How can code this problem in CVX(with the help of e.g. SeDuMi) to find S?

1 
Y=AS + N
size of   S:  K × T 
size of  A: M × K
min norm(p,1)
subject to 
[frobenius norm of(Y-AS)]^2≤β^2
p(i)=norm(one row of the S,2)
P=[P(i),....,p(K)];

How can code this problem in CVX(with the help of e.g. SeDuMi) to find S?

2

This looks like a good old fashioned sum-of-norms problem. Then only trick here is that you want the norms of the rows of S, and CVX’s norms function nominally looks at the norms of the columns. An easy way to fix that is to just transpose S.

cvx_begin
    variable S(K,T)
    minimize(sum(norms(S')))
    subject to
        norm(Y-A*S,'fro')<=beta
cvx_end
3

Or alternatively use sum(norms(S,2,2)) ?