An extended sparse model for blind image deblurring

Blind image deblurring is a classical ill-posed problem that usually requires constraints on the clean image, the blur kernel, and noise to make it well-posed. Recently, a simple yet effective sparse norm l e is proposed, which adds two widely-adopted sparse norms, i.e., l 0 and l 1 . By using l e t...

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Bibliographic Details
Published in:Signal, image and video processing image and video processing, 2024-03, Vol.18 (2), p.1863-1877
Main Authors: Ge, Xianyu, Liu, Jing, Hu, Dandan, Tan, Jieqing
Format: Article
Language:English
Subjects:
Algorithms
Computer Imaging
Computer Science
Ill posed problems
Image enhancement
Image Processing and Computer Vision
Multimedia Information Systems
Original Paper
Pattern Recognition and Graphics
Signal,Image and Speech Processing
Vision
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Summary:Blind image deblurring is a classical ill-posed problem that usually requires constraints on the clean image, the blur kernel, and noise to make it well-posed. Recently, a simple yet effective sparse norm l e is proposed, which adds two widely-adopted sparse norms, i.e., l 0 and l 1 . By using l e to regularize the gradients of the clean image, and l 2 + ∇ l e as the noise fitting function, an enhanced sparse model for blind image deblurring is established and achieves surprisingly attractive results. In this paper, inspired by the facts that the gradients of a natural image tend to obey a heavy-tailed distribution, and the noise exhibits spatial randomness, we propose a more flexible model called the extended sparse model which can take the enhanced sparse model as a special case. Specifically, for the image gradients, we suggest a improved sparse norm l P , which is developed from l 0 and l p ( 0 < p ≤ 1 ) . Furthermore, we constrain the second-order derivative of noise to boost the percentage of high-frequencies in the fidelity such that the recovery focuses more on high-frequencies that are erased in the blurry image. Based on the half-quadratic splitting method and a variant of the generalized iterated shrinkage algorithm (GISA), we provide an effective optimization scheme for the overall model. Extensive evaluations of benchmark datasets and real images indicate the superiority of the proposed method against state-of-the-art deblurring algorithms.
ISSN:1863-1703
1863-1711
DOI:10.1007/s11760-023-02888-2