Study of ordinary differential equation approach to l1 minimization

Department of Electrical Engineering, Walchand College of Engineering, Sangli, Maharashtra, India 416 415

Prof. K. S. Mallikarjuna Rao

Industrial Engineering and Operation Research(IEOR) Department, Indian Institute of Technology (IIT) Bombay, Mumbai,India 400 076

Abstract

The main aim of project is to study the algorithm for $l_1$minimization using the ordinary differential equation approach for under-determined linear system along with the underlying mathematics. The minimal $l_1$ norm has pivotal role in compressed sensing and diversified applications in signal and image processing. In this project, I have focused on analysing and understanding the discrete algorithm which has been proposed in [3] by implementing and carrying extensive simulations in MATLAB. The results obtained through simulations are compared with ISTA (4) for further analysis.

Keywords: convex, explicit discretization, implicit discretization, sub-differential, vector norm.

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