Control subgradient algorithm for image $$\ell _1$$ℓ1 regularization. Issue 1 (December 2015)

• Record Type: Journal Article
• Authors: El Mouatasim, Abdelkrim; Wakrim, Mohammed
• Is Part Of: Signal, image and video processing. Volume 9:Issue 1(2015)
• Page Start: 275
• Page End: 283
• Publication Date: 2015-12
• Subjects: Subgradient algorithm -- Nesterov algorithm -- Step-size control -- $$\ell _1$$ℓ1 Regularization -- Image deblurring; Signal processing -- Digital techniques -- Periodicals; Image processing -- Digital techniques -- Periodicals; Digital video -- Periodicals; 621.3822
• DOI: 10.1007/s11760-015-0815-z
• Languages: English
• ISSNs: 1863-1703

Abstract

Abstract We consider the class of subgradient methods for solving minimization of a nonsmooth convex function regularized by the discretized $$\ell _1$$ ℓ 1 norm models arising in image processing. This class of methods is attractive due to its simplicity; however, they are also known to converge quite slowly. In this paper, we present a control subgradient algorithm (CSA) which preserves the computational simplicity of subgradient methods, but with a convergence rate which is proven to be significantly better, both theoretically and practically. Initial promising numerical results for wavelet-based image deblurring demonstrate the capabilities of CSA.