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Robust Binary Image Deconvolution with Positive Semidefinite Programming
Yijiang Shen,Edmund Y. Lam,Ngai Wong
IAENG International Journal of Applied Mathematics , 2007,
Abstract:
Blind Image Deconvolution Algorithm for Camera-shake Deblurring Based on Variational Bayesian Estimation
基于变分贝叶斯估计的相机抖动模糊图像的盲复原算法

Sun Shao-jie,Wu Qiong,Li Guo-hui,
孙韶杰
,吴琼,李国辉

电子与信息学报 , 2010,
Abstract: Motion blur due to camera shaking during exposure is one common phenomena of image degradation. Based on the variational Bayesian estimation theory and the statistical characteristic of the natural images gradient, a blind image deconvolution algorithm is proposed to restore camera-shake blurred image. In addition, based on sub-region detection and Fuzzy filter, a deringing method is proposed to reduce ringing effect, which is not avoided in the process of image deconvolution. The experimental results show that the algorithm of blind image deconvolution can effectively remove the motion blur caused by camera shaking, and can effectively reduce the ringing effect, while preserve the image edge and details well and improve the quality of the restored image.
A Clearer Picture of Blind Deconvolution  [PDF]
Daniele Perrone,Paolo Favaro
Computer Science , 2014,
Abstract: Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort resulted in the deployment of effective algorithms, the theoretical findings generated contrasting views on why these approaches worked. On the one hand, one could observe experimentally that alternating energy minimization algorithms converge to the desired solution. On the other hand, it has been shown that such alternating minimization algorithms should fail to converge and one should instead use a so-called Variational Bayes approach. To clarify this conundrum, recent work showed that a good image and blur prior is instead what makes a blind deconvolution algorithm work. Unfortunately, this analysis did not apply to algorithms based on total variation regularization. In this manuscript, we provide both analysis and experiments to get a clearer picture of blind deconvolution. Our analysis reveals the very reason why an algorithm based on total variation works. We also introduce an implementation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the state of the art.
Image Deconvolution in the Moment Domain
Barmak Honarvar Shakibaei and Jan Flusser
Gate to Computer Sciece and Research , 2014, DOI: 10.15579/gcsr.vol1.ch5
Abstract: We propose a novel algorithm for image deconvolution from the geometric moments(GMs) of a degraded image by a circular or elliptical Gaussian point-spread function(PSF). In the proposed scheme, to show the invertibility of the moment equation in a closed form, we establish a relationship between the moments of the degraded image and the moments of the original image and the Gaussian PSF. The proposed inverted formula paves the way to reconstruct the original image using the Stirling numbers of the first kind. We validate the theoretical analysis of the proposed scheme and confirm its feasibility through the comparative studies.
Variational Semi-blind Sparse Deconvolution with Orthogonal Kernel Bases and its Application to MRFM  [PDF]
Se Un Park,Nicolas Dobigeon,Alfred O. Hero
Statistics , 2013,
Abstract: We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior distributions are specified for the PSF and the 3D image. Joint image reconstruction and PSF estimation is then performed within a Bayesian framework, using a variational algorithm to estimate the posterior distribution. The image prior distribution imposes an explicit atomic measure that corresponds to image sparsity. Importantly, the proposed Bayesian deconvolution algorithm does not require hand tuning. Simulation results clearly demonstrate that the semi-blind deconvolution algorithm compares favorably with previous Markov chain Monte Carlo (MCMC) version of myopic sparse reconstruction. It significantly outperforms mismatched non-blind algorithms that rely on the assumption of the perfect knowledge of the PSF. The algorithm is illustrated on real data from magnetic resonance force microscopy (MRFM).
A Robust Orthogonal Adaptive Approach to SISO Deconvolution  [cached]
J. E. Cousseau,C. Muravchik,P. D. Do?ate
EURASIP Journal on Advances in Signal Processing , 2004, DOI: 10.1155/s168761720440420x
Abstract: This paper formulates in a common framework some results from the fields of robust filtering, function approximation with orthogonal basis, and adaptive filtering, and applies them for the design of a general deconvolution processor for SISO systems. The processor is designed to be robust to small parametric uncertainties in the system model, with a partially adaptive orthogonal structure. A simple gradient type of adaptive algorithm is applied to update the coefficients that linearly combine the fixed robust basis functions used to represent the deconvolver. The advantages of the design are inherited from the mentioned fields: low sensitivity to parameter uncertainty in the system model, good numerical and structural behaviour, and the capability of tracking changes in the systems dynamics. The linear equalization of a simple ADSL channel model is presented as an example including comparisons between the optimal nominal, adaptive FIR, and the proposed design.
Application of Blind Deconvolution Algorithm for Image Restoration  [PDF]
D. SRINIVASA RAO,,K. SELVANI DEEPTHI,,K. MONI SUSHMA DEEP
International Journal of Engineering Science and Technology , 2011,
Abstract: Image restoration is the process of recovering the original image from the degraded image and also understand the image without any artifacts errors. Image restoration methods can be considered asdirect techniques when their results are produced in a simple one step fashion. Equivalently, indirect techniques can be considered as those in which restoration results are obtained after a number ofiterations. Known restoration techniques such as inverse filtering and Wiener Filtering can be considered as simple direct restoration techniques. The problem with such methods is that they require knowledge of the blur function that is point-spread function (PSF), which is, unfortunately, usually not available when dealing with image blurring . In this paper Blind deconvolution for image restoration is discussed which is the recovery of a sharp version of a blurred image when the blur kernel is unknown. The fundamental task of image deblurring is to de-convolute the blurred/degraded image withthe PSF that exactly describes the distortion. Firstly, the original image is degraded using the Degradation Model. It can be done by Gaussian Filter which is low-pass filter used to blur in image. Inthe edges of degraded image, the ringing effect due to high frequency drop-off can be detected using Canny Edge detection methods. This ringing effect should be removed before restoration using edge trapping. After removing the ringing effect, blind Deconvolution algorithm is applied to the blurred images. It is possible to renovate the original image without having specific knowledge of degradation filter, additive noise and image spectral density. Recent algorithms have afforded dramatic progress, yet many aspects of the problem remain challenging and hard to understand. The goal of this paper is to analyze and evaluate recent blind deconvolution lgorithms both theoretically and experimentally.
Robust Inference with Variational Bayes  [PDF]
Ryan Giordano,Tamara Broderick,Michael Jordan
Statistics , 2015,
Abstract: In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior and likelihood, since this choice is made by the modeler and is necessarily somewhat subjective. Despite the fundamental importance of the problem and a considerable body of literature, the tools of robust Bayes are not commonly used in practice. This is in large part due to the difficulty of calculating robustness measures from MCMC draws. Although methods for computing robustness measures from MCMC draws exist, they lack generality and often require additional coding or computation. In contrast to MCMC, variational Bayes (VB) techniques are readily amenable to robustness analysis. The derivative of a posterior expectation with respect to a prior or data perturbation is a measure of local robustness to the prior or likelihood. Because VB casts posterior inference as an optimization problem, its methodology is built on the ability to calculate derivatives of posterior quantities with respect to model parameters, even in very complex models. In the present work, we develop local prior robustness measures for mean-field variational Bayes(MFVB), a VB technique which imposes a particular factorization assumption on the variational posterior approximation. We start by outlining existing local prior measures of robustness. Next, we use these results to derive closed-form measures of the sensitivity of mean-field variational posterior approximation to prior specification. We demonstrate our method on a meta-analysis of randomized controlled interventions in access to microcredit in developing countries.
Mammographic image restoration using maximum entropy deconvolution  [PDF]
A Jannetta,J C Jackson,C J Kotre,I P Birch,K J Robson,R Padgett
Physics , 2005, DOI: 10.1088/0031-9155/49/21/011
Abstract: An image restoration approach based on a Bayesian maximum entropy method (MEM) has been applied to a radiological image deconvolution problem, that of reduction of geometric blurring in magnification mammography. The aim of the work is to demonstrate an improvement in image spatial resolution in realistic noisy radiological images with no associated penalty in terms of reduction in the signal-to-noise ratio perceived by the observer. Images of the TORMAM mammographic image quality phantom were recorded using the standard magnification settings of 1.8 magnification/fine focus and also at 1.8 magnification/broad focus and 3.0 magnification/fine focus; the latter two arrangements would normally give rise to unacceptable geometric blurring. Measured point-spread functions were used in conjunction with the MEM image processing to de-blur these images. The results are presented as comparative images of phantom test features and as observer scores for the raw and processed images. Visualization of high resolution features and the total image scores for the test phantom were improved by the application of the MEM processing. It is argued that this successful demonstration of image de-blurring in noisy radiological images offers the possibility of weakening the link between focal spot size and geometric blurring in radiology, thus opening up new approaches to system optimization.
Transits against Fainter Stars: The Power of Image Deconvolution  [PDF]
Penny D. Sackett,Micha?l Gillon,Daniel D. R. Bayliss,David T. F. Weldrake,Brandon Tingley
Physics , 2009, DOI: 10.1017/S1743921308026239
Abstract: Compared to bright star searches, surveys for transiting planets against fainter (V=12-18) stars have the advantage of much higher sky densities of dwarf star primaries, which afford easier detection of small transiting bodies. Furthermore, deep searches are capable of probing a wider range of stellar environments. On the other hand, for a given spatial resolution and transit depth, deep searches are more prone to confusion from blended eclipsing binaries. We present a powerful mitigation strategy for the blending problem that includes the use of image deconvolution and high resolution imaging. The techniques are illustrated with Lupus-TR-3 and very recent IR imaging with PANIC on Magellan. The results are likely to have implications for the CoRoT and KEPLER missions designed to detect transiting planets of terrestrial size.
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