Summary
Photos from fields like medicine and astronomy often suffer from grainy or blurry spots called noise and blur, which makes it hard to see details clearly. The researchers studied a special type of noise called Poisson noise and how it affects images that may or may not have known blur patterns. They used mathematical tools called reweighted l1 penalties and minimax concave penalties to better preserve edges while cleaning up these images. Their method involves solving a complex problem with a step-by-step algorithm that they proved works well. Testing on various images showed their approach effectively improves image clarity even when the blur pattern is unknown.
Poisson noiseimage denoisingimage deblurringblind image restorationnonblind image restorationpoint spread functiontotal variationreweighted l1 regularizationminimax concave penaltyalternating direction method of multipliers
Abstract
Images are important tools in various sciences. Despite the development of photo-taking tools, creating clear and image without noise remains challenging in practice. In particular, Poisson noise has an effect on medical and astronomical images, and reduces their quality. Additionally, blur is another factor that has an effect on image quality. The problem of image restoration becomes very complicated when we have no information about the Point Spread Function (PSF). These types of problems are known as blind case. However, in some images, such as some astronomical images, the type of PSF can be specified, and these types of problems are known as nonblind problems. Total Variation (TV) is a widely used method for solving such inverse problems, where the selection of the penalty function is the most critical factor that affects the method's performance. In this paper, to improve edge preservation, we employ a reweighted $\ell_1$-regularization of the fractional order derivative. Furthermore, we propose a nonblind and blind image deblurring approach under Poisson noise using the Minimax Concave Penalty (MCP), which is a continuous, sparsity promoting, and nearly unbiased regularizer. This formulation leads to a nonconvex optimization model. To solve the proposed model, we introduce an efficient numerical algorithm based on the Alternating Direction Method of Multipliers (ADMM) and provide an analysis of its convergence. Finally, the effectiveness of the proposed algorithm are demonstrated through extensive experiments on various images.