Wavelet frame based Poisson noise removal and image deblurring

The recovery of sparse signal from noisy data arises in various application fields. One widely known approach for Gaussian noise image restoration with wavelet frame based sparse representation is the l0 norm regularized variational model. In this paper, the sparse and nonconvex noncontinuous l0 norm regularized model is proposed to recover the Poisson noise and blurred image. Then the resulted optimization problem is solved by the alternating direction method of multipliers(ADMM) scheme and two different approaches are adopted to solve the ADMM scheme in the numerical experiments. Extensive simulation results verify the convergence of the proposed algorithm and indicate that the proposed l0 norm based nonconvex model is efficient and comparable with some state-of-the-art approaches.