Edge adaptive hybrid regularization model for image deblurring

Abstract

The parameter selection is crucial to regularization based image restoration methods. Generally speaking, a spatially fixed parameter for regularization item in the whole image does not perform well for both edge and smooth areas. A larger parameter of regularization item reduces noise better in smooth areas but blurs edge regions, while a small parameter sharpens edge but causes residual noise. In this paper, an automated spatially adaptive regularization model, which combines the harmonic and TV models, is proposed for reconstruction of noisy and blurred images. In the proposed model, it detects the edges and then spatially adjusts the parameters of Tikhonov and TV regularization terms for each pixel according to the edge information. Accordingly, the edge information matrix will be also dynamically updated during the iterations. Computationally,the newly-established model is convex, which can be solved by the semi-proximal alternating direction method of multipliers (sPADMM) with a linear-rate convergence rate. Numerical simulation results demonstrate that the proposed model effectively reserves the image edges and eliminates the noise and blur at the same time. In comparison to state-of-the-art algorithms, it outperforms other methods in terms of PSNR, SSIM and visual quality.

Difference of anisotropic and isotropic TV for segmentation under blur and Poisson noise

“…For future directions, we are interested in other nonconvex regularization, such as ℓ 1 /ℓ 2 on the gradient (Wang et al, 2021(Wang et al, , 2022Wu et al, 2022a), ℓ p , 0 < p < 1, on the gradient (Hintermüller and Wu, 2013;Li Y. et al, 2020;Wu et al, 2021b), and transformed total variation (Huo et al, 2022), as alternatives to AITV. On the other hand, we can develop AITV variants of weighted TV or adaptive TV (Wu et al, 2021a; Zhang et al, 2022). Moreover, we plan to determine how to make the sparsity parameter α in AITV adaptable to each image.…”

3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization

“…To efficiently restore blurry Poissonian images, various optimization models with regularization terms were developed and further solved by efficient algorithms. The most commonly used regularization is the total variation (TV) regularization [12][13][14][15][16][17][18][19]. Dey et al [12] enhanced the RL algorithm by the TV regularization; Harmany et al [13] solved the TV regularized model by sequential quadratic approximations; Bonettini and Ruggiero [14] combined a Poisson log-likelihood data fidelity term with the TV regularization term and used an alternating extragradient algorithm to solve the model; Figueiredo and Bioucas-Dias [15] solved the model by the alternating direction method of multipliers; Liyan et al [16] proposed a dictionary learning model in addition to the TV regularization for Poissonian image restoration.…”

An Automatic Pixel-Wise Multi-Penalty Approach to Image Restoration

“…The study [15] assesses two-penalty regularization, incorporating L 0 and L 2 penalty terms to tackle nonlinear ill-posed problems and analyzes its regularizing characteristics. In [16], an automated spatially adaptive regularization model combining harmonic and Total Variation (TV) terms is introduced. This model is dependent on two regularization parameters and two edge information matrices.…”