Spatially dependent regularization parameter selection for total generalized variation-based image denoising

• Published in: Computational & applied mathematics Vol. 37; no. 1; pp. 277 - 296
• Main Authors: Ma, Tian-Hui, Huang, Ting-Zhu, Zhao, Xi-Le
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2018; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Computational mathematics; Computational Mathematics and Numerical Analysis; Image processing; Image restoration; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematical models; Mathematics; Mathematics and Statistics; Noise reduction; Optimization; Regularization; Visual perception driven algorithms; Visual signals; Alternating minimization; 90C26 (Nonconvex programming); Spatially dependent regularization parameter selection; Total generalized variation (TGV); Image denoising; 68U10 (Image processing)
• ISSN: 0101-8205; 2238-3603; 1807-0302
• DOI: 10.1007/s40314-016-0342-8

We propose a novel image denoising model based on the total generalized variation (TGV) regularization. In the model, a spatially dependent regularization parameter is utilized to adaptively fit the local image features, resulting in further exploitation of the denoising potential of the TGV regularization. The proposed model is formulated under a joint optimization framework, by which the estimations of the restored image and the regularization parameter are achieved simultaneously. Furthermore, the model is general purpose that can handle various types of noise occurring in image processing. An alternating minimization-based numerical scheme is especially developed, which leads to an efficient algorithmic solution to the nonconvex optimization problem. Numerical experiments are reported to illustrate the effectiveness of our model in terms of both peak signal-to-noise ratio and visual perception.