  When the signal does not have a sparse structure but has sparsity under a
certain transformation domain, Nam et al. \cite{NS} introduced the cosparse
analysis model, which provides a dual perspective on the sparse representation
model. This paper mainly discusses the error estimation of non-convex
$\ell_p(0<p<1)$ relaxation cosparse optimization model with noise condition.
Compared with the existing literature, under the same conditions, the value
range of the $\Omega$-RIP constant $\delta_{7s}$ given in this paper is wider.
When $p=0.5$ and $\delta_{7s}=0.5$, the error constants $C_0$ and $C_1$ in this
paper are better than those corresponding results in the literature
\cite{Cand,LiSong1}. Moreover, when $0<p<1$, the error results of the
non-convex relaxation method are significantly smaller than those of the convex
relaxation method. The experimental results verify the correctness of the
theoretical analysis and illustrate that the $\ell_p(0<p<1)$ method can provide
robust reconstruction for cosparse optimization problems.
