Minimizing L (1) over L (2) norms on the gradient

Wang, Chao1,2; Tao, Min3; Chuah, Chen-Nee2; Nagy, James4; Lou, Yifei5

2022-06-01

10.1088/1361-6420/ac64fb

INVERSE PROBLEMS   影响因子和分区

0266-5611

1361-6420

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.

L (1) L (2) minimization piecewise constant images alternating direction method of multipliers global convergence

SCI ; EI

英语

第一

HKRGC[CityU11301120] ; NSF CCF HDR TRIPODS Grant[1934568] ; Natural Science Foundation of China[11971228] ; Jiangsu Provincial National Natural Science Foundation of China[BK20181257] ; NSF["DMS-1819042","CAREER 1846690"] ; NIH[5R01CA181171-04]

Mathematics ; Physics

Mathematics, Applied ; Physics, Mathematical

WOS:000792472200001

IOP Publishing Ltd

20222112136879

Computerized tomography ; Frequency multiplying circuits ; Image enhancement ; Magnetic resonance imaging ; Medical applications ; Medical imaging

Biomedical Engineering:461.1 ; Magnetism: Basic Concepts and Phenomena:701.2 ; Electronic Circuits Other Than Amplifiers, Oscillators, Modulators, Limiters, Discriminators or Mixers:713.5 ; Computer Applications:723.5 ; Imaging Techniques:746

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Dept Stat & Data Sci, Shenzhen 518055, Peoples R China
2.Univ Calif Davis, Dept Elect & Comp Engn, Davis, CA 95616 USA
3.Nanjing Univ, Dept Math, Natl Key Lab Novel Software Technol, Nanjing 210093, Peoples R China
4.Emory Univ, Dept Math, Atlanta, GA 30322 USA
5.Univ Texas Dallas, Dept Math Sci, Richardson, TX 75080 USA

Wang, Chao,Tao, Min,Chuah, Chen-Nee,et al. Minimizing L (1) over L (2) norms on the gradient[J]. INVERSE PROBLEMS,2022,38(6).

Wang, Chao,Tao, Min,Chuah, Chen-Nee,Nagy, James,&Lou, Yifei.(2022).Minimizing L (1) over L (2) norms on the gradient.INVERSE PROBLEMS,38(6).

Wang, Chao,et al."Minimizing L (1) over L (2) norms on the gradient".INVERSE PROBLEMS 38.6(2022).