Image restoration based on fractional-order model with decomposition: texture and cartoon

• Published in: Computational & applied mathematics Vol. 40; no. 8
• Main Authors: Yan, Shaowen, Ni, Guoxi, Zeng, Tieyong
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.12.2021; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Decomposition; Image restoration; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Regularization; Texture; 49M41; Fractional order; Deblurring and denoising; 65K10; Texture; Nonconvex; ADMM; Wavelet frame
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-021-01681-6

Inspired by the work of Daubechies and Teschke (Appl Comput Harmon Anal 19(1):1–16. https://doi.org/10.1016/j.acha.2004.12.004 , 2005), we propose an image deblurring and denoising method based on fractional-order model with simultaneous decomposition. We use fractional-order derivative as the regularization term of cartoon part to avoid blocky effect. We replace the BV regularization term by B q β ( L p ( Ω ) ) term, and B 1 - 1 ( L 1 ( Ω ) ) term for the regularization of texture part. To promote sparsity, we add a nonconvex regularization term which is the weighted difference of l 1 -norm and l 2 -norm based on wavelet frame to the regularization term. The model can be solved by alternating direction method of multipliers (ADMM). The comparative experimental results show that the capability of preserving the edges and textural details of our algorithms. Our fractional-order algorithms are superior to that of traditional integer-order algorithms especially for images with texture.