Image restoration by minimizing zero norm of wavelet frame coefficients
Image restoration by minimizing zero norm of wavelet frame coefficients
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DOI：
10.1088/0266-5611/32/11/115004
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发表时间：
2016-11-01
期刊：
影响因子：
2.1
通讯作者：
Zhang, Xue
中科院分区：
文献类型：
--
作者：
Bao, Chenglong;Dong, Bin;Zhang, Xue
本文针对l(0)范数正则化小波帧平衡图像复原问题，提出了外推近端迭代硬阈值（EPIHT）算法和带线搜索的EPIHT算法。在Kurdyka-Lojasiewicz性质的理论框架下，我们证明了两种算法生成的序列收敛到一个具有线性收敛速率的局部极小值。此外，对稀疏信号重建和基于小波帧的图像恢复问题（包括CT重建、图像去模糊）的大量数值实验表明，基于l(0)范数的正则化模型比一些流行的正则化模型有所改进，以及所提算法的计算效率。
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-Lojasiewicz 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.