l0-l20 Toolbox

l_0-minimization or l_20-minimization solver

Usage

OMP.m

Orthogonal Matching Pursuit (OMP) solver for l_0 minimization problem:

minimize ||x||_1 subject to y = Ax,

function [x, Out] = OMP(A,y,varargin)

Required inputs

A -- an m x n matrix

y -- an m x 1 vector

Optional inputs

'maxIter' -- maximum number of iterations

'StopTolerance' -- stopping tolerance

Outputs

x -- last iterate (hopefully an approximate solution)

Out.iter -- # of iterations taken

GOMP.m

Group Orthogonal Matching Pursuit for l_20 minimization problem:

minimiza ||x||_{2,1} subject to y = Ax,

Required inputs

A -- an m x n matrix

y -- an m x 1 vector

group -- an n-entry vector whose i-th entry is the group number of x_i, the group index should start with 1, end with c, where c is the # of group

Optional inputs

'maxIter' -- maximum number of iterations

'StopTolerance' -- stopping tolerance

Outputs

x -- last iterate (hopefully an approximate solution)

Out.iter -- # of iterations taken

BOMP.m

Block Orthogonal Matching Pursuit for l_20 minimization problem:

minimiza ||x||_{2,1} subject to y = Ax,

Required inputs

A -- an m x n matrix

y -- an m x 1 vector

group -- an n-entry vector whose i-th entry is the group number of x_i

Optional inputs

'maxIter' -- maximum number of iterations

'StopTolerance' -- stopping tolerance

Outputs

x -- last iterate (hopefully an approximate solution)

Out.iter -- # of iterations taken