The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
An EM algorithm for wavelet-based image restoration
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 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.
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Citations
Cites
Maximum Likelihood from Incomplete Data Via the EM Algorithm
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NTIRE 2017 Challenge on Single Image Super-Resolution: Dataset and Study
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Self-citationA Fast Total Variation Minimization Method for Image Restoration
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Fast 3D reconstruction method for differential phase contrast X-ray CT
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Metadata
- Authors
- Figueiredo, M. A. T., & Nowak, R. D.
- Venue
- IEEE Transactions on Image Processing
- Published
- 2003-08
- Volume
- 12
- Issue
- 8
- Pages
- 906-916
- ISSN
- 1057-7149 (ISSN-L)
- OpenAlex
- W2110505738
- Cited by
- 1,219
- References
- 1
- FWCI
- 19.67
- Type
- journal article
- Language
- en
- Open access
- closed
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