Variational Bayesian Blind Image Deconvolution: A review

Ruiz, Pablo; Zhou, Xu; Mateos, Javier; Molina, Rafael; Katsaggelos, Aggelos K.

doi:10.1016/j.dsp.2015.04.012

Cited by 66 publications

(47 citation statements)

References 88 publications

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“…Blind deconvolution (BD) for deblurring is one of the most extensively studied topics in image processing [1], [2]. Essentially, blurring of images is modeled as convolution of images and kernels.…”

Section: Introductionmentioning

confidence: 99%

“…In such cases, SI BD methods fail in kernel estimation and also in deconvolution [1]. Although specialized BD methods for nonuniform blur have been recently developed, they can only handle certain types of blur, e.g., motion, defocus, or locally uniform blur [2]. Consequently, the applicability of BD to general blurry images remains limited.…”

Section: Introductionmentioning

confidence: 99%

“…As our focus is to enable flexible SV BD rather than seeking for better image priors, we use an image prior based on total variation (TV) that is known to be effective for VB-based BD [31]. Meanwhile, priors for kernels have been also proposed in SI BD [2], [35]. We discuss our choice of a prior for the proposed field of kernels during model construction in Sect.…”

Section: Other Topics (1) Variational Bayesmentioning

confidence: 99%

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Shift-Variant Blind Deconvolution Using a Field of Kernels

Sonogashira

Iiyama

Minoh

2017

IEICE Trans. Inf. & Syst.

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Motoharu SONOGASHIRA†a) , Nonmember, Masaaki IIYAMA †b) , Member, and Michihiko MINOH †c) , Fellow SUMMARY Blind deconvolution (BD) is the problem of restoring sharp images from blurry images when convolution kernels are unknown. While it has a wide range of applications and has been extensively studied, traditional shift-invariant (SI) BD focuses on uniform blur caused by kernels that do not spatially vary. However, real blur caused by factors such as motion and defocus is often nonuniform and thus beyond the ability of SI BD. Although specialized methods exist for nonuniform blur, they can only handle specific blur types. Consequently, the applicability of BD for general blur remains limited. This paper proposes a shift-variant (SV) BD method that models nonuniform blur using a field of kernels that assigns a local kernel to each pixel, thereby allowing pixelwise variation. This concept is realized as a Bayesian model that involves SV convolution with the field of kernels and smoothing of the field for regularization. A variationalBayesian inference algorithm is derived to jointly estimate a sharp latent image and a field of kernels from a blurry observed image. Owing to the flexibility of the field-of-kernels model, the proposed method can deal with a wider range of blur than previous approaches. Experiments using images with nonuniform blur demonstrate the effectiveness of the proposed SV BD method in comparison with previous SI and SV approaches. key words: blind deconvolution, deblurring, shift-variant, variational Bayes IntroductionBlind deconvolution (BD) for deblurring is one of the most extensively studied topics in image processing [1], [2]. Essentially, blurring of images is modeled as convolution of images and kernels. Deconvolution is the inverse of this process, which effectively restores sharp images from blurry ones. The objective of BD is to perform deconvolution when kernels are unknown, which is often the case in practice [1]. Since undesirable blur is quite common in the real world, BD has a wide range of applications, e.g., mobile photography [3], computational photography [4], computer vision [5], astronomical imaging [6], and biomedical imaging [7].Traditional shift-invariant (SI) BD assumes uniform blur produced by kernels that do not vary spatially across images, such as the example in Fig. 1 (b). However, in reality blur kernels often spatially vary, producing nonuni- . For example, independently moving objects produce different effects of motion blur, and objects distant from a camera are more subject to defocus blur than close objects. Blur is often more complex since both motion and defocus blur can simultaneously occur, as shown in Fig. 1 (c). In such cases, SI BD methods fail in kernel estimation and also in deconvolution [1]. Although specialized BD methods for nonuniform blur have been recently developed, they can only handle certain types of blur, e.g., motion, defocus, or locally uniform blur [2]. Consequently, the applicability of BD to general blurry images remains limited.I...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Other Topics (1) Variational Bayesmentioning

confidence: 99%

See 1 more Smart Citation

Shift-Variant Blind Deconvolution Using a Field of Kernels

Sonogashira

Iiyama

Minoh

2017

IEICE Trans. Inf. & Syst.

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“…However, the opposite problem of determining the initial state, given a final one is extremely difficult. Problems of the latter kind are referred as ill-posed inverse problems [1][2][3].Diffusion taking place on networks, in the forward direction, is well studied. One class of models originally used to describe epidemics is the Susceptible-InfectedRecovered (SIR) model [4,5].…”

mentioning

confidence: 99%

“…However, the opposite problem of determining the initial state, given a final one is extremely difficult. Problems of the latter kind are referred as ill-posed inverse problems [1][2][3].…”

mentioning

confidence: 99%

Morphological inversion of complex diffusion

Nguyen

Vural

2017

Phys. Rev. E

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Epidemics, neural cascades, power failures, and many other phenomena can be described by a diffusion process on a network. To identify the causal origins of a spread, it is often necessary to identify the triggering initial node. Here we define a new morphological operator and use it to detect the origin of a diffusive front, given the final state of a complex network. Our method performs better than algorithms based on distance (closeness) and Jordan centrality. More importantly, our method is applicable regardless of the specifics of the forward model, and therefore can be applied to a wide range of systems such as identifying the patient zero in an epidemic, pinpointing the neuron that triggers a cascade, identifying the original malfunction that causes a catastrophic infrastructure failure, and inferring the ancestral species from which a heterogeneous population evolves.A sugar piece placed in tea will erode and eventually dissolve. Given the initial shape of the piece, it is trivial to predict its final distribution. However, the opposite problem of determining the initial state, given a final one is extremely difficult. Problems of the latter kind are referred as ill-posed inverse problems [1][2][3].Diffusion taking place on networks, in the forward direction, is well studied. One class of models originally used to describe epidemics is the Susceptible-InfectedRecovered (SIR) model [4,5]. Variations include SI, SIS, SIRS, etc. Others include more realistic delay conditions, such as an incubation period for the infection [6]. Similar models are used to describe neural cascades [7], traffic jams [8] and infrastructure failures [9].Accordingly, a successful method of inverting diffusion on complex networks can help identify patient zero in an epidemic outbreak, pinpoint neurons that trigger a cognitive cascades, remedy the parts of the road network that initiate congestion, and determine malfunctions that lead to cascading failures. In the weak selection limit, evolution can be thought as diffusion on a genotype network [10,11], so diffusion inversion may be used to identify ancestral species.Here we address the problem of identifying the origin of a diffusive process taking place on a complex network, given the its final state. We refer to the influenced nodes as the candidate set C. Any member of C may be the node from which the diffusion originated. We refer to this node as the seed, s, and to the forward model as M .Presently, there are two approaches to identify s. The first uses probability marginals from Bayesian methods [12][13][14][15][16][17][18][19][20][21]. In some cases, it is possible to sample the state space using Monte Carlo simulations [13]. However, this is only feasible for small networks. Message-passing algorithms can approximate the marginals efficiently [12,[14][15][16], however these algorithms are model specific: for every M , one must invent new approximations, heuristic assumptions and analytic calculations.In contrast, the second class of methods works independent of the forward ...

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Wavelet‐Based Image Deconvolution and Reconstruction

Pustelnik

Benazza-Benhayia²,

Zheng

et al. 2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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Image deconvolution and reconstruction are inverse problems which are encountered in a wide array of applications. Due to the ill-posedness of such problems, their resolution generally relies on the incorporation of prior information through regularizations, which may be formulated in the original data space or through a suitable linear representation. In this article, we show the benefits which can be drawn from frame representations, such as wavelet transforms. We present an overview of recovery methods based on these representations: (i) variational formulations and non-smooth convex optimization strategies, (ii) Bayesian approaches, especially Monte Carlo Markov Chain methods and variational Bayesian approximation techniques, and (iii) Stein-based approaches. A brief introduction to blind deconvolution is also provided.

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Variational Bayesian Blind Image Deconvolution: A review

Cited by 66 publications

References 88 publications

Shift-Variant Blind Deconvolution Using a Field of Kernels

Shift-Variant Blind Deconvolution Using a Field of Kernels

Morphological inversion of complex diffusion

Wavelet‐Based Image Deconvolution and Reconstruction

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