Method of Lagrange Multipliers for Normalized Zero Norm Minimization

Abstract

We present a normalization of the p-norm. A compressive sensing criterion is proposed using the normalized zero norm. Based on the method of Lagrange multipliers, we derive the solution of the proposed optimization framework. It turns out that the new solution is a limit case of the least fractional norm solution for p=0, where its fixed-point iteration algorithm can readily follow an existing algorithm. The derivation of the minimal normalized zero norm solution herein gives a relation in the aspect of Lagrange multiplier method to existing works that invoke least fractional norm and least pseudo zero norm criteria. © 2022 Bamrung Tausiesakul.