Variational Bayesian Image Restoration Based on a Product of $t$-Distributions Image Prior

Chantas, Giannis; Galatsanos, Nikolaos; Likas, Aristidis; Saunders, Michael A.

doi:10.1109/tip.2008.2002828

Cited by 93 publications

(104 citation statements)

References 25 publications

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“…Note that, if A is the identity matrix, one recovers the usual proximity operator prox f : R N → R N , which is at the core of numerous convex optimization algorithms (see [33,34,35] for tutorials and use for multicomponent image processing). 1 We are now ready to provide Algorithm 1 for the minimization of function F :…”

Section: Minimization Strategymentioning

confidence: 99%

“…Real-life video sequences are usually blurred due to the overall effect of different factors such as defocus, motion blur, and optical blur. These degraded videos can typically be modeled as the noisy convolution of original ones with the impulse response of some blur kernel, also called point spread function (PSF) [1,2,3]. Thereby, a deconvolution process becomes mandatory for retrieving a visually sharp video [4].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An alternating proximal approach for blind video deconvolution

Abboud¹,

Chouzenoux

Pesquet

et al. 2019

Signal Processing: Image Communication

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Blurring occurs frequently in video sequences captured by consumer devices, as a result of various factors such as lens aberrations, defocus, relative camerascene motion, and camera shake. When it comes to the contents of archive documents such as old films and television shows, the degradations are even more serious due to several physical phenomena happening during the sensing, transmission, recording, and storing processes. We propose in this paper a versatile formulation of blind video deconvolution problems that seeks to estimate both the sharp unknown video sequence and the underlying blur kernel from an observed video. This inverse problem is ill-posed, and an appropriate solution can be obtained by modeling it as a nonconvex minimization problem. We provide a novel iterative algorithm to solve it, grounded on the use of recent advances in convex and nonconvex optimization techniques, and having the ability of including numerous well-known regularization strategies.

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Section: Minimization Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An alternating proximal approach for blind video deconvolution

Abboud¹,

Chouzenoux

Pesquet

et al. 2019

Signal Processing: Image Communication

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show abstract

“…While in image restoration there have been several attempts to combine image priors [7][8][9], no such attempts have been made in the SR literature apart from our conference paper [10], from which the present paper grows. In [9] a Student's t Product of Experts (PoE) image prior model was proposed and learnt from the observations. In [8] the PoE prior was learnt using a large training set of images and also stochastic sampling methods.…”

Section: Introductionmentioning

confidence: 99%

“…In [8] the PoE prior was learnt using a large training set of images and also stochastic sampling methods. A combination of the TV image prior model and the PoE model of [9] has been recently proposed in [11]. This method can be considered a spatially adaptive version of the TV model which furthermore, as the method in [9], has the ability to simultaneously enforce different properties on the image.…”

Section: Introductionmentioning

confidence: 99%

Bayesian combination of sparse and non-sparse priors in image super resolution

Villena¹,

Vega²,

Babacan³

et al. 2013

Digital Signal Processing

105

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In this paper the application of image prior combinations to the Bayesian Super Resolution (SR) image registration and reconstruction problem is studied. Two sparse image priors, a Total Variation (TV) prior and a prior based on the 1 norm of horizontal and vertical first order differences (f.o.d.), are combined with a non-sparse Simultaneous Auto Regressive (SAR) prior. Since, for a given observation model, each prior produces a different posterior distribution of the underlying High Resolution (HR) image, the use of variational approximation will produce as many posterior approximations as priors we want to combine. A unique approximation is obtained here by finding the distribution on the HR image given the observations that minimizes a linear convex combination of Kullback-Leibler (KL) divergences. We find this distribution in closed form. The estimated HR images are compared with the ones obtained by other SR reconstruction methods.

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“…Recently, a Bayesian inference framework which requires the approximation of the prior partition function and is based on the variational approximation was proposed to handle the simultaneous parameter and image estimation [14]. An alternative image model has recently been proposed based on the combination of several image priors [11], [23] and [16]. It combines in product form multiple probabilistic models.…”

mentioning

confidence: 99%

Variational Bayesian Image Restoration With a Product of Spatially Weighted Total Variation Image Priors

Chantas

Galatsanos

Molina

et al. 2010

IEEE Trans. on Image Process.

104

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Abstract-In this paper a new image prior is introduced and used in image restoration. This prior is based on products of spatially weighted Total Variations (TV). These spatial weights provide this prior with the flexibility to better capture local image features than previous TV based priors. Bayesian inference is used for image restoration with this prior via the variational approximation. The proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms. Numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state-of-the-art restoration algorithms.

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Variational Bayesian Image Restoration Based on a Product of $t$-Distributions Image Prior

Cited by 93 publications

References 25 publications

An alternating proximal approach for blind video deconvolution

An alternating proximal approach for blind video deconvolution

Bayesian combination of sparse and non-sparse priors in image super resolution

Variational Bayesian Image Restoration With a Product of Spatially Weighted Total Variation Image Priors

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