Edge Adaptive Hybrid Regularization Model For Image Deblurring

TL;DR

This paper introduces an adaptive regularization model for image deblurring that dynamically adjusts parameters based on edge detection, effectively preserving edges while reducing noise and blur.

Contribution

It proposes a novel convex model combining harmonic and TV regularization with spatially adaptive parameters guided by edge information, solved efficiently using sPADMM.

Findings

Outperforms state-of-the-art algorithms in PSNR and SSIM

Effectively preserves image edges while removing noise and blur

Achieves linear convergence rate with sPADMM

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.