A L_0 sparse analysis prior for blind poissonian image deconvolution

Gong, Xiaojin; Lai, Baisheng; Xiang, Zhiyu

doi:10.1364/oe.22.003860

Cited by 14 publications

(5 citation statements)

References 14 publications

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“…For this purpose, in the case of Gaussian noise we have selected the methods proposed by Cuesta et al [38], fractional-order total variation using proximity algorithm (FTV-PA) [57], R-NL [58], Adaptive Regularization with the Structure Tensor [59]., the full fractional anisotropic diffusion (FFAD) [60] and overlapping group sparsity (OLGS) [40] for comparative analysis. For the case of Poisson noise, comparison is performed with the methods such as fourth-order partial differential equation filter (FOPDEF) [12], TV-Poi [61], OGS-ADM [62], Framelet based (BPID-FR) [63], spatially adaptive (RLSATV) [64] and sparse based (TV-L0) [65]. The work of TV-Poi and OGS-ADM is based on the TV and overlapping group sparsity based prior for Poisson noise image deblurring.…”

Section: Comparative Analysismentioning

confidence: 99%

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

2019

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Denoising images subjected to Gaussian and Poisson noise has attracted attention in many areas of image processing. This paper introduces an image denoising framework using higher order fractional overlapping group sparsity prior to sparser image representation constraint. The proposed prior has a capability of avoiding staircase effects in both edges and oscillatory patterns (textures). We adopt the alternating direction method of multipliers for optimizing the proposed objective function by converting it into a constrained optimization problem using variable splitting approach. Finally, we conduct experiments on various degraded images and compare our results with those of several state-of-the-art methods. The numerical results show that the proposed fractional order image denoising framework improves the peak signal to noise ratio of an image by preserving the textures and eliminating the staircases effects. This leads to visually pleasant restored images which exhibit a higher value of Structural SIMilarity score when compared to that of other methods. INDEX TERMS Image denoising, fractional-order, Gaussian and Poisson noise, overlapping group sparsity, alternating direction method of multipliers.

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Section: Comparative Analysismentioning

confidence: 99%

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

2019

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“…According to the properties of optical blur, some works introduced priors or assumptions in the blind method to estimate optical blur kernel [ 16 , 17 , 18 , 19 ]. However, the optical blur is spatially varying, so some fields of the blurred image may not have sufficient information to estimate the PSFs.…”

Section: Related Workmentioning

confidence: 99%

Optimal PSF Estimation for Simple Optical System Using a Wide-Band Sensor Based on PSF Measurement

Zheng

Huang

Pan

et al. 2018

Sensors

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Simple optical system imaging is a method to simplify optical systems by removing aberrations using image deconvolution. The point spread function (PSF) used in deconvolution is an important factor that affects the image quality. However, it is difficult to obtain optimal PSFs. The blind estimation of PSFs relies heavily on the information in the image. Measured PSFs are often misused because real sensors are wide-band. We present an optimal PSF estimation method based on PSF measurements. Narrow-band PSF measurements at a single depth are used to calibrate the optical system; these enable the simulation of real lenses. Then, we simulate PSFs in the wavelength pass range of each color channel all over the field. The optimal PSFs are computed according to these simulated PSFs. The results indicated that the use of the optimal PSFs significantly reduces the artifacts caused by misuse of PSFs, and enhances the image quality.

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“…Xu et al 21 adopted L0-norm for image smoothing which can be used as a fundamental tool for edge enhancement, removal of clip-art compression artifacts, and detail magnification. Gong et al 22 used the L0-norm of the wavelet to construct a sparse regularization term for restoring Poisson-blurred images. Xu et al 23 proposed a blind image deconvolution method using a piecewise function to approximate the L0-norm, effectively modeling the distribution of image gradients and achieving excellent results.…”

Section: Introductionmentioning

confidence: 99%

Image denoising based on hybrid L0 and L1-norm regularization

Han,

Yang,

Dong

2024

Sixth Conference on Frontiers in Optical Imaging and Technology: Novel Imaging Systems

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In cases of insufficient lighting conditions, the obtained images of optical systems usually suffer from heavy noise, which subsequently has a negative impact on tasks like image segmentation, target detection, and edge extraction. Image denoising requires preserving the integrity of original information while eliminating irrelevant data from the signal. Regularization is an effective way to improve the performance of denoising algorithms, it achieves this by introducing additional constraints to ensure stable solutions. In this paper, we propose a hybrid regularization method which is based on the weighted combination of the L0-norm and L1-norm of image gradients. In order to obtain reliable denoising results, we have also developed a highly efficient alternately minimization algorithm to solve the resulting complex optimization problem. The algorithm utilizes variable splitting and Lagrange multipliers to determine the optimal solution, effectively transforming the initial problem into a simple convex optimization problem and a quadratic optimization problem, which can be rapidly solved in frequency domain. In the end, we conducted experiments to prove the efficiency of the proposed method. The results show that it is stable, efficient and the quality of the denoised images is comparable to some state-of-the-art methods.

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A L_0 sparse analysis prior for blind poissonian image deconvolution

Cited by 14 publications

References 14 publications

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

A Framework for Image Denoising Using First and Second Order Fractional Overlapping Group Sparsity (HF-OLGS) Regularizer

Optimal PSF Estimation for Simple Optical System Using a Wide-Band Sensor Based on PSF Measurement

Image denoising based on hybrid L0 and L1-norm regularization

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