Image restoration by minimizing zero norm of wavelet frame coefficients

In this paper, we propose two algorithms, namely the extrapolated proximal iterative hard thresholding (EPIHT) algorithm and the EPIHT algorithm with line-search, for solving the ℓ 0 -norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of Kurdyka–Łojasiewicz property, we show that the sequences generated by the two algorithms converge to a local minimizer with linear convergence rate. Moreover, extensive numerical experiments on sparse signal reconstruction and wavelet frame based image restoration problems including CT reconstruction, image deblur, demonstrate the improvement of ℓ 0 -norm based regularization models over some prevailing ones, as well as the computational efficiency of the proposed algorithms.