Open AccessSimple algorithm for L 1‐norm regularisation‐based compressed sensing and image restoration
Author(s) -
Qin Shun
Publication year - 2020
Publication title -
iet image processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.401
H-Index - 45
eISSN - 1751-9667
pISSN - 1751-9659
DOI - 10.1049/iet-ipr.2020.0194
Subject(s) - norm (philosophy) , compressed sensing , algorithm , mathematical optimization , image restoration , computer science , discontinuity (linguistics) , simple (philosophy) , image (mathematics) , mathematics , image processing , artificial intelligence , philosophy , epistemology , political science , law , mathematical analysis
L 1‐norm regularisation plays an important role in compressed sensing reconstruction and image restoration. However, the discontinuity of L 1‐norm function makes solving the involved optimisation problem very challenging with traditional optimisation methods. In this article, a simple but efficient algorithm is proposed for the L 1‐norm regularised compressed sensing and image restoration problem. In the proposed algorithm, the L 1‐norm regularised optimisation problem is converted to a non‐linear optimisation problem with L 1‐norm approximation by a smoothening function, which then can be solved by existing powerful non‐linear optimisation methods. The simulation results show that the proposed algorithm is more efficient and results in a higher accurate solution. Compared to existing methods, the proposed algorithm is very easy to implement and promising for applications in medical and biological imaging.