An EM Algorithm for Wavelet-Based Image Restoration

An EM Algorithm for Wavelet-Based Image Restoration (2002)

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by Mario A.T. Figueiredo , Robert D. Nowak

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Datum	Value	Source
TITLE	An EM Algorithm for Wavelet-Based Image Restoration	user correction - Legacy Corrections
AUTHOR NAME	Mario A.T. Figueiredo	user correction
AUTHOR AFFIL	Institute of Telecommunications and the Department of Electrical and Computer	user correction
AUTHOR ADDR	Engineering, Instituto Superior Tecnico, 1049-001 Lisboa, Portugal (E-mail:	user correction
AUTHOR NAME	Robert D. Nowak	user correction
AUTHOR AFFIL	M. Figueiredo is with the Institute of Telecommunications and the Department of Electrical and Computer	user correction
AUTHOR ADDR	Engineering, Instituto Superior Tecnico, 1049-001 Lisboa, Portugal (E-mail:	user correction
ABSTRACT	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 terms of the wavelet coecients, 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 very demanding optimization methods. The EM algorithm herein proposed combines the efficient image representation oered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier domain. The algorithm alternates between an E-step based on the fast Fourier transform (FFT) and a DWT-based M-step, resulting in an ecient iterative process requiring O(N log N) operations per iteration. Thus, it is the rst image restoration algorithm that optimizes a wavelet-based penalized likelihood criterion and has computational complexity comparable to that of standard wavelet denoising or frequency domain deconvolution methods. 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 outperforms several of the best existing methods in benchmark tests, and in some cases is also much less computationally demanding.	user correction
YEAR	2002	user correction - Legacy Corrections
CITATIONS	32 found	ParsCit 1.0