Deconvolving Poissonian images by a novel hybrid variational model

Chen, Dai-Qiang; Cheng, Lizhi

doi:10.1016/j.jvcir.2011.07.007

Cited by 17 publications

(12 citation statements)

References 42 publications

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“…In this example, for TV based methods, we only consider the isotropic case since the isotropic TV usually behaves better than the anisotropic version [11,35].…”

Section: Comparison With Other State-of-the-art Methodsmentioning

confidence: 99%

Image restoration using total variation with overlapping group sparsity

Liu

Huang

Selesnick

et al. 2015

Information Sciences

149

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a b s t r a c tImage restoration is one of the most fundamental issues in imaging science. Total variation regularization is widely used in image restoration problems for its capability to preserve edges. In the literature, however, it is also well known for producing staircase artifacts. In this work we extend the total variation with overlapping group sparsity, which we previously developed for one dimension signal processing, to image restoration. A convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem. In the experiments, we compare our method with several state-of-the-art methods. The results illustrate the efficiency and effectiveness of the proposed method in terms of PSNR and computing time.

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“…In this example, for TV based methods, we only consider the isotropic case since the isotropic TV usually behaves better than the anisotropic version [11,35].…”

Section: Comparison With Other State-of-the-art Methodsmentioning

confidence: 99%

Image restoration using total variation with overlapping group sparsity

Liu

Huang

Selesnick

et al. 2015

Information Sciences

149

View full text Add to dashboard Cite

show abstract

“…In this method, tailored for general smooth saddle-point problems, the step-size parameter can be adaptively computed so that the convergence of the scheme can be proved under mild assumptions. For other efficient methods solving the restoration problem of blurred images corrupted by Poisson noise with the TV function, we refer the reader to [28][29][30][31] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Deblurring Poisson noisy images by total variation with overlapping group sparsity

Jiang

Liu

2016

Applied Mathematics and Computation

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“…However, non-Gaussian noises are also presented in the real imaging, e.g., Poisson noise is generally observed in photon-limited images such as electronic microscopy [1], positron emission tomography [2] and single photon emission computerized tomography [3]. Due to its important applications in medical imaging, linear inverse problems in presence of Poisson noise have received much interest in literature [8,14,15]. The likelihood probability of the Poisson noisy data f is given by…”

Section: Introductionmentioning

confidence: 99%

“…Since the pixel values of images represent the number of 2 discrete photons incident over a given time interval in this application, we demand that u ≥ 0 in model (1.6). Another selection for the regularizer term is the wavelet tight framelets [6,7,8], which have also been proved to be efficient but may need more computational cost associated with the wavelet transform and inverse transform. In the last several years, the relationship between the total variation and wavelet framelet has also been revealed [9,10].…”

Section: Introductionmentioning

confidence: 99%

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Inexact alternating direction method based on Newton descent algorithm with application to Poisson image deblurring

Chen

2016

SIViP

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The recovery of images from the observations that are degraded by a linear operator and further corrupted by Poisson noise is an important task in modern imaging applications such as astronomical and biomedical ones. Gradient-based regularizers involve the popular total variation semi-norm have become standard techniques for Poisson image restoration due to its edgepreserving ability. Various efficient algorithms have been developed for solving the corresponding minimization problem with non-smooth regularization terms. In this paper, motivated by the idea of the alternating direction minimization algorithm and the Newton's method with upper convergent rate, we further propose inexact alternating direction methods utilizing the proximal Hessian matrix information of the objective function, in a way reminiscent of Newton descent methods. Besides, we also investigate the global convergence of the proposed algorithms under certain conditions. Finally, we illustrate that the proposed algorithms outperform the current state-of-the-art algorithms through numerical experiments on Poisson image deblurring.

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Deconvolving Poissonian images by a novel hybrid variational model

Cited by 17 publications

References 42 publications

Image restoration using total variation with overlapping group sparsity

Image restoration using total variation with overlapping group sparsity

Deblurring Poisson noisy images by total variation with overlapping group sparsity

Inexact alternating direction method based on Newton descent algorithm with application to Poisson image deblurring

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