Xue Zhang (张雪), 上海交通大学


Proximal Iterative Hard Thresholding Methods for Wavelet Frame Based Image Restoration


We consider a proximal iterative hard thresholding algorithms for L_0-norm regularized wavelet frame balanced approach for image restoration, based on recently studied Kurdyka-Lojasiewicz property. In particular, we study the convergence of two algorithms, namely proximal iterative hard thresholding (PIHT) algorithm and extrapolated proximal iterative hard thresholding algorithm for solving this class of problems. We first demonstrate that, given an initial point, the sequence generated by PIHT will converge to a local minimizer of the objective function and the sequential error rate is at o(1/k). Then, we show the convergence of EPIHT by proving that the sequence generated by this algorithm is bounded, and any accumulation point of the sequence is a local minimizer of the objective function. Furthermore, we conduct numerical experiments on compressive sensing sparse signal reconstruction and wavelet frame based image restoration, such as CT reconstruction, image deblurring and parallel MRI image reconstruction, to demonstrate the improvement of L0-norm based regularization models as well as the effectiveness of the proposed algorithms compared some prevailing L1-norm based models and algorithms. We also show in some numerical experiments that the iteration complexity of the proposed EPIHT is lower than that of PIHT.


Likun Hou, Bin Dong, Zuowei Shen and Xiaoqun Zhang

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