Blind image deconvolution revisited
TL;DR: The article discusses the major approaches, such as projection based blind deconvolution and maximum likelihood restoration, which were overlooked previously (see ibid., no.5, 1996).
Abstract: The article discusses the major approaches, such as projection based blind deconvolution and maximum likelihood restoration, we overlooked previously (see ibid., no.5, 1996). We discuss them for completeness along with some other works found in the literature. As the area of blind image restoration is a rapidly growing field of research, new methods are constantly being developed.
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16 Nov 2012TL;DR: The article introduces digital image restoration to the reader who is just beginning in this field, and provides a review and analysis for the readers who may already be well-versed in image restoration.
Abstract: The article introduces digital image restoration to the reader who is just beginning in this field, and provides a review and analysis for the reader who may already be well-versed in image restoration. The perspective on the topic is one that comes primarily from work done in the field of signal processing. Thus, many of the techniques and works cited relate to classical signal processing approaches to estimation theory, filtering, and numerical analysis. In particular, the emphasis is placed primarily on digital image restoration algorithms that grow out of an area known as "regularized least squares" methods. It should be noted, however, that digital image restoration is a very broad field, as we discuss, and thus contains many other successful approaches that have been developed from different perspectives, such as optics, astronomy, and medical imaging, just to name a few. In the process of reviewing this topic, we address a number of very important issues in this field that are not typically discussed in the technical literature.
1,588 citations
14 May 2007
TL;DR: In this article, a Bayesian framework for blind image deconvolution is proposed, which is based on the Bayesian model of blind image blur and noise in a multispectral image.
Abstract: BLIND IMAGE DECONVOLUTION: PROBLEM FORMULATION AND EXISTING APPROACHES Tom E. Bishop, S. Derin Babacan, Bruno Amizic, Aggelos K. Katsaggelos, Tony Chan, and Rafael Molina Introduction Mathematical Problem Formulation Classification of Blind Image Deconvolution Methodologies Bayesian Framework for Blind Image Deconvolution Bayesian Modeling of Blind Image Deconvolution Bayesian Inference Methods in Blind Image Deconvolution Non-Bayesian Blind Image Deconvolution Models Conclusions References BLIND IMAGE DECONVOLUTION USING BUSSGANG TECHNIQUES: APPLICATIONS TO IMAGE DEBLURRING AND TEXTURE SYNTHESIS Patrizio Campisi, Alessandro Neri, Stefania Colonnese, Gianpiero Panci, and Gaetano Scarano Introduction Bussgang Processes Single-Channel Bussgang Deconvolution Multichannel Bussgang deconvolution Conclusions References BLIND MULTIFRAME IMAGE DECONVOLUTION USING ANISOTROPIC SPATIALLY ADAPTIVE FILTERING FOR DENOISING AND REGULARIZATION Vladimir Katkovnik, Karen Egiazarian, and Jaakko Astola Introduction Observation Model and Preliminaries Frequency Domain Equations Projection Gradient Optimization Anisotropic LPA-ICI Spatially Adaptive Filtering Blind Deconvolution Algorithm Identifiability and Convergence Simulations Conclusions Acknowledgments References BAYESIAN METHODS BASED ON VARIATIONAL APPROXIMATIONS FOR BLIND IMAGE DECONVOLUTION Aristidis Likas and Nikolas P. Galatsanos Introduction Background on Variational Methods Variational Blind Deconvolution Numerical Experiments Conclusions and Future Work APPENDIX A: Computation of the Variational Bound F(q,?) APPENDIX B: Maximization of F(q,?) References DECONVOLUTION OF MEDICAL IMAGES FROM MICROSCOPIC TO WHOLE BODY IMAGES Oleg V. Michailovich and Dan R. Adam Introduction Nonblind Deconvolution Blind Deconvolution in Ultrasound Imaging Blind Deconvolution in SPECT Blind Deconvolution in Confocal Microscopy Summary References BAYESIAN ESTIMATION OF BLUR AND NOISE IN REMOTE SENSING IMAGING Andre Jalobeanu, Josiane Zerubia, and Laure Blanc-Feraud Introduction The Forward Model Bayesian Estimation: Invert the Forward Model Possible Improvements and Further Development Results Conclusions Acknowledgments References DECONVOLUTION AND BLIND DECONVOLUTION IN ASTRONOMY Eric Pantin, Jean-luc Starck, and Fionn Murtagh Introduction The Deconvolution Problem Linear Regularized Methods CLEAN Bayesian Methodology Iterative Regularized Methods Wavelet-Based Deconvolution Deconvolution and Resolution Myopic and Blind Deconvolution Conclusions and Chapter Summary Acknowledgments References MULTIFRAME BLIND DECONVOLUTION COUPLED WITH FRAME REGISTRATION AND RESOLUTION ENHANCEMENT Filip Sroubek, Jan Flusser, and Gabriel Cristobal Introduction Mathematical Model Polyphase Formulation Reconstruction of Volatile Blurs Blind Superresolution Experiments Conclusions Acknowledgments References BLIND RECONSTRUCTION OF MULTIFRAME IMAGERY BASED ON FUSION AND CLASSIFICATION Dimitrios Hatzinakos, Alexia Giannoula, and Jianxin Han Introduction System Overview Recursive Inverse Filtering with Finite Normal-Density Mixtures (RIF-FNM) Optimal Filter Adaptation Effects of Noise The Fusion and Classification Recursive Inverse Filtering Algorithm (FAC-RIF) Experimental Results Final Remarks References BLIND DECONVOLUTION AND STRUCTURED MATRIX COMPUTATIONS WITH APPLICATIONS TO ARRAY IMAGING Michael K. Ng and Robert J. Plemmons Introduction One-Dimensional Deconvolution Formulation Regularized and Constrained TLS Formulation Numerical Algorithms Two-Dimensional Deconvolution Problems Numerical Examples Application: High-Resolution Image Reconstruction Concluding Remarks and Current Work Acknowledgments References INDEX
404 citations
TL;DR: It is shown how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations.
Abstract: Following the hierarchical Bayesian framework for blind deconvolution problems, in this paper, we propose the use of simultaneous autoregressions as prior distributions for both the image and blur, and gamma distributions for the unknown parameters (hyperparameters) of the priors and the image formation noise. We show how the gamma distributions on the unknown hyperparameters can be used to prevent the proposed blind deconvolution method from converging to undesirable image and blur estimates and also how these distributions can be inferred in realistic situations. We apply variational methods to approximate the posterior probability of the unknown image, blur, and hyperparameters and propose two different approximations of the posterior distribution. One of these approximations coincides with a classical blind deconvolution method. The proposed algorithms are tested experimentally and compared with existing blind deconvolution methods
235 citations
Cites methods from "Blind image deconvolution revisited..."
...The objective of blind deconvolution methods is to obtain estimates of and based on and prior knowledge about the unknown quantities and the noise....
[...]
01 Jan 2015
TL;DR: A multichannel blind restoration technique for linearly degraded images without the explicit knowledge of either the Point Spread Function (PSF) or the original image is proposed.
Abstract: Images may be degraded for many reasons for example, out-of-focus optics produce blurred images, and variations in electronic imaging components introduce noise. Reducing blur or noise or both in images is known as image restoration. Multi-channel blind image restoration recovers an original image from several blurred versions without any knowledge of the blur function. In many applications the image to be processed has a multi-channel nature; i.e., there are several image planes available, called channels with redundant as well as complementary information. Here we propose a multichannel blind restoration technique for linearly degraded images without the explicit knowledge of either the Point Spread Function (PSF) or the original image. The blurred noisy image is compressed using 8 by 8 blocks DCT and filtered using zonal filter. The proposed restoration involves a DCT domain zonal filtering pre-processing followed by a post-processing step of time domain deconvolution. The technique applies to situations on which the scene consists of a finite support object against a uniformly black, gray or white and color backgrounds. Preliminary simulations in noise-free and noisy cases are conducted. The results are compared with standard Median filter for image denoising and the proposed blind restoration scheme is shown to exhibit improvement in SNR.
212 citations
TL;DR: An algorithm based on spatial tessellation and approximation of each triangle patch in the Delaunay triangulation by a bivariate polynomial is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames.
Abstract: An algorithm based on spatial tessellation and approximation of each triangle patch in the Delaunay (1934) triangulation (with smoothness constraints) by a bivariate polynomial is advanced to construct a high resolution (HR) high quality image from a set of low resolution (LR) frames. The high resolution algorithm is accompanied by a site-insertion algorithm for update of the initial HR image with the availability of more LR frames till the desired image quality is attained. This algorithm, followed by post filtering, is suitable for real-time image sequence processing because of the fast expected (average) time construction of Delaunay triangulation and the local update feature.
187 citations
References
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TL;DR: Its performance in the presence of noise is found to be superior to that of other blind deconvolution algorithms and the algorithm is developed further to incorporate functional forms of the point-spread function with unknown parameters.
Abstract: A blind deconvolution algorithm based on the Richardson–Lucy deconvolution algorithm is presented. Its performance in the presence of noise is found to be superior to that of other blind deconvolution algorithms. Results are presented and compared with results obtained from implementation of a Weiner filter blind deconvolution algorithm. The algorithm is developed further to incorporate functional forms of the point-spread function with unknown parameters. In the presence of noise the point-spread function can be evaluated with 1.0% error, and the object can be reconstructed with a quality near that of the deconvolution process with a known point-spread function.
469 citations
TL;DR: In this paper, a blind deconvolution method was proposed to identify and remove the convolutional distortion in order to reconstruct the tissue response, thus enhancing the diagnostic quality of the ultrasonic image.
Abstract: We address the problem of improving the spatial resolution of ulrasound images through blind deconvolution. The ultrasound image formation process in the RF domain can be expressed as a spatio-temporal convolution between the tissue response and the ultrasonic system response, plus additive noise. Convolutional components of the dispersive attenuation and aberrations introduced by propagating through the object being imaged are also incorporated in the ultrasonic system response. Our goal is to identify and remove the convolutional distortion in order to reconstruct the tissue response, thus enhancing the diagnostic quality of the ultrasonic image. Under the assumption of an independent, identically distributed, zero-mean, non-Gaussian tissue response, we were able to estimate distortion kernels using bicepstrum operations on RF data. Separate 1D distortion kernels were estimated corresponding to axial and lateral image lines and used in the deconvolution process. The estimated axial kernels showed similarities to the experimentally measured pulse-echo wavelet of the imaging system. Deconvolution results from B-scan images obtained with clinical imaging equipment showed a 2.5-5.2 times gain in lateral resolution, where the definition of the resolution has been based on the width of the autocovariance function of the image. The gain in axial resolution was found to be between 1.5 and 1.9.
135 citations
TL;DR: Object and visual comparisons are presented with the linear minimum mean-squared-error (LMMSE) and the regularized least-squares (RLS) estimator and show that the RCTLS estimator reduces significantly ringing artifacts around edges as compared to the two other approaches.
Abstract: In this paper, the problem of restoring an image distorted by a linear space-invariant (LSI) point-spread function (PSF) that is not exactly known is formulated as the solution of a perturbed set of linear equations. The regularized constrained total least-squares (RCTLS) method is used to solve this set of equations. Using the diagonalization properties of the discrete Fourier transform (DFT) for circulant matrices, the RCTLS estimate is computed in the DFT domain. This significantly reduces the computational cost of this approach and makes its implementation possible even for large images. An error analysis of the RCTLS estimate, based on the mean-squared-error (MSE) criterion, is performed to verify its superiority over the constrained total least-squares (CTLS) estimate. Numerical experiments for different errors in the PSF are performed to test the RCTLS estimator. Objective and visual comparisons are presented with the linear minimum mean-squared-error (LMMSE) and the regularized least-squares (RLS) estimator. Our experiments show that the RCTLS estimator reduces significantly ringing artifacts around edges as compared to the two other approaches. >
132 citations
TL;DR: An algorithm for the identification of the blur and the restoration of a noisy blurred image that is exploited in computing the maximum likelihood estimates of the original image and the additive noise.
Abstract: The authors describe an algorithm for the identification of the blur and the restoration of a noisy blurred image. The original image and the additive noise are modeled as zero-mean Gaussian random processes. Their covariance matrices are unknown parameters. The blurring process is specified by its point spread function, which is also unknown. Maximum likelihood estimation is used to find these unknown parameters. In turn, the expectation-maximization (EM) algorithm is exploited in computing the maximum likelihood estimates. In applying the EM algorithm, the original image is part of the complete data; its estimate is computed in the E-step of the EM iterations. Explicit iterative expressions are derived for the estimation. Experimental results on simulated and photographically blurred images are shown. >
113 citations
TL;DR: The problem of identifying the image and blur parameters and restoring a noisy blurred image is addressed and two algorithms for identification/restoration, based on two different choices of complete data, are derived and compared.
Abstract: In this paper, the problem of identifying the image and blur parameters and restoring a noisy blurred image is addressed. Specifying the blurring process by its point spread function (PSF), the blur identification problem is formulated as the maximum likelihood estimation (MLE) of the PSF. Modeling the original image and the additive noise as zeromean
Gaussian processes, the MLE of their covariance matrices is also computed. An iterative approach, called the EM (expectation-maximization) algorithm, is used to find the maximum likelihood estimates ofthe relevant unknown parameters. In applying the EM algorithm, the original image is chosen to be part of the complete data; its estimate is computed in the
E-step of the EM iterations and represents the restored image. Two algorithms for identification/restoration, based on two different choices of complete data, are derived and compared. Simultaneous blur identification and restoration is performed by the first algorithm, while the identification of the blur results from a separate minimization in the second algorithm. Experiments with simulated and photographically blurred images
are shown.
109 citations