Title :
Convergence Analysis of the FOCUSS Algorithm
Author :
Kan Xie ; Zhaoshui He ; Cichocki, Andrzej
Author_Institution :
Sch. of Autom., Guangdong Univ. of Technol., Guangzhou, China
Abstract :
Focal Underdetermined System Solver (FOCUSS) is a powerful and easy to implement tool for basis selection and inverse problems. One of the fundamental problems regarding this method is its convergence, which remains unsolved until now. We investigate the convergence of the FOCUSS algorithm in this paper. We first give a rigorous derivation for the FOCUSS algorithm by exploiting the auxiliary function. Following this, we further prove its convergence by stability analysis.
Keywords :
convergence; mathematics computing; FOCUSS algorithm; auxiliary function; basis selection; convergence analysis; focal underdetermined system solver; inverse problems; stability analysis; Algorithm design and analysis; Convergence; Educational institutions; Learning systems; Optimization; Signal processing algorithms; Vectors; Auxiliary function; Focal Underdetermined System Solver (FOCUSS) algorithm; convergence; global convergence theorem; global convergence theorem.;
Journal_Title :
Neural Networks and Learning Systems, IEEE Transactions on
DOI :
10.1109/TNNLS.2014.2323985
