Simple algorithm for <i>L</i> 1‐norm regularisation‐based compressed sensing and image restoration

Abstract

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.