  In this paper we revisit one of the classical problems of compressed sensing.
Namely, we consider linear under-determined systems with sparse solutions. A
substantial success in mathematical characterization of an $\ell_1$
optimization technique typically used for solving such systems has been
achieved during the last decade. Seminal works \cite{CRT,DOnoho06CS} showed
that the $\ell_1$ can recover a so-called linear sparsity (i.e. solve systems
even when the solution has a sparsity linearly proportional to the length of
the unknown vector). Later considerations \cite{DonohoPol,DonohoUnsigned} (as
well as our own ones \cite{StojnicCSetam09,StojnicUpper10}) provided the
precise characterization of this linearity. In this paper we consider the
so-called structured version of the above sparsity driven problem. Namely, we
view a special case of sparse solutions, the so-called block-sparse solutions.
Typically one employs $\ell_2/\ell_1$-optimization as a variant of the standard
$\ell_1$ to handle block-sparse case of sparse solution systems. We considered
systems with block-sparse solutions in a series of work
\cite{StojnicCSetamBlock09,StojnicUpperBlock10,StojnicICASSP09block,StojnicJSTSP09}
where we were able to provide precise performance characterizations if the
$\ell_2/\ell_1$-optimization similar to those obtained for the standard
$\ell_1$ optimization in \cite{StojnicCSetam09,StojnicUpper10}. Here we look at
a similar class of systems where on top of being block-sparse the unknown
vectors are also known to have components of the same sign. In this paper we
slightly adjust $\ell_2/\ell_1$-optimization to account for the known signs and
provide a precise performance characterization of such an adjustment.
