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Journal articles on the topic 'Decomposition (Mathematics) Filters (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

Cotronei, Mariantonia, Milvia Rossini, Tomas Sauer, and Elena Volontè. "Filters for anisotropic wavelet decompositions." Journal of Computational and Applied Mathematics 349 (March 2019): 316–30. http://dx.doi.org/10.1016/j.cam.2018.09.015.

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LI, SHUTAO. "MULTISENSOR REMOTE SENSING IMAGE FUSION USING STATIONARY WAVELET TRANSFORM: EFFECTS OF BASIS AND DECOMPOSITION LEVEL." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 01 (2008): 37–50. http://dx.doi.org/10.1142/s0219691308002203.

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Stationary wavelet transform is an efficient algorithm for remote sensing image fusion. In this paper, we investigate the effects of orthogonal/biorthogonal filters and decomposition depth on using stationary wavelet analysis for fusion. Spectral discrepancy and spatial distortion are used as quality measures. Empirical results lead to some recommendations on the wavelet filter parameters for use in remote sensing image fusion applications.

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3

Jun, Young Bae, and Aiyared Iampan. "Shift Up-Filters and Decompositions of Up-Filters in Up-Algebras." Missouri Journal of Mathematical Sciences 31, no. 1 (2019): 36–45. http://dx.doi.org/10.35834/mjms/1559181624.

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Su, Lo-Chyuan, Yue-Dar Jou, and Fu-Kun Chen. "Improved Computing-Efficiency Least-Squares Algorithm with Application to All-Pass Filter Design." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/249021.

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All-pass filter design can be generally achieved by solving a system of linear equations. The associated matrices involved in the set of linear equations can be further formulated as a Toeplitz-plus-Hankel form such that a matrix inversion is avoided. Consequently, the optimal filter coefficients can be solved by using computationally efficient Levinson algorithms or Cholesky decomposition technique. In this paper, based on trigonometric identities and sampling the frequency band of interest uniformly, the authors proposed closed-form expressions to compute the elements of the Toeplitz-plus-Ha

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KIM, WONKOO, and CHING-CHUNG LI. "ON PRECONDITIONING MULTIWAVELET SYSTEMS FOR IMAGE COMPRESSION." International Journal of Wavelets, Multiresolution and Information Processing 01, no. 01 (2003): 51–74. http://dx.doi.org/10.1142/s0219691303000049.

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This paper presents a study on applications of multiwavelet analysis to image compression. The biorthogonality and perfect reconstruction conditions are applied to multiwavelet filters. As a multiwavelet filter bank has multiple channels of inputs, the data structure of inputs to the multiwavelet system should be taken into consideration in multiwavelet decomposition and reconstruction algorithms. We investigate the data initialization problem by considering prefilters and postfilters that may give more efficient representations of the decomposed data. The interpolation postfilter and prefilte

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Et. al., Gutta Srinivas Rao,. "Morphological Transformation In Poor Lighting Images For Image Contrast Enhancement." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 5 (2021): 1559–68. http://dx.doi.org/10.17762/turcomat.v12i5.2127.

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The paper presents a novel algorithm for the computation of the image decomposition using a morphological filter with reconstruction. The target applications are image contrast enhancement especially those with high dynamic content. Both bright and dark regions contrast enhancement were considered. A new hardware efficient implementation of decomposition is presented. Following decomposition in 5 levels of detail a local contrast enhancement is performed. The new reconstruction algorithm and its hardware implementation as proposed is shown to be independent on structural element size and that

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Tiddeman, Bernard, and Morteza Ghahremani. "Principal Component Wavelet Networks for Solving Linear Inverse Problems." Symmetry 13, no. 6 (2021): 1083. http://dx.doi.org/10.3390/sym13061083.

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In this paper we propose a novel learning-based wavelet transform and demonstrate its utility as a representation in solving a number of linear inverse problems—these are asymmetric problems, where the forward problem is easy to solve, but the inverse is difficult and often ill-posed. The wavelet decomposition is comprised of the application of an invertible 2D wavelet filter-bank comprising symmetric and anti-symmetric filters, in combination with a set of 1×1 convolution filters learnt from Principal Component Analysis (PCA). The 1×1 filters are needed to control the size of the decompositio

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Fathee, Hala N., Osman N. Ucan, Jassim M. Abdul-Jabbar, and Oguz Bayat. "Efficient Unconstrained Iris Recognition System Based on CCT-Like Mask Filter Bank." Mathematical Problems in Engineering 2019 (May 15, 2019): 1–10. http://dx.doi.org/10.1155/2019/6575019.

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In this paper, a new personal identification method based on unconstrained iris recognition is presented. We apply a nontraditional step for feature extraction where a new circular contourlet filter bank is used to capture the iris characteristics. This idea is based on a new geometrical image transform called the circular contourlet transform (CCT). An efficient multilevel and multidirectional contourlet decomposition method is needed to form a reduced-length quantized feature vector with improved performance. The CCT transform provides both multiscale and multioriented analysis of iris featu

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9

FUJINOKI, KENSUKE, and SHUNSUKE ISHIMITSU. "TRIANGULAR BIORTHOGONAL WAVELETS WITH EXTENDED LIFTING." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 04 (2013): 1360002. http://dx.doi.org/10.1142/s0219691313600023.

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We present a new family of triangular biorthogonal wavelets that is defined on a triangular lattice by introducing a new operation to generalize two-dimensional lifting, which we call twist. The resulting filters inherit several remarkable features of the early triangular biorthogonal wavelet filters such as the hexagonal symmetry of low-pass filters, symmetrical arrangement of three high-pass filters on the lattice, and that the wavelet decomposition produces uniform energy distributions over three detail components, preserving the isotropy of decomposed images. Additionally, these filters ar

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Karatoprak, Erinc, and Serhat Seker. "An Improved Empirical Mode Decomposition Method Using Variable Window Median Filter for Early Fault Detection in Electric Motors." Mathematical Problems in Engineering 2019 (February 19, 2019): 1–9. http://dx.doi.org/10.1155/2019/8015295.

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This paper proposes an improved Empirical Mode Decomposition (EMD) method by using variable window size median filters during the Intrinsic Mode Functions (IMFs) generation. Compared to the traditional EMD, the improved EMD, namely, Median EMD (MEMD), helps to reduce mode-mixing providing an improvement in terms of separating the fundamental frequencies per IMF. The MEMD method applies the EMD to the signal and then applies a variable window size median filter to the resulting IMFs. A narrow window is used for high frequency components where a broader window is used for the lower frequency com

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11

McWhorter, Francis I., and John A. Tague. "High speed implementation of certain adaptive filters: A novel Toeplitz matrix decomposition approach." Circuits, Systems, and Signal Processing 12, no. 4 (1993): 495–502. http://dx.doi.org/10.1007/bf01188091.

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12

Mertzios, Vassilis G., and Anastasios N. Venetsanopoulos. "Block decomposition structures for the fast modular implementation of two-dimensional digital filters." Circuits, Systems, and Signal Processing 8, no. 2 (1989): 163–85. http://dx.doi.org/10.1007/bf01599936.

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13

Deng, Yaohua, Sicheng Chen, Bingjing Li, Jiayuan Chen, and Liming Wu. "Study and Testing of Processing Trajectory Measurement Method of Flexible Workpiece." Mathematical Problems in Engineering 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/798274.

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Flexible workpiece includes the materials like elasticity spline, textile fabric, and polyurethane sponge, due to the fact that processing trajectory is composed by small arc or small line segment primitives and the deformation of the flexible workpiece during the processing trajectory, making the captured image of processing trajectory not clear, the edge of processing image over local uneven gray, and also the pixels of boundaries between the processing trajectory image edge and background organizations not obvious. This paper takes corner search of processing trajectory as the cut-in-point,

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14

WANG, Y. Y., and Y. LU. "Implementation of the Notch Filters Using Subband Decomposition." IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E90-A, no. 6 (2007): 1224–27. http://dx.doi.org/10.1093/ietfec/e90-a.6.1224.

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15

Litichevskiy, D. V. "PYRAMID SCHEME FOR CONSTRUCTING BIORTHOGONAL WAVELET CODES OVER FINITE FIELDS." Prikladnaya Diskretnaya Matematika, no. 51 (2021): 101–19. http://dx.doi.org/10.17223/20710410/51/5.

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The existence of a biorthogonal decomposition of the space V of dimension n over the field GF(q) is constructively proved, namely, two representations of it are obtained as direct sums of subspaces V = W0⊕W1⊕. . .⊕WJ⊕VJ and V = W˜0⊕W˜1⊕. . .⊕W˜J⊕V˜J ,such that at the j-th level of the decomposition, for 0 < j 6 J, Vj−1 = Vj⊕Wj , V˜j−1 == V˜j ⊕ W˜j , the subspace Vj is orthogonal to W˜j , and the subspace Wj is orthogonal to V˜j . The partition of the space at the j-th level is made with the help of pairs of level filters (hj, gj) and (h˜j, g˜j), for the construction of which the correspondi

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Mertzios, B. G., and A. N. Venetsanopoulos. "Implementation of matrix decomposition structures of 2-D digital filters via VLSI array processors." Circuits Systems and Signal Processing 14, no. 1 (1995): 39–55. http://dx.doi.org/10.1007/bf01183747.

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17

Zhang, Zhong, Hiroshi Toda, Takashi Imamura, and Tetsuo Miyake. "A novel variable filter band discrete wavelet transform: Theory and principle." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (2014): 1460006. http://dx.doi.org/10.1142/s0219691314600066.

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It is well-known that a mother wavelet for the discrete wavelet transform (DWT) has the band-pass filter characteristic with octave width in the frequency domain and can be used for octave analysis. However, it is possible that the octave analysis is not necessarily the most suitable to match the analysis signal. In this study, in order to construct the most suitable basis to match the analysis signal, a novel variable-filter band discrete wavelet transform (VFB-DWT) is proposed. It is achieved by using variable-band filters instead of conventional decomposition and reconstruction sequences, w

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18

Barszcz, Tomasz. "Decomposition of Vibration Signals into Deterministic and Nondeterministic Components and its Capabilities of Fault Detection and Identification." International Journal of Applied Mathematics and Computer Science 19, no. 2 (2009): 327–35. http://dx.doi.org/10.2478/v10006-009-0028-0.

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Decomposition of Vibration Signals into Deterministic and Nondeterministic Components and its Capabilities of Fault Detection and IdentificationThe paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem. A short description of the theory of adaptive filters is presented. When an adaptive filter uses the delayed version of the input signal as the reference signal, it is possible to divide the signal into a deterministic (gear and shaft related) part and a nondeterministic (noise and rolling bearings) part. The

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19

AMRANI, OFER, AMIR AVERBUCH, TAMIR COHEN, and VALERY A. ZHELUDEV. "SYMMETRIC INTERPOLATORY FRAMELETS AND THEIR ERASURE RECOVERY PROPERTIES." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 04 (2007): 541–66. http://dx.doi.org/10.1142/s0219691307001896.

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A new class of wavelet-type frames in signal space that uses (anti)symmetric waveforms is presented. The construction employs interpolatory filters with rational transfer functions. These filters have linear phase. They are amenable either to fast cascading or parallel recursive implementation. Robust error recovery algorithms are developed by utilizing the redundancy inherent in frame expansions. Experimental results recover images when (as much as) 60% of the expansion coefficients are either lost or corrupted. The proposed approach inflates the size of the image through framelet expansion a

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20

Runyi Yu and A. Baradarani. "Design of Halfband Filters for Orthogonal Wavelets via Sum of Squares Decomposition." IEEE Signal Processing Letters 15 (2008): 437–40. http://dx.doi.org/10.1109/lsp.2008.923791.

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21

Brander, O., and B. DeFacio. "The role of filters and the singular-value decomposition for the inverse Born approximation." Inverse Problems 2, no. 4 (1986): 375–93. http://dx.doi.org/10.1088/0266-5611/2/4/006.

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22

JACQUES, LAURENT, and JEAN-PIERRE ANTOINE. "MULTISELECTIVE PYRAMIDAL DECOMPOSITION OF IMAGES: WAVELETS WITH ADAPTIVE ANGULAR SELECTIVITY." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 05 (2007): 785–814. http://dx.doi.org/10.1142/s0219691307002051.

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Many techniques have been devised these last ten years to add an appropriate directionality concept in decompositions of images from the specific transformations of a small set of atomic functions. Let us mention, for instance, works on directional wavelets, steerable filters, dual-tree wavelet transform, curvelets, wave atoms, ridgelet packets, etc. In general, features that are best represented are straight lines or smooth curves as those defining contours of objects (e.g. in curvelets processing) or oriented textures (e.g. wave atoms, ridgelet packets). However, real images present also a s

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23

Longbotham, Harold, and David Eberly. "Statistical properties, fixed points, and decomposition with WMMR filters." Journal of Mathematical Imaging and Vision 2, no. 2-3 (1992): 99–116. http://dx.doi.org/10.1007/bf00118584.

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24

Zhou, Xiaohui. "Wavelet transform on regression trend curve and its application in financial data." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 05 (2020): 2050040. http://dx.doi.org/10.1142/s021969132050040x.

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In this paper, wavelet transform on a regression curve is investigated by using length-preserving projection and its application in financial data is also discussed. First, properties of wavelet filters on the regression trend curves are studied and two-scale equation of wavelet function is deduced on the regression trend curves. Second, the decomposition and reconstruction algorithm of discrete wavelet transform on regression trend curves is derived. Finally, two examples in financial data are given for discussion, based on decomposition and reconstruction algorithms on regression trend curve

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Zhou, Xiaohang, Deshan Shan, and Qiao Li. "Morphological Filter-Assisted Ensemble Empirical Mode Decomposition." Mathematical Problems in Engineering 2018 (September 17, 2018): 1–12. http://dx.doi.org/10.1155/2018/5976589.

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In the ensemble empirical mode decomposition (EEMD) algorithm, different realizations of white noise are added to the original signal as dyadic filter banks to overcome the mode mixing problems of empirical mode decomposition (EMD). However, not all the components in white noise are necessary, and the superfluous components will introduce additional mode mixing problems. To address this problem, morphological filter-assisted ensemble empirical mode decomposition (MF-EEMD) was proposed in this paper. First, a new method for determining the structuring element shape and size was proposed to impr

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Bhattacharjee, Sankha Subhra, and Nithin V. George. "Nearest Kronecker Product Decomposition Based Linear-in-The-Parameters Nonlinear Filters." IEEE/ACM Transactions on Audio, Speech, and Language Processing 29 (2021): 2111–22. http://dx.doi.org/10.1109/taslp.2021.3084755.

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27

KUMARI, R. SHANTHA SELVA, and V. SADASIVAM. "DE-NOISING AND BASELINE WANDERING REMOVAL OF ELECTROCARDIOGRAM USING DOUBLE DENSITY DISCRETE WAVELET." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 03 (2007): 399–415. http://dx.doi.org/10.1142/s0219691307001823.

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In this paper, an off-line double density discrete wavelet transform based de-noising and baseline wandering removal methods are proposed. Different levels decomposition is used depending upon the noise level, so as to give a better result. When the noise level is low, three levels decomposition is used. When the noise level is medium, four levels decomposition is used. When the noise level is high, five levels decomposition is used. Soft threshold technique is applied to each set of wavelet detail coefficients with different noise level. Donoho's estimator is used as a threshold for each set

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Čiegis, R., O. Iliev, and Z. Lakdawala. "On Parallel Numerical Algorithms for Simulating Industrial Filtration Problems." Computational Methods in Applied Mathematics 7, no. 2 (2007): 118–34. http://dx.doi.org/10.2478/cmam-2007-0007.

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AbstractThe performance of oil filters used in the automotive industry can be significantly improved, especially when computer simulation is an essential component of the design process. In this paper, we consider parallel numerical algorithms for solving mathematical models describing the process of filtration, filtering solid particles out of liquid oil. The Navier — Stokes — Brinkmann system of equations is used to describe the laminar flow of incompressible isothermal oil. The space discretization in the complicated filter geometry is based on the finite-volume method. Special care is take

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Schweid, Stuart, and T. K. Sarkar. "A Sufficiency Criteria for Orthogonal QMF Filters to Ensure Smooth Wavelet Decompositions." Applied and Computational Harmonic Analysis 2, no. 1 (1995): 61–67. http://dx.doi.org/10.1006/acha.1995.1005.

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HASAN, AHMED M., KHAIRULMIZAM SAMSUDIN, ABDUL RAHMAN RAMLI, and RAJA SYAMSUL AZMIR. "COMPARATIVE STUDY ON WAVELET FILTER AND THRESHOLDING SELECTION FOR GPS/INS DATA FUSION." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 03 (2010): 457–73. http://dx.doi.org/10.1142/s0219691310003572.

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Navigation and guidance of an autonomous vehicle require determination of the position and velocity of the vehicle. Therefore, fusing the Inertial Navigation System (INS) and Global Positioning System (GPS) is important. Various methods have been applied to smooth and predict the INS and GPS errors. Recently, wavelet de-noising methodologies have been applied to improve the accuracy and reliability of the GPS/INS system. In this work, analysis of real data to identify the optimal wavelet filter for each GPS and INS component for high quality error estimation is presented. A comprehensive compa

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Tay, D. "Comments on “Design of Halfband Filters for Orthogonal Wavelets Via Sum of Squares Decomposition”." IEEE Signal Processing Letters 16, no. 2 (2009): 109–11. http://dx.doi.org/10.1109/lsp.2008.2006702.

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32

Gunzburger, Max, Traian Iliescu, and Michael Schneier. "A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows." IMA Journal of Numerical Analysis 40, no. 2 (2019): 886–913. http://dx.doi.org/10.1093/imanum/dry094.

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Abstract Partial differential equations (PDEs) are often dependent on input quantities that are uncertain. To quantify this uncertainty PDEs must be solved over a large ensemble of parameters. Even for a single realization this can be a computationally intensive process. In the case of flows governed by the Navier–Stokes equations, an efficient method has been devised for computing an ensemble of solutions. To further reduce the computational cost of this method, an ensemble-proper orthogonal decomposition (POD) method was recently proposed. The main contribution of this work is the introducti

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Frei, Mark G., and Ivan Osorio. "Intrinsic time-scale decomposition: time–frequency–energy analysis and real-time filtering of non-stationary signals." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2078 (2006): 321–42. http://dx.doi.org/10.1098/rspa.2006.1761.

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We introduce a new algorithm, the intrinsic time-scale decomposition (ITD), for efficient and precise time–frequency–energy (TFE) analysis of signals. The ITD method overcomes many of the limitations of both classical (e.g. Fourier transform or wavelet transform based) and more recent (empirical mode decomposition based) approaches to TFE analysis of signals that are nonlinear and/or non-stationary in nature. The ITD method decomposes a signal into (i) a sum of proper rotation components, for which instantaneous frequency and amplitude are well defined, and (ii) a monotonic trend. The decompos

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Zhao, Wei, Huiguang Li, Liying Zou, and Wenjuan Huang. "Nonlinear Unknown Input Observer Based on Singular Value Decomposition Aided Reduced Dimension Cubature Kalman Filter." Mathematical Problems in Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/1267380.

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The paper presents a nonlinear unknown input observer (NUIO) based on singular value decomposition aided reduced dimension Cubature Kalman filter (SVDRDCKF) for a special class of nonlinear systems, the nonlinearity of which is only caused by part of its states. Firstly, the algorithm of general NUIO is discussed and the unknown input observer based on singular value decomposition aided Cubature Kalman filter (SVDCKF) given. Then a special nonlinear system model with unknown input is introduced. Based on the proposed model and the corresponding NUIO, the equivalent integral form with partial s

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Dogariu, Laura-Maria, Cristian-Lucian Stanciu, Camelia Elisei-Iliescu, Constantin Paleologu, Jacob Benesty, and Silviu Ciochină. "Tensor-Based Adaptive Filtering Algorithms." Symmetry 13, no. 3 (2021): 481. http://dx.doi.org/10.3390/sym13030481.

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Tensor-based signal processing methods are usually employed when dealing with multidimensional data and/or systems with a large parameter space. In this paper, we present a family of tensor-based adaptive filtering algorithms, which are suitable for high-dimension system identification problems. The basic idea is to exploit a decomposition-based approach, such that the global impulse response of the system can be estimated using a combination of shorter adaptive filters. The algorithms are mainly tailored for multiple-input/single-output system identification problems, where the input data and

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Macpherson, Dugald. "Maximal subgroups of infinite dimensional general linear groups." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 53, no. 3 (1992): 338–51. http://dx.doi.org/10.1017/s144678870003651x.

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AbstractLet k be an infinite cardinal, F a field, and let GL(k, F) be the group of all non-singular linear transformations on a ki-dimensional vector space V over F. Various examples are given of maximal subgroups of GL(k, F). These include (i) stabilizers of families of subspaces of V which are like filters or ideals on a set, (ii) almost stabilizers of certain subspaces of V, (iii) almost stabilizers of a direct decomposition of V into two k-dimensional subspaces.It is also noted that GL(k, F) is not the union of any chain of length k of proper subgroups.

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Antonelli, Laura, Valentina De Simone, and Daniela di Serafino. "Spatially Adaptive Regularization in Image Segmentation." Algorithms 13, no. 9 (2020): 226. http://dx.doi.org/10.3390/a13090226.

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We present a total-variation-regularized image segmentation model that uses local regularization parameters to take into account spatial image information. We propose some techniques for defining those parameters, based on the cartoon-texture decomposition of the given image, on the mean and median filters, and on a thresholding technique, with the aim of preventing excessive regularization in piecewise-constant or smooth regions and preserving spatial features in nonsmooth regions. Our model is obtained by modifying a well-known image segmentation model that was developed by T. Chan, S. Esedo

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Rajaguru, Harikumar, and Vijayakumar Thangavel. "Wavelets and Morphological Operators Based Classification of Epilepsy Risk Levels." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/813197.

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The objective of this paper is to compare the performance of Singular Value Decomposition (SVD), Expectation Maximization (EM), and Modified Expectation Maximization (MEM) as the postclassifiers for classifications of the epilepsy risk levels obtained from extracted features through wavelet transforms and morphological filters from EEG signals. The code converter acts as a level one classifier. The seven features such as energy, variance, positive and negative peaks, spike and sharp waves, events, average duration, and covariance are extracted from EEG signals, out of which four parameters lik

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Bhattacharjee, Sankha Subhra, Krishna Kumar, and Nithin V. George. "Nearest Kronecker Product Decomposition Based Generalized Maximum Correntropy and Generalized Hyperbolic Secant Robust Adaptive Filters." IEEE Signal Processing Letters 27 (2020): 1525–29. http://dx.doi.org/10.1109/lsp.2020.3017106.

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Su, Ke, Xiaoli Lu, and Wei Liu. "An Improved Filter Method for Nonlinear Complementarity Problem." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/450829.

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The nonlinear complementarity problem can be reformulated as a nonlinear programming whose objective function may be nonsmooth. For this case, we use decomposition strategy to decompose the nonsmooth function into a smooth one and a nonsmooth one. Together with filter method, we present an improved filter algorithm with decomposition strategy for solving nonlinear complementarity problem, which has better numerical results compared to the method that without the filter technique. Under mild conditions, the global convergent property is shown. In the end, the numerical example is reported.

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Williams, T., M. Ahmadi, and W. C. Miller. "Design of 2D FIR and IIR Digital Filters with Canonical Signed Digit Coefficients Using Singular Value Decomposition and Genetic Algorithms." Circuits, Systems & Signal Processing 26, no. 1 (2007): 69–89. http://dx.doi.org/10.1007/s00034-005-1015-9.

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Nino-Ruiz, Elias D., Adrian Sandu, and Xinwei Deng. "An Ensemble Kalman Filter Implementation Based on Modified Cholesky Decomposition for Inverse Covariance Matrix Estimation." SIAM Journal on Scientific Computing 40, no. 2 (2018): A867—A886. http://dx.doi.org/10.1137/16m1097031.

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Runyi Yu and A. Baradarani. "Reply to “Comments on 'Design of Halfband Filters for Orthogonal Wavelets via Sum of Squares Decomposition' ”." IEEE Signal Processing Letters 16, no. 2 (2009): 112. http://dx.doi.org/10.1109/lsp.2008.2009824.

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Liu, Zhiting, Yuhua Wang, Wenwei Zheng, and Yuexia Zhou. "The improved noise reduction method for the vibration signal based on variational mode decomposition." Filomat 34, no. 15 (2020): 4975–83. http://dx.doi.org/10.2298/fil2015975l.

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The variational model decomposition (VMD) has a problem that is dificult to determine the number of intrinsic mode functions (IMF).We use the leaked energy to determine the number of IMFs. And we use the energy concentration rate of the IMF?s autocorrelation function and the correlation coefficient between the IMFs and the original signal, define Q as the ratio of the energy concentration and the correlation coefficient, and use Q to determine the noise IMFs in the IMFs. Then, we filter the noise IMFs and use the remaining IMFs to reconstruct signal to achieve noise reduction. Finally, we use

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Aldhaheri, Rabah W. "Design of 2-D Linear Phase Digital Filters Using Schur Decomposition and Symmetries." Multidimensional Systems and Signal Processing 15, no. 1 (2004): 65–81. http://dx.doi.org/10.1023/b:mult.0000003933.41677.03.

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Xu, Tengxian, Yongqin Yang, Mengxing Huang, Han Wang, Di Wu, and Qu Yi. "Tensor-Based Angle and Range Estimation Method in Monostatic FDA-MIMO Radar." Mathematical Problems in Engineering 2020 (August 12, 2020): 1–8. http://dx.doi.org/10.1155/2020/5720189.

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In the paper, joint angle and range estimation issue for monostatic frequency diverse array multiple-input multiple-output (FDA-MIMO) is proposed, and a tensor-based framework is addressed to solve it. The proposed method exploits the multidimensional structure of matched filters in FDA-MIMO radar. Firstly, stack the received data to form a third-order tensor so that the multidimensional structure information of the received data can be acquired. Then, the steering matrices contain the angle and rang information are estimated by using the parallel factor (PARAFAC) decomposition. Finally, the a

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Xie, Yuan, Kan Xie, Junjie Yang, and Shengli Xie. "Underdetermined Blind Source Separation Combining Tensor Decomposition and Nonnegative Matrix Factorization." Symmetry 10, no. 10 (2018): 521. http://dx.doi.org/10.3390/sym10100521.

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Underdetermined blind source separation (UBSS) is a hot topic in signal processing, which aims at recovering the source signals from a number of observed mixtures without knowing the mixing system. Recently, expectation-maximization algorithm shows a great potential in the UBSS. However, the final separation results depend strongly on the parameter initialization, leading to poor separation performance. In this paper, we propose an effective algorithm that combines tensor decomposition and nonnegative matrix factorization (NMF). In the proposed algorithm, we first employ tensor decomposition t

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Yao, Qing-He, and Qing-Yong Zhu. "Investigation of the Contamination Control in a Cleaning Room with a Moving AGV by 3D Large-Scale Simulation." Journal of Applied Mathematics 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/570237.

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The motions of the airflow induced by the movement of an automatic guided vehicle (AGV) in a cleanroom are numerically studied by large-scale simulation. For this purpose, numerical experiments scheme based on domain decomposition method is designed. Compared with the related past research, the high Reynolds number is treated by large-scale computation in this work. A domain decomposition Lagrange-Galerkin method is employed to approximate the Navier-Stokes equations and the convection diffusion equation; the stiffness matrix is symmetric and an incomplete balancing preconditioned conjugate gr

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Deng, Tian-Bo, and Masayuki Kawamata. "Design of separable-denominator 2-D digital filters using the reduced-dimensional decomposition model." Multidimensional Systems and Signal Processing 3, no. 1 (1992): 89–96. http://dx.doi.org/10.1007/bf01941020.

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Schaworonkow, Natalie, and Bradley Voytek. "Enhancing oscillations in intracranial electrophysiological recordings with data-driven spatial filters." PLOS Computational Biology 17, no. 8 (2021): e1009298. http://dx.doi.org/10.1371/journal.pcbi.1009298.

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In invasive electrophysiological recordings, a variety of neural oscillations can be detected across the cortex, with overlap in space and time. This overlap complicates measurement of neural oscillations using standard referencing schemes, like common average or bipolar referencing. Here, we illustrate the effects of spatial mixing on measuring neural oscillations in invasive electrophysiological recordings and demonstrate the benefits of using data-driven referencing schemes in order to improve measurement of neural oscillations. We discuss referencing as the application of a spatial filter.

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