Majorization-Minimization Algorithms for Wavelet-Based Image Restoration

Standard formulations of image/signal deconvolution under wavelet-based priors/regularizers lead to very high-dimensional optimization problems involving the following difficulties: the non-Gaussian (heavy-tailed) wavelet priors lead to objective functions which are nonquadratic, usually nondifferen...

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Vydáno v:IEEE transactions on image processing Ročník 16; číslo 12; s. 2980 - 2991
Hlavní autoři: Figueiredo, M.A.T., Bioucas-Dias, J.M., Nowak, R.D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York, NY IEEE 01.12.2007
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Algorithms
Applied sciences
Computational efficiency
Convergence of numerical methods
Convolution
Deconvolution
Detection, estimation, filtering, equalization, prediction
Exact sciences and technology
Image deconvolution
Image denoising
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Image restoration
Information Storage and Retrieval - methods
Information, signal and communications theory
Iterative algorithms
majorization-minimization (MM) algorithms
Materials handling
Mathematical models
Miscellaneous
Noise reduction
Numerical Analysis, Computer-Assisted
Optimization
Optimization methods
Pattern Recognition, Automated - methods
regularization
Reproducibility of Results
Sensitivity and Specificity
Signal and communications theory
Signal processing
Signal Processing, Computer-Assisted
Signal, noise
Studies
Telecommunications
Telecommunications and information theory
wavelets
Image deconvolution
image restoration
optimization
majorization-minimization (MM) algorithms
regularization
wavelets
Performance evaluation
Singularity
Separability
Image processing
Noise reduction
Iterative method
Image restoration
Algorithm
Optimization
Convolution
Wavelet transformation
Least squares method
Signal processing
Objective function
Numerical convergence
ISSN:1057-7149, 1941-0042
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Shrnutí:Standard formulations of image/signal deconvolution under wavelet-based priors/regularizers lead to very high-dimensional optimization problems involving the following difficulties: the non-Gaussian (heavy-tailed) wavelet priors lead to objective functions which are nonquadratic, usually nondifferentiable, and sometimes even nonconvex; the presence of the convolution operator destroys the separability which underlies the simplicity of wavelet-based denoising. This paper presents a unified view of several recently proposed algorithms for handling this class of optimization problems, placing them in a common majorization-minimization (MM) framework. One of the classes of algorithms considered (when using quadratic bounds on nondifferentiable log-priors) shares the infamous ¿singularity issue¿ (SI) of ¿iteratively re weighted least squares¿ (IRLS) algorithms: the possibility of having to handle infinite weights, which may cause both numerical and convergence issues. In this paper, we prove several new results which strongly support the claim that the SI does not compromise the usefulness of this class of algorithms. Exploiting the unified MM perspective, we introduce a new algorithm, resulting from using bounds for nonconvex regularizers; the experiments confirm the superior performance of this method, when compared to the one based on quadratic majorization. Finally, an experimental comparison of the several algorithms, reveals their relative merits for different standard types of scenarios.
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ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2007.909318