An EM algorithm for wavelet-based image restoration
An EM algorithm for wavelet-based image restoration
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DOI：
10.1109/tip.2003.814255
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发表时间：
2003-08-01
影响因子：
10.6
通讯作者：
Nowak, RD
中科院分区：
文献类型：
--
作者：
Figueiredo, MAT;Nowak, RD
本文介绍了一种期望最大化（EM）算法的图像恢复（反卷积）的基础上制定在小波域的惩罚似然。正则化是通过促进重建与低复杂性，表示在小波系数，利用众所周知的稀疏小波表示。以前的工作已经调查了基于小波的恢复，但除了某些特殊情况下，所得到的标准近似解决或需要苛刻的优化方法。本文提出的EM算法将离散小波变换（DWT）提供的有效图像表示与在傅立叶域中获得的卷积算子的对角化相结合。因此，它是一种通用的方法，以小波为基础的图像恢复与标准小波去噪方案或频域反卷积方法的计算复杂度相媲美。该算法在基于快速傅立叶变换（FFT）的E步和基于DWT的M步之间交替，导致每次迭代需要O（N log N）操作的高效迭代过程。研究了算法的收敛性，证明了在较弱的条件下，算法收敛于全局最优恢复。此外，我们的新方法在基准测试中与现有的最佳方法相比具有竞争力，在某些情况下更好。
This paper introduces an expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with low-complexity, expressed in the wavelet coefficients, taking advantage of the well known sparsity of wavelet representations. Previous works have investigated wavelet-based restoration but, except for certain special cases, the resulting criteria are solved approximately or require demanding optimization methods. The EM algorithm herein proposed combines the efficient image representation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier domain. Thus, it is a general-purpose approach to wavelet-based image restoration with computational complexity comparable to that of standard wavelet denoising schemes or of frequency domain deconvolution methods. The algorithm alternates between an E-step based on the fast Fourier transform (FFT) and a DWT-based M-step, resulting in an efficient iterative process requiring O(N log N) operations per iteration. The convergence behavior of the algorithm is investigated, and it is shown that under mild conditions the algorithm converges to a globally optimal restoration. Moreover, our new approach performs competitively with, in some cases better than, the best existing methods in benchmark tests.