Minimizing L1 over L2 norms on the gradient. (1st June 2022)

• Record Type: Journal Article
• Authors: Wang, Chao; Tao, Min; Chuah, Chen-Nee; Nagy, James; Lou, Yifei
• Is Part Of: Inverse problems. Volume 38:Number 6(2022)
• Publication Date: 2022-06-01
• Subjects: L1/L2 minimization -- piecewise constant images -- alternating direction method of multipliers -- global convergence; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac64fb
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this paper, we study the L 1 / L 2 minimization on the gradient for imaging applications. Several recent works have demonstrated that L 1 / L 2 is better than the L 1 norm when approximating the L 0 norm to promote sparsity. Consequently, we postulate that applying L 1 / L 2 on the gradient is better than the classic total variation (the L 1 norm on the gradient) to enforce the sparsity of the image gradient. Numerically, we design a specific splitting scheme, under which we can prove subsequential and global convergence for the alternating direction method of multipliers (ADMM) under certain conditions. Experimentally, we demonstrate visible improvements of L 1 / L 2 over L 1 and other nonconvex regularizations for image recovery from low-frequency measurements and two medical applications of magnetic resonance imaging and computed tomography reconstruction. Finally, we reveal some empirical evidence on the superiority of L 1 / L 2 over L 1 when recovering piecewise constant signals from low-frequency measurements to shed light on future works.