  In this paper we study the $\ell_p$-analysis optimization ($0<p\leq1$)
problem for cosparse signal recovery. We establish a bound for recovery error
via the restricted $p$-isometry property over any subspace. We further prove
that the nonconvex $\ell_q$-analysis optimization can do recovery with a lower
sample complexity and in a wider range of cosparsity than its convex
counterpart. In addition, we develop an iteratively reweighted method to solve
the optimization problem under a variational framework. Empirical results of
preliminary computational experiments illustrate that the nonconvex method
outperforms its convex counterpart.
