Unified optimization framework for L2, L1, and/or L0 constrained image reconstruction

Abstract

In this paper, we propose a unified optimization framework for L2, L1, and/or L0 constrained image reconstruction. First, we generalize cost functions for image reconstruction, which consist of a fidelity term with L2 norm and constraint terms with L2, L1, and/or L0 norms. This generalized cost function covers many types of existing cost functions for image reconstruction. Then, we show that this generalized cost function can be optimized by the alternating direction method of multipliers (ADMM). The ADMM is a well-known iterative optimization approach for convex problems. Experimental results demonstrate that the proposed unified optimization framework is applicable to a wide range of applications.