Fast L0-based image deconvolution with variational Bayesian inference and majorization-minimization

Zhang, Ganchi; Kingsbury, Nick

doi:10.1109/globalsip.2013.6737081

Cited by 5 publications

(15 citation statements)

References 12 publications

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“…Similar to the argument in [14], we find that Q should be positive definite to ensure convergence and hence:…”

Section: Model Formulationmentioning

confidence: 99%

“…Because S needs to be of size P × P , when P > G, its diagonal is an expanded form of s where each s i is repeated g i times [14].…”

Section: Model Formulationmentioning

confidence: 99%

“…To update the variables appearing in (9), we construct a 3-layer hierarchical prior as described in [14]. To be more specific, we impose Gamma distributions for both inverse signal variance s and its rate parameter b:…”

Section: Continuation Strategiesmentioning

confidence: 99%

“…In addition, VBMM has demonstrated the potential of group-sparse modeling. For instance, the real and imaginary parts of the dual-tree complex wavelet transform (DT CWT) coefficients are clustered into single groups for Bayesian inference [14]. However, tree-structured dependencies among wavelet coefficients were not fully utilized in VBMM in [14].…”

Section: Introductionmentioning

confidence: 99%

“…This paper builds on a hierarchical Bayesian modeling of wavelet coefficients proposed in [14], which is derived from a group-sparse GSM model. Based on a combination of variational Bayesian (VB) inference with a subband-adaptive Majorization Minimization (MM) method, the VBMM algorithm in [14] effectively simplifies computation of the posterior distribution and finds good solutions in the non-convex search space. In addition, VBMM has demonstrated the potential of group-sparse modeling.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Image deconvolution using tree-structured Bayesian group sparse modeling

Zhang

Roberts

Kingsbury

2014

2014 IEEE International Conference on Image Processing (ICIP)

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“…Similar to the argument in [14], we find that Q should be positive definite to ensure convergence and hence:…”

Section: Model Formulationmentioning

confidence: 99%

“…Because S needs to be of size P × P , when P > G, its diagonal is an expanded form of s where each s i is repeated g i times [14].…”

Section: Model Formulationmentioning

confidence: 99%

Section: Continuation Strategiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Image deconvolution using tree-structured Bayesian group sparse modeling

Zhang

Roberts

Kingsbury

2014

2014 IEEE International Conference on Image Processing (ICIP)

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Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

Zhang

Kingsbury

2015

Digital Signal Processing

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a r t i c l e i n f o a b s t r a c tArticle history: Available online xxxx Keywords: Image restoration Wavelet group-sparse modeling Variational Bayesian inference Majorization minimization Dual-tree complex waveletsIn this work, we present a recent wavelet-based image restoration framework based on a group-sparse Gaussian scale mixture model. A hierarchical Bayesian estimation is derived using a combination of variational Bayesian inference and a subband-adaptive majorization-minimization method that simplifies computation of the posterior distribution. We show that both of these iterative methods can converge together without needing nested loops, and thus good solutions can be found rapidly in the nonconvex search space. We also integrate our method, variational Bayesian with majorization minimization (VBMM), with tree-structured modeling of the wavelet coefficients. This extension achieves significant gains in performance over the coefficient-sparse version of the algorithm. The experimental results demonstrate that the proposed method and its tree-structured extensions are effective for various imaging applications such as image deconvolution, image superresolution and compressive sensing magnetic resonance imaging (MRI) reconstruction, and that they outperform more conventional sparsityinducing methods based on the l 1 -norm.

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A Comprehensive Review of Blind Deconvolution Techniques for Image Deblurring

Satish¹,

Srikantaswamy²,

Ramaswamy³

2020

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Image Deblurring is a very popular area of research in all over the world. It is an illposed problem which still does not have an ideal solution. Therefore, in order to analyse the research problems and to understand the statement of image deblurring we look in to the state-of-the-art methods proposed in various recent publications. Hence, the present study is focused on the overall review of the techniques used in image deblurring and their solutions to tackle the illposed problem using mathematical model. Based on the overall technique simple MAP model falls short in either deriving accurate convergence to the global optimum or computational implementation. Convergence of the algorithm is the most important factor for the effective performance of Lo and L1 norms for regularizers for theoretical applications. The importance of the choice of the correct estimator and the role of various priors in solving the imaging inverse problem using the MAP estimation method is discussed. The consequence of different priors to the rate of convergence of the MAP algorithm and its computational complexity are studied and tabulated.

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Fast L0-based image deconvolution with variational Bayesian inference and majorization-minimization

Cited by 5 publications

References 12 publications

Image deconvolution using tree-structured Bayesian group sparse modeling

Image deconvolution using tree-structured Bayesian group sparse modeling

Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

A Comprehensive Review of Blind Deconvolution Techniques for Image Deblurring

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