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spg_mmv

SPG_MMV Solve multi-measurement basis pursuit denoise (BPDN)

Calling Sequence

[x, r, g, info] = spg_mmv(A0, B0, sigma, options)

Parameters

A0 :

(IN) is an m-by-n matrix, explicit or an operator.

B0 :

(IN) is an m-by-g matrix.

sigma :

(IN) is a nonnegative scalar (noise); see (BPDN)

options :

(IN) is a structure of options from spgSetParms

x :

(OUT) is a solution of the problem

r :

(OUT) is the residual, r = b - Ax

g :

(OUT) is the gradient, g = -A'r

info :

(OUT) is a structure with output information

Description

(BPDN) minimize ||X||_1,2 subject to ||A X - B||_2,2 <= SIGMA,

where A is an M-by-N matrix, B is an M-by-G matrix, and SIGMA is a nonnegative scalar. In all cases below, A can be an explicit M-by-N matrix or matrix-like object for which the operations A*x and A'*y are defined (i.e., matrix-vector multiplication with A and its adjoint.)

Also, A can be a function handle that points to a function with the signature

v = A(w,mode) which returns v = A *w if mode == 1; v = A'*w if mode == 2.

X = SPG_MMV(A,B,SIGMA) solves the BPDN problem. If SIGMA=0 or SIGMA=[], then the basis pursuit (BP) problem is solved; i.e., the constraints in the BPDN problem are taken as AX=B.

X = SPG_MMV(A,B,SIGMA,OPTIONS) specifies options that are set using SPGSETPARMS.

[X,R,G,INFO] = SPG_BPDN(A,B,SIGMA,OPTIONS) additionally returns the residual R = B - A*X, the objective gradient G = A'*R, and an INFO structure. (See SPGL1 for a description of this last output argument.)

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