthesis (CWAS) algorithm is presented. This algorithm is based on a discrete version of the Complex Continuous Wavelet Transform (CCWT) which analyzes the input signal in a frame-to-frame approach and under variable frequency resolution per octave. After summarizing several Time-Frequency Distributions (TFD), concretely the standard Short Time Fourier Transform (STFT), the Pseudo Wigner–Ville Distribution (PWVD), reassignment and complex wavelets, a comparative study of the accuracy in the instantaneous frequency (IF) estimation is shown. The comparative study includes three different signal processing tools (based on the summarized TFD): the Time-Frequency Toolbox (TFTB) of François Auger, the High Resolution Spectrographic Routines (HRSR) of Sean Fulop and the proposed CWAS algorithm. A set of eight synthetic signals have been analyzed using six different methods: the regular STFT spectrogram, the PWVD, their corresponding reassigned versions, the Nelson crossed spectrum method and finally the Complex Continuous Wavelet Transform (CCWT). Finally, two- and three-dimensional Time-Frequency representations of the IF provided by the CWAS algorithm are presented.

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Chao-Tsung Huang, Po-Chih Tseng, and Liang-Gee Chen. "Generic RAM-based architectures for two-dimensional discrete wavelet transform with line-based method." IEEE Transactions on Circuits and Systems for Video Technology 15, no. 7 (2005): 910–20. http://dx.doi.org/10.1109/tcsvt.2005.848307.

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Palmer, Stuart, and Xungai Wang. "Evaluating the Robustness of Objective Pilling Classification with the Two- Dimensional Discrete Wavelet Transform." Textile Research Journal 74, no. 2 (2004): 140–45. http://dx.doi.org/10.1177/004051750407400210.

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Mishra, D. C., and R. K. Sharma. "Application of algebra and discrete wavelet transform in two-dimensional data (RGB-images) security." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 06 (2014): 1450040. http://dx.doi.org/10.1142/s0219691314500404.

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In this cryptosystem, we have considered RGB images for two-dimensional (2D) data security. Security of RGB images during transmission is a major concern, discussed globally. This paper proposes a novel technique for color image security by random hill cipher (RHC) over SLn(𝔽) domain associated with 2D discrete wavelet transform. Existing techniques have discussed the security of image data on the basis of the keys only (which provide only one layer of security for image data), but in the proposed cryptosystem, the keys and the arrangement of RHC parameters are imperative for correct decryption of color image data. Additionally, key multiplication side (pre or post) with the RGB image data should inevitably be known, to correctly decrypt the encrypted image data. So, the proposed cryptosystem provides three layers of security for RGB image data. In this approach, we have considered keys from the special linear group over a field 𝔽, which provides enormous key-space for the proposed cryptosystem. A computer simulation on standard examples and results is given to support the fixture of the scheme. Security analysis, and detailed comparison between formerly developed techniques and proposed cryptosystem are also discussed for the robustness of the technique. This method will have large potential usage in the digital RGB image processing and the security of image data.

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Yocky, David A. "Image merging and data fusion by means of the discrete two-dimensional wavelet transform." Journal of the Optical Society of America A 12, no. 9 (1995): 1834. http://dx.doi.org/10.1364/josaa.12.001834.

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Vijayaraju, P., B. Sripathy, D. Arivudainambi, and S. Balaji. "Hybrid Memetic Algorithm With Two-Dimensional Discrete Haar Wavelet Transform for Optimal Sensor Placement." IEEE Sensors Journal 17, no. 7 (2017): 2267–78. http://dx.doi.org/10.1109/jsen.2017.2662951.

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Alaba, Simegnew Yihunie, and John E. Ball. "WCNN3D: Wavelet Convolutional Neural Network-Based 3D Object Detection for Autonomous Driving." Sensors 22, no. 18 (2022): 7010. http://dx.doi.org/10.3390/s22187010.

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Three-dimensional object detection is crucial for autonomous driving to understand the driving environment. Since the pooling operation causes information loss in the standard CNN, we designed a wavelet-multiresolution-analysis-based 3D object detection network without a pooling operation. Additionally, instead of using a single filter like the standard convolution, we used the lower-frequency and higher-frequency coefficients as a filter. These filters capture more relevant parts than a single filter, enlarging the receptive field. The model comprises a discrete wavelet transform (DWT) and an inverse wavelet transform (IWT) with skip connections to encourage feature reuse for contrasting and expanding layers. The IWT enriches the feature representation by fully recovering the lost details during the downsampling operation. Element-wise summation was used for the skip connections to decrease the computational burden. We trained the model for the Haar and Daubechies (Db4) wavelets. The two-level wavelet decomposition result shows that we can build a lightweight model without losing significant performance. The experimental results on KITTI’s BEV and 3D evaluation benchmark show that our model outperforms the PointPillars-based model by up to 14% while reducing the number of trainable parameters.

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Shahbazian, Mehdi, and Saeed Shahbazian. "Simultaneous Least Squares Wavelet Decomposition for Multidimensional Irregularly Spaced Data." Applied Mechanics and Materials 239-240 (December 2012): 1213–18. http://dx.doi.org/10.4028/www.scientific.net/amm.239-240.1213.

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The multidimensional Discrete Wavelet Transform (DWT) has been widely used in signal and image processing for regularly sampled data. For irregularly sampled data, however, other techniques should be used including the Least Square Wavelet Decomposition (LSWD). The commonly used level by level (sequential) wavelet decomposition, which calculates the wavelet coefficients in each resolution separately, may result in a gross interpolation error. To overcome this drawback, a different approach called the Simultaneous Least Square Wavelet Decomposition, which computes all wavelet coefficients simultaneously, have been proposed by the authors. In this paper, we extend the simultaneous LSWD approach to the multidimensional case and show that this method has excellent reconstruction property for two dimensional irregularly spaced data.

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Pan, Xiao Zhong, and Hao Ming Wang. "The Detection Method of Image Regional Forgery Based DWT and 2DIMPCA." Advanced Materials Research 532-533 (June 2012): 692–96. http://dx.doi.org/10.4028/www.scientific.net/amr.532-533.692.

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Copy-Move is a common forgery in the research ﬁeld of digital image forensics, this paper proposes a detection approach based on wavelet transform and two-dimensional image principal component analysis. After reducing the image dimension by Discrete Wavelet Transform(DWT)，2DIMPCA is applied to the fixed sized overlapping blocks of a low-frequency image in the wavelet sub-band to yield a reduced dimension representation from the horizontal direction and the vertical direction. The eigenvectors are then lexicographically sorted, the forgery part are localized by detecting for all neighborhood vectors by a certain threshold. The experiments demonstrate that the proposed approach can not only localize the copy forgery regions accurately, but also reduce the amount of computation and improve the detection efﬁciency.

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Sudhakar Ilango, S., V. Seenivasagam, and R. Madhumitha. "Hybrid two-dimensional dual tree—biorthogonal wavelet transform and discrete wavelet transform with fuzzy inference filter for robust remote sensing image compression." Cluster Computing 22, S6 (2018): 13473–86. http://dx.doi.org/10.1007/s10586-018-1982-9.

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Nian, Yongjian, Ke Xu, Jianwei Wan, Ling Wang, and Mi He. "Block-based KLT compression for multispectral images." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 04 (2016): 1650029. http://dx.doi.org/10.1142/s0219691316500296.

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An efficient lossy compression algorithm for multispectral images based on block Karhunen–Loève transform (KLT) is proposed. First, a two-dimensional discrete wavelet transform is performed on each band of multispectral images to remove the spatial correlation. Subsequently, each band is partitioned into non-overlapping blocks of the same size, and the transform coefficients of each block in the wavelet domain are treated as a single object. Blocks that are co-located in the spectral orientation are affected by an adaptive Karhunen–Loève transform to remove their spectral correlation. Finally, embedded block coding with optimized truncation is performed on all principal components to generate the final bit-stream. Experimental results show that the proposed algorithm, based on block KLT, outperforms the algorithm based on global KLT, without significant increase of complexity.

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Barua, S., J. E. Carletta, K. A. Kotteri, and A. E. Bell. "An efficient architecture for lifting-based two-dimensional discrete wavelet transforms." Integration 38, no. 3 (2005): 341–52. http://dx.doi.org/10.1016/j.vlsi.2004.07.010.

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Bazine, Razika, Huayi Wu, and Kamel Boukhechba. "Spectral DWT Multilevel Decomposition with Spatial Filtering Enhancement Preprocessing-Based Approaches for Hyperspectral Imagery Classification." Remote Sensing 11, no. 24 (2019): 2906. http://dx.doi.org/10.3390/rs11242906.

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In this paper, spectral–spatial preprocessing using discrete wavelet transform (DWT) multilevel decomposition and spatial filtering is proposed for improving the accuracy of hyperspectral imagery classification. Specifically, spectral DWT multilevel decomposition (SDWT) is performed on the hyperspectral image to separate the approximation coefficients from the detail coefficients. For each level of decomposition, only the detail coefficients are spatially filtered instead of being discarded, as is often adopted by the wavelet-based approaches. Thus, three different spatial filters are explored, including two-dimensional DWT (2D-DWT), adaptive Wiener filter (AWF), and two-dimensional discrete cosine transform (2D-DCT). After the enhancement of the spectral information by performing the spatial filter on the detail coefficients, DWT reconstruction is carried out on both the approximation and the filtered detail coefficients. The final preprocessed image is fed into a linear support vector machine (SVM) classifier. Evaluation results on three widely used real hyperspectral datasets show that the proposed framework using spectral DWT multilevel decomposition with 2D-DCT filter (SDWT-2DCT_SVM) exhibits a significant performance and outperforms many state-of-the-art methods in terms of classification accuracy, even under the constraint of small training sample size, and execution time.

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Wang, Bangbing, Bo Sun, Jiaxin Wang, et al. "Removal of ‘strip noise’ in radio-echo sounding data using combined wavelet and 2-D DFT filtering." Annals of Glaciology 61, no. 81 (2019): 124–34. http://dx.doi.org/10.1017/aog.2019.4.

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ABSTRACTRadio-echo sounding (RES) can be used to understand ice-sheet processes, englacial flow structures and bed properties, making it one of the most popular tools in glaciological exploration. However, RES data are often subject to ‘strip noise’, caused by internal instrument noise and interference, and/or external environmental interference, which can hamper measurement and interpretation. For example, strip noise can result in reduced power from the bed, affecting the quality of ice thickness measurements and the characterization of subglacial conditions. Here, we present a method for removing strip noise based on combined wavelet and two-dimensional (2-D) Fourier filtering. First, we implement discrete wavelet decomposition on RES data to obtain multi-scale wavelet components. Then, 2-D discrete Fourier transform (DFT) spectral analysis is performed on components containing the noise. In the Fourier domain, the 2-D DFT spectrum of strip noise keeps its linear features and can be removed with a ‘targeted masking’ operation. Finally, inverse wavelet transforms are performed on all wavelet components, including strip-removed components, to restore the data with enhanced fidelity. Model tests and field-data processing demonstrate the method removes strip noise well and, incidentally, can remove the strong first reflector from the ice surface, thus improving the general quality of radar data.

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Baozhi, Cheng. "Anomaly targets detection of hyperspectral imagery based on wavelet transform and sparse representation." MATEC Web of Conferences 232 (2018): 02054. http://dx.doi.org/10.1051/matecconf/201823202054.

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The research of anomaly target detection algorithm in hyperspectral imagery is a hot issue, which has important research value. In order to overcome low efficiency of current anomaly target detection in hyperspectral image, an anomaly detection algorithm for hyperspectral images based on wavelet transform and sparse representation was proposed. Firstly, two-dimensional discrete wavelet transform is used to denoise the hyperspectral image, and the new hyperspectral image data are obtained. Then, the results of anomaly target detection are obtained by using sparse representation theory. The real AVIRIS hyperspectral imagery data sets are used in the experiments. The results show that the detection accuracy and false alarm rate of the propoesd algorithm are better than RX and KRX algorithm.

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M. Abdul-Jabbar, Jassim, and Zahraa Talal Abed Al-Mokhtar. "Design and FPGA Implementation of Two-Dimensional Discrete Wavelet Transform Architectures Using Raster-Scan Method." AL-Rafdain Engineering Journal (AREJ) 22, no. 2 (2014): 60–72. http://dx.doi.org/10.33899/rengj.2014.87323.

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Tian, Xin, Lin Wu, Yi-Hua Tan, and Jin-Wen Tian. "Efficient Multi-Input/Multi-Output VLSI Architecture for Two-Dimensional Lifting-Based Discrete Wavelet Transform." IEEE Transactions on Computers 60, no. 8 (2011): 1207–11. http://dx.doi.org/10.1109/tc.2010.178.

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ZHANG, ZHONG, NARIYA KOMAZAKI, TAKASHI IMAMURA, TETSUO MIYAKE, and HIROSHI TODA. "DIRECTIONAL SELECTION OF TWO-DIMENSIONAL COMPLEX DISCRETE WAVELET TRANSFORM AND ITS APPLICATION TO IMAGE PROCESSING." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 04 (2010): 659–76. http://dx.doi.org/10.1142/s0219691310003705.

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In this study, a novel direction selection method using the two-dimensional complex discrete wavelet transform (2D-CDWT) is proposed. In order to achieve arbitrary direction selection, the directional filters are first designed. Calculation procedure of directional selection can be shown as follows: (1) The 16 sub-images are generally generated from the original image by the 2D-CDWT without a down-sampling process and the 12 sub-images that correspond to the high-frequency components are selected. (2) The 12 sub-images are filtered by using the designed directional filter. (3) The down-sampling process is carried out and the resulting images are obtained. Furthermore, this method is applied to the surface analysis of a wafer, and it is confirmed that our method is effective in detecting irregular direction components.

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Nayak, Deepak Ranjan, Ratnakar Dash, and Banshidhar Majhi. "Brain MR image classification using two-dimensional discrete wavelet transform and AdaBoost with random forests." Neurocomputing 177 (February 2016): 188–97. http://dx.doi.org/10.1016/j.neucom.2015.11.034.

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Kovac, Ondrej, Jan Mihalik, and Iveta Gladisova. "Convolution implementation with a novel approach of DGHM multiwavelet image transform." Journal of Electrical Engineering 68, no. 6 (2017): 455–62. http://dx.doi.org/10.1515/jee-2017-0080.

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AbstractThe purpose of this paper is to develop convolution implementation of DGHM (Donovan, Geronimo, Harding, Massopust) multiwavelet image transform using a new approach of ordering wavelet coefficients at the second and higher levels. Firstly, the method of implementation of one-dimensional discrete multiwavelet transform (1D DMWT) for DGHM multiwavelet using discrete convolution and scalar filters is presented. Then, convolution implementation of DGHM multiwavelet image transform by application of 1D DMWT for two dimensions (2D) in a separable way is proposed. Next, the second level of 2D DMWT is performed in three possible ways. The novelty of the proposed implementation is in reordering of L subband wavelet coefficients at the first level into one subimage. The results are evaluated as the energy ratios between the transformed images in L subband at the second level and the input original image. According to the experimental results, the developed implementation of 2D DMWT is approximately 5% more effective in energy compression than the ones most commonly mentioned in the literature. This paper shows a possibility of convolution implementation of 2D DMWT with higher energy compression.

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Jlaiel, Khouloud. "Exploring fourier transformations: benefits, limitations, and applications in analyzing two-dimensional right rectangular prism’s magnetic field." Geosciences and Engineering 12, no. 1 (2024): 57–74. https://doi.org/10.33030/geosciences.2024.01.004.

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Fourier Transformations are crucial in signal processing, offering a unique approach for complex data analysis. This paper explores their advantages and limitations, explaining key concepts like Fourier Transformation, Fourier series, Discrete Fourier Transform, and Continuous Fourier Transform, focusing on practical applications. The strengths, such as signal decomposition into frequency components, are exemplified through a case study on the total magnetic field of two-dimensional right rectangular prisms. However, limitations arise with non-stationary signals due to the assumption of stationarity. Alternative methods like the Wavelet Transformation and Short-Time Fourier Transformation are briefly discussed. Serving as a practical guide, this paper aids researchers in utilizing Fourier Transformations while recognizing scenarios where alternative techniques may be more suitable.

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MISHRA, D. C., R. K. SHARMA, MAYANK DAWAR, and M. HANMANDLU. "TWO LAYERS OF SECURITY FOR COLOR VIDEO BY MATRIX AFFINE CIPHER WITH TWO-DIMENSIONAL DISCRETE WAVELET TRANSFORM." Fractals 23, no. 04 (2015): 1550037. http://dx.doi.org/10.1142/s0218348x15500371.

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In this cryptosystem, we have presented a novel technique for security of video data by using matrix affine cipher (MAC) combined with two-dimensional discrete wavelet transform (2D-DWT). Existing schemes for security of video data provides only one layer of security, but the presented technique provides two layers of security for video data. In this cryptosystem, keys and arrangement of MAC parameters are imperative for decryption process. In this cryptosystem, if the attacker knows about all the exact keys, but has no information about the specific arrangement of MAC parameters, then the information of original video cannot be recovered from the encrypted video. Experimental results on standard examples support to the robustness and appropriateness of the presented cryptosystem of video encryption and decryption. The statistical analysis of the experimental results based on standard examples critically examine the behavior of the proposed technique. Comparison between existing schemes for security of video with the presented cryptosystem is also provided for the robustness of the proposed cryptosystem.

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Gong, Rui Kun, Ya Nan Zhang, Chong Hao Wang, and Li Jing Zhao. "Application of the Compound Model of BP Neural Networks and Wavelet Transform in Image Definition Identification." Advanced Materials Research 605-607 (December 2012): 2265–69. http://dx.doi.org/10.4028/www.scientific.net/amr.605-607.2265.

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First, the background, significance and general implementation of the image definition identification are introduced. Then, basic theory of wavelet transform and neural network is expounded. An identification method of image definition based on the composite model of wavelet analysis and neural network is suggested．The two—dimensional discrete wavelet transformation is used to filter image signal and extract its brim character which is input into BP neural network for identification. 4 layers of BP neural network are constructed to perform image definition identification. The compound model is first trained by 90 images from the training set, and then is tested by 87 images from the testing set. The results show that this is a very effective identification method which can obtain a higher recognition rate.

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Journal articles on the topic 'Two Dimensional Discrete Wavelet Transform'

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