Stochastic nonlinear image restoration using the wavelet transform

The dominant methodology for image restoration is to stabilize the problem by including a roughness penalty in addition to faithfulness to the data. Among various choices, concave stabilizers stand out for their boundary detection capabilities, but the resulting cost function to be minimized is gene...

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Bibliographic Details
Published in:IEEE transactions on image processing 2003-08, Vol.12 (8), p.890-905
Main Authors: Robini, M.C., Magnin, I.E.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Computational modeling
Convergence
Cost function
Discontinuity
Discrete wavelet transforms
Exact sciences and technology
Frequency
Image processing
Image restoration
Information, signal and communications theory
Mathematical models
Pattern recognition
Signal processing
Simulated annealing
Stochastic processes
Stochasticity
Studies
Telecommunications and information theory
Wavelet domain
Wavelet transforms
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Summary:The dominant methodology for image restoration is to stabilize the problem by including a roughness penalty in addition to faithfulness to the data. Among various choices, concave stabilizers stand out for their boundary detection capabilities, but the resulting cost function to be minimized is generally multimodal. Although simulated annealing is theoretically optimal to take up this challenge, standard stochastic algorithms suffer from two drawbacks: i) practical convergence difficulties are encountered with second-order prior models and ii) it remains computationally demanding to favor the formation of smooth contour lines by taking the discontinuity field explicitly into account. This work shows that both weaknesses can be overcome in a multiresolution framework by means of the 2-D discrete wavelet transform (DWT). We first propose to improve convergence toward global minima by single-site updating on the wavelet domain. For this purpose, a new restricted DWT space is introduced and a theoretically sound updating mechanism is constructed on this subspace. Next, we suggest to incorporate the smoothness of the discontinuity field via an additional penalty term defined on the high frequency subbands. The resulting increase in complexity is small and the approach requires the specification of a unique extra parameter for which an explicit selection formula is derived.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2003.812330