Abstract
The ℓ0 “norm” regularized variational model is widely used in signal/image restoration. It is suitable for sparsity based regularization model design. This paper proposes a wavelet frame based Poisson noise removal model is proposed and the alternating direction method of multipliers (ADMM) is adopted to solve the corresponding optimization problem. Due to the nonconvex and noncontinuous property of the objective function with ℓ0 term, plenty of results in the literature cannot be directly applied to verifying the convergence of this ADMM based algorithm. We established the convergence property of the proposed algorithm for Poisson noise image restoration and reconstruction. This theoretical foundation is valuable to guarantee the stability performance of the algorithm in numerical simulation. Numerical experiments on different image processing tasks, such as gray image deblurring, CT image reconstruction and graph data denoising, also verified the effectiveness of this newly proposed nonconvex and nonsmooth model. Moreover all the results are possible to be extended to more general nonconvex noncontinuous optimization problem.
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