  Compressed sensing (CS) demonstrates that a sparse, or compressible signal
can be acquired using a low rate acquisition process below the Nyquist rate,
which projects the signal onto a small set of vectors incoherent with the
sparsity basis. In this paper, we propose a new framework for compressed
sensing recovery problem using iterative approximation method via L0
minimization. Instead of directly solving the unconstrained L0 norm
optimization problem, we use the linearization and proximal points techniques
to approximate the penalty function at each iteration. The proposed algorithm
is very simple, efficient, and proved to be convergent. Numerical simulation
demonstrates our conclusions and indicates that the algorithm can improve the
reconstruction quality.
