An underdetermined multi-measurement vector linear regression problem is considered where the parameter matrix is row-sparse and where an additional constraint fixes the number of nonzero elements in the active rows. Even if this additional constraint offers side structure information that could be exploited to improve the estimation accuracy, it is highly nonconvex and must be dealt with with caution. A detection algorithm is proposed that capitalizes on compressed sensing results and on the generalized distributive law (message passing on factor graphs).