Sparse MMV representation problem

1

hello everybody,

I want to solve sparse representation problem with CVX toolbox. I have a NxL matrix X. matrix X have only few nonzero rows. I have system of equations Y=AX. Y is MxL matrix of measurements (M<N). Matrix A is sensing matrix of size MxN. I want to recover X from measurements Y. therefore, I have to solve the following optimization problem.(Y and A are known)

min Relax(X)
subject to Y=A*X

Relax(.) is a function that applies norm 1 to the vector t. (N*1)vector t consists of the norm 2 of each rows of matrix X! i.e Relax(X)= norm1(t) and t(i)=norm2(X(i,:))

I cant transform my objective function into a language that CVX can understand and solve.
please tell me how I should change the problem objective and constraints that CVX could solve it.

2

Since the elements of t are positive, the 1-norm is nothing more than the sum. Just try replacing that 1-norm with a sum, and see if that fixes it.