Academic literature on the topic 'Digital Image Processing, Image Reconstruction-Restoration, Deconvolution'

In some cases, there is some damage to an image caused by interference during the image capture process. Blurred image damage can be overcome by deconvolution digital image processing. There are various methods to repair the image blur damage, including using the Regularized, Wiener, and Lucy Richardson deconvolution methods. Each blurring image repair method produces a different debluring result of image processing. Image comparison application was built to compare the ability of image restoration results to a Motion Blur image with the algorithms used in deconvolution. Image restoration comparison parameters used include determining the MSE and PSNR values between the test image and the deconvolved image. The results of implementing the comparative application of Motion Blur image improvement to 270 blur simulations consisting of 9 different levels of image blurring, obtained the average PSNR value for Wiener's deconvolution = 59.16dB, Lucy Richardson = 26.92dB and Regularized = 36.94dB.Keywords:Image Restoration; Lucy Richardson; Motion Blur; Regularized; Wiener.

Light microscopic techniques for visualizing biomolecules and biochemical processes in situ have become indispensable in studies concerning the structural organization of supramolecular assemblies in cells and of processes during the cell cycle, transformation, differentiation, and development. Confocal laser scanning microscopy offers a number of advantages for the in situ localization and quantitation of fluorescence labeled targets and probes: (i) rejection of interfering signals emanating from out-of-focus and adjacent structures, allowing the “optical sectioning” of the specimen and 3-D reconstruction without time consuming deconvolution; (ii) increased spatial resolution; (iii) electronic control of contrast and magnification; (iv) simultanous imaging of the specimen by optical phenomena based on incident, scattered, emitted, and transmitted light; and (v) simultanous use of different fluorescent probes and types of detectors.We currently use a confocal laser scanning microscope CLSM (Zeiss, Oberkochen) equipped with 3-laser excitation (u.v - visible) and confocal optics in the fluorescence mode, as well as a computer-controlled X-Y-Z scanning stage with 0.1 μ resolution.

We report on two alternative simple methods to detect counterparts of cosmic gamma-ray bursts (GRBs) and optical transients (OTs). We report on the development and tests of an alternative optical all-sky monitor recently tested at the Karlovy Vary Observatory. The monitor is based on a Peleng 8 mm fish-eye lens (1 : 3,5–1 : 16) and CANON EOS 350D digital CCD camera. This type of monitor represents a low-cost device suitable for easy replication and still able to detect brighter optical transients simultaneously to GRB triggers. Such OTs have been observed for some of the GRBs such as GRB990123, GRB060117, or recently GRB080319 indicating that some fraction of GRBs can generate optical transient emission accessible by simple small aperture instrumentation as described here. These efforts are accompanied by development of dedicated programmes to access and to evaluate all-sky images; these efforts will be also briefly described. The All-Sky Monitor is a space variant optical system and its point spread function (PSF) has not uniform shape in the field of view. The processing and measuring of image data is complicated, and sophisticated deconvolution algorithms are used for image restoration. The second method is the GRB detection based on their ionospheric response.

Image deconvolution is an important pre-processing step in image analysis which may be combined with denoising, also an important image restoration technique, and prepares the image to facilitate diagnosis in the case of medical images and further processing such as segmentation and registration. Considering the variational approach to this problem, regularisation is a vital component for reconstructing meaningful information and the problem of defining appropriate regularisation is an active research area. An important question in image deconvolution is how to obtain a restored image which has sharp edges where required but also allows smooth regions. Many of the existing regularisation methods allow for one or the other but struggle to obtain good results with both. Consequently, there has been much work in the area of variational image reconstruction in finding regularisation techniques which can provide good quality restoration for images which have both smooth regions and sharp edges. In this paper, we propose a new regularisation technique for image reconstruction in the blind and non-blind deconvolution problems where the precise cause of blur may or may not be known. We present experimental results which demonstrate that this method of regularisation is beneficial for restoring images and blur functions which contain both jumps in intensity and smooth regions.

A new method for the reconstruction of blurred digital images damaged by separable motion blur is established. The main attribute of the method is based on multiple applications of the least squares solutions of certain matrix equations which define the separable motion blur in conjunction with known image deconvolution techniques. The key feature of the proposed algorithms is reflected in the fact that they can be used only in symbiosis with other image restoration algorithms.

Image deconvolution is an important problem, which has seen plenty of progress in the last decades. Due to its ill-posedness, a common approach is to formulate the reconstruction as an optimization problem[Formula: see text] regularized by an additional sparsity-enforcing term. This term is often modeled as an [Formula: see text] norm measured in the domain of a suitable signal transform. The resulting optimization problem can be solved by an iterative approach via Landweber iterations with soft thresholding of the transform coefficients. Previous approaches focused on thresholding in the wavelet-domain. In particular, recent work [C. Vonesch and M. Unser, A fast thresholded Landweber algorithm for wavelet-regularized multidimensional deconvolution, IEEE Trans. Image Process. 17(4) (2008) 539–549.] has shown that the use of Shannon wavelets results in particularly efficient reconstruction algorithms. The present paper extends this approach to Shannon shearlets, which we also introduce in this work. We show that for anisotropic blurring filters, such as the motion blur, the novel shearlet-based approach allows for further a improvement in efficiency. In particular, we observe that for such kernels using shearlets instead of wavelets improves the quality of image restoration and SERG, when compared after the same number of iterations.

This paper discusses the use of the interpolation method for the sequential calculation of the Fourier spectrum (IMSCS) for retouching and restoration of missing (shaded) image fragments. The proposed approach can be used with any form of a missing image fragment. Such image processing can give good results even at a significantly high percentage of missing image fragments. The method of digital virtual image reconstruction proposed here is strictly based on a scientific approach; as the source data, it uses all the data available (the image itself is the object to be recovered). Therefore, it is free from the human factor, because of which subjective changes can be introduced in the image under processing. The results presented indicate a significant increase in the quality of digital images (increasing the information content), which can offer helpful auxiliary tools for professionals using these images for their practical purposes.

The principle of image super-resolution reconstruction (SR) is to pass one or more low-resolution (LR) images through information processing technology to obtain the final high-resolution (HR) image. Convolutional neural networks (CNN) have achieved better results than traditional methods in the process of an image super-resolution reconstruction. However, if the number of neural network layers is increased blindly, it will cause a significant increase in the amount of calculation, increase the difficulty of training the network, and cause the loss of image details. Therefore, in this paper, we use a novel and effective image super-resolution reconstruction technique via fast global and local residual learning model (FGRLR). The principle is to directly train a low-resolution small image on a neural network without enlarging it. This will effectively reduce the amount of calculation. In addition, the stacked local residual block (LRB) structure is used for non-linear mapping, which can effectively overcome the problem of image degradation. After extracting features, use 1 × 1 convolution to perform dimensional compression, and expand the dimensions after non-linear mapping, which can reduce the calculation amount of the model. In the reconstruction layer, deconvolution is used to enlarge the image to the required size. This also reduces the number of parameters. We use skip connections to use low-resolution information for reconstructing high-resolution images. Experimental results show that the algorithm can effectively shorten the running time without affecting the quality of image restoration.

Off-axis electron holography has been applied to crystal structure images using digital image processing.Three important factors pertaining to the correction of aberrations in electron holography are:(1)interference fringes narrower than one third of the required resolution,(2)a Signal to Noise (S-N) ratio in the hologram which is high enough for high resolution reconstruction, and(3)the estimation of the amount of aberrations.We have obtained interference fringes with a spacing of below 0.03 nm , which is sufficient for a resolution of 0.1 nm in the reconstructed image. The S-N ratio depends on the instrument used to record the hologram and whether the specimen causes strong scattering or weak scattering.Some ways of estimating the amount of aberration have been proposed. Here we adopted an algorithm which involves minimizing the contrast of the reconsturcted image by optimizing the processing parameters (Cs and df), because it is applicable not only to weak phase objects but also to general phase objects and, in principle, only one hologram is needed to determiner the parameters.

We introduce a novel ultra-high-resolution Digital Terrain Model (DTM) processing system using a combination of photogrammetric 3D reconstruction, image co-registration, image super-resolution restoration, shape-from-shading DTM refinement, and 3D co-alignment methods. Technical details of the method are described, and results are demonstrated using a 4 m/pixel Trace Gas Orbiter Colour and Stereo Surface Imaging System (CaSSIS) panchromatic image and an overlapping 6 m/pixel Mars Reconnaissance Orbiter Context Camera (CTX) stereo pair to produce a 1 m/pixel CaSSIS Super-Resolution Restoration (SRR) DTM for different areas over Oxia Planum on Mars—the future ESA ExoMars 2022 Rosalind Franklin rover’s landing site. Quantitative assessments are made using profile measurements and the counting of resolvable craters, in comparison with the publicly available 1 m/pixel High-Resolution Imaging Experiment (HiRISE) DTM. These assessments demonstrate that the final resultant 1 m/pixel CaSSIS DTM from the proposed processing system has achieved comparable and sometimes more detailed 3D reconstruction compared to the overlapping HiRISE DTM.

稀疏性在最近的圖像恢復技術發展中起到了重要作用。在這個碩士研究中，我們專注於兩種通過信號稀疏性假設相聯繫的圖像恢復問題。具體來講，在第一個圖像恢復問題中，信號本身在某些變換域是稀疏的，例如小波變換。在本研究的第二部分，信號並非傳統意義上的稀疏，但它可以用很少的幾個參數來表示--亦即信號具有稀疏的表示。我們希望通過講述一個「雙城記」，聯繫起這兩個稀疏圖像重建問題。
在第二章中，我們提出了一種創新的算法框架，用於解決信號稀疏假設下的圖像恢復問題。重建圖像的目標函數，由一個數據保真項和`1正則項組成。然而，我們不是直接估計重建的圖像，而是專注於如何獲得重建的這個過程。我們的策略是將這個重建過程表示成基本閾值函數的線性組合（LET）：這些線性係數可以通過最小化目標函數解得。然後，可以更新閾值函數并迭代這個過程（i-LET）。這種線性參數化的主要優點是可以大幅降低問題的規模-每次我們只需解決一個線性係數維度大小的優化問題（通常小於十），而不是整個圖像大小的問題。如果閾值函滿足一定的條件，迭代LET算法可以保證全局的收斂性。多個測試圖像在不同噪音水平和不同卷積核類型的測試清楚地表明，我們提出的框架在所需運算時間和迭代循環次數方面，通常超越當今最好水平。
在第三章中，我們擴展了有限創新率採樣框架至某一種特定二維曲線。我們用掩模函數的解來間接定義這個二維曲線。這裡，掩模函數可以表示為有限數目的正弦信號加權求和。因此，從這個角度講，我們定義的二維曲線具有「有限創新率」（FRI）。由於與定義曲線相關聯的指示器圖像沒有帶寬限制，因而根據經典香農採樣定理，不能在有限數量的採樣基礎上獲得完全重建。然而，我們證明，仍然可以設計一個針對指示器圖像採樣的框架，實現完美重構。此外，對於這一方法的空間域解釋，使我們能夠拓展嚴格的FRI曲線模型用於描述自然圖像的邊緣，可以在各種圖像處理的問題中保持圖像的邊緣。我們用一個潛在的在圖像上採樣中的應用作為示例。
Sparsity has played an important role in recent developments of various image restoration techniques. In this MPhil study, we focus on two different types of image restoration problems, which are related by the sparsity assumptions. Specifically, in the first image restoration problem, the signal (i.e. the restored image) itself is sparse in some transformation domain, e.g. wavelet. While in the second part of this study, the signal is not sparse in the traditional sense but that it can be parametrized with a few parameters hence having a sparse representation. Our goal is to tell a "tale of two cities" and to show the connections between the two sparse image restoration problems in this thesis.
In Chapter 2, we proposed a novel algorithmic framework to solve image restoration problems under sparsity assumptions. As usual, the reconstructed image is the minimum of an objective functional that consists of a data fidelity term and an ℓ₁ regularization. However, instead of estimating the reconstructed image that minimizes the objective functional directly, we focus on the restoration process that maps the degraded measurements to the reconstruction. Our idea amounts to parameterizing the process as a linear combination of few elementary thresholding functions (LET) and solve for the linear weighting coefficients by minimizing the objective functional. It is then possible to update the thresholding functions and to iterate this process (i-LET). The key advantage of such a linear parametrization is that the problem size reduces dramatically--each time we only need to solve an optimization problem over the dimension of the linear coefficients (typically less than 10) instead of the whole image dimensio . With the elementary thresholding functions satisfying certain constraints, global convergence of the iterated LET algorithm is guaranteed. Experiments on several test images over a wide range of noise levels and different types of convolution kernels clearly indicate that the proposed framework usually outperform state-of-theart algorithms in terms of both CPU time and number of iterations.
In Chapter 3, we extended the sampling framework for signals with finite rate of innovation to a specific class of two-dimensional curves, which are defined implicitly as the roots of a mask function. Here the mask function has a parametric representation as weighted summation of a finite number of sinusoids, and therefore, has finite rate of innovation [1]. The associated indicator image of the defined curve is not bandlimited and cannot be perfectly reconstructed based on the classical Shannon's sampling theorem. Yet, we show that it is possible to devise a sampling scheme and have a perfect reconstruction from finite number of (noiseless) samples of the indicator image with the annihilating filter method (also known as Prony's method). Robust reconstruction algorithms with noisy samples are also developed. Furthermore, the new spatial domain interpretation of the annihilating filter enables us to generalize the exact FRI curve model to characterize edges of a natural image. We can impose the annihilation constraint to preserve edges in various image processing problems. We exemplified the effectiveness of the annihilation constraint with a potential application in image up-sampling.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Detailed summary in vernacular field only.
Pan, Hanjie.
Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 69-74).
Abstracts also in Chinese.
Acknowledgments --- p.iii
Abstract --- p.vii
Contents --- p.xii
List of Figures --- p.xv
List of Tables --- p.xvii
Chapter 1 --- Introduction --- p.1
Chapter 1.1 --- Sampling Sparse Signals --- p.1
Chapter 1.2 --- Thesis Organizations and Contributions --- p.3
Chapter 2 --- An Iterated Linear Expansion of Thresholds for ℓ₁-based Image Restoration --- p.5
Chapter 2.1 --- Introduction --- p.5
Chapter 2.1.1 --- Problem Description --- p.5
Chapter 2.1.2 --- Approaches to Solve the Problem --- p.6
Chapter 2.1.3 --- Proposed Approach --- p.8
Chapter 2.1.4 --- Organization of the Chapter --- p.9
Chapter 2.2 --- Basic Ingredients --- p.9
Chapter 2.2.1 --- Iterative Reweighted Least Square Methods --- p.9
Chapter 2.2.2 --- Linear Expansion of Thresholds (LET) --- p.11
Chapter 2.3 --- Iterative LET Restoration --- p.15
Chapter 2.3.1 --- Selection of i-LET Bases --- p.15
Chapter 2.3.2 --- Convergence of the i-LET Scheme --- p.16
Chapter 2.3.3 --- Examples of i-LET Bases --- p.18
Chapter 2.4 --- Experimental Results --- p.23
Chapter 2.4.1 --- Deconvolution with Decimated Wavelet Transform --- p.24
Chapter 2.4.2 --- Deconvolution with Redundant Wavelet Transform --- p.28
Chapter 2.4.3 --- Algorithm Complexity Analysis --- p.29
Chapter 2.4.4 --- Choice of Regularization Weight λ --- p.30
Chapter 2.4.5 --- Deconvolution with Cycle Spinnings --- p.30
Chapter 2.5 --- Summary --- p.31
Chapter 3 --- Sampling Curves with Finite Rate of Innovation --- p.33
Chapter 3.1 --- Introduction --- p.33
Chapter 3.2 --- Two-dimensional Curves with Finite Rate of Innovation --- p.34
Chapter 3.2.1 --- FRI Curves --- p.34
Chapter 3.2.2 --- Interior Indicator Image --- p.35
Chapter 3.2.3 --- Acquisition of Indicator Image Samples --- p.36
Chapter 3.3 --- Reconstruction of the Annihilable Curves --- p.37
Chapter 3.3.1 --- Annihilating Filter Method --- p.37
Chapter 3.3.2 --- Relate Fourier Transform with Spatial Domain Samples --- p.39
Chapter 3.3.3 --- Reconstruction of Annihilation Coe cients --- p.39
Chapter 3.3.4 --- Reconstruction with Model Mismatch --- p.42
Chapter 3.3.5 --- Retrieval of the Annihilable Curve Amplitudes --- p.46
Chapter 3.4 --- Dealing with Non-ideal Low-pass Filtered Samples --- p.48
Chapter 3.5 --- Generalization of the FRI Framework for Natural Images --- p.49
Chapter 3.5.1 --- Spatial Domain Interpretation of the Annihilation Equation --- p.50
Chapter 3.5.2 --- Annihilable Curve Approximation of Image Edges --- p.51
Chapter 3.5.3 --- Up-sampling with Annihilation Constraint --- p.53
Chapter 3.6 --- Conclusion --- p.57
Chapter 4 --- Conclusions --- p.59
Chapter 4.1 --- Thesis Summary --- p.59
Chapter 4.2 --- Perspectives --- p.60
Chapter A --- Proofs and Derivations --- p.61
Chapter A.1 --- Proof of Lemma 3 --- p.61
Chapter A.2 --- Proof of Theorem 2 --- p.62
Chapter A.3 --- Efficient Implementation of IRLS Inner Loop with Matlab --- p.63
Chapter A.4 --- Derivations of the Sampling Formula (3.7) --- p.64
Chapter A.5 --- Correspondence between the Spatial and Fourier Domain Samples --- p.65
Chapter A.6 --- Optimal Post-filter Applied to Non-ideal Samples --- p.66
Bibliography --- p.69

High quality image /video has become an integral part in our day-to-day life ranging from many areas of science, engineering and medical diagnosis. All these imaging applications call for high resolution, properly focused and crisp images. However, in real situations obtaining such a high quality image is expensive, and in some cases it is not practical. In imaging systems such as digital camera, blur and noise degrade the image quality. The recorded images look blurred, noisy and unable to resolve the finer details of the scene, which are clearly notable under zoomed conditions. The post processing techniques based on computational methods extract the hidden information and thereby improve the quality of the captured images. The study in this thesis focuses on deconvolution and eventually blind de-convolution problem of a single frame captured at low light imaging conditions arising from digital photography/surveillance imaging applications. Our intention is to restore a sharp image from its blurred and noisy observation, when the blur is completely known/unknown and such inverse problems are ill-posed/twice ill-posed. This thesis consists of two major parts. The first part addresses deconvolution/blind deconvolution problem using Bayesian approach with fuzzy logic based gradient potential as a prior functional. In comparison with analog cameras, artifacts are visible in digital cameras when the images are enlarged and there is a demand to enhance the resolution. The increased resolution can be in spatial, temporal or even in both the dimensions. Super resolution reconstruction methods reconstruct images/video containing spectral information beyond that is available in the captured low resolution images. The second part of the thesis addresses resolution enhancement of observed monochromatic/color images using multiple frames of the same scene. This reconstruction problem is formulated in Bayesian domain with an aspiration of reducing blur, noise, aliasing and increasing the spatial resolution. The image is modeled as Markov random field and a fuzzy logic filter based gradient potential is used to differentiate between edge and noisy pixels. Suitable priors are adaptively applied to obtain artifact free/reduced images. In this work, all our approaches are experimentally validated using standard test images. The Matlab based programming tools are used for carrying out the validation. The performance of the approaches are qualitatively compared with results of recently proposed methods. Our results turn out to be visually pleasing and quantitatively competitive.

Tse Fu Wing.
"June 2000."
Thesis (Ph.D.)--Chinese University of Hong Kong, 2000.
Includes bibliographical references (p. 172-177).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Mode of access: World Wide Web.
Abstracts in English and Chinese.