1 June 1997 Regularized image restoration in multiresolution spaces
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Optical Engineering, 36(6), (1997). doi:10.1117/1.601368
Abstract
A regularized image restoration model in multiresolution spaces is proposed. The image is transformed in the wavelet domain, and the restored image is found as the solution of a constrained meansquared- error optimization. The image energies in the subbands of a wavelet decomposition of the image set the constraints of the optimization problem. A closed-form relationship of the image energy in the wavelet channels is derived. The restored image is obtained by solving iteratively the equation that sets the derivative of the error norm equal to zero. The Lagrange multiplier that corresponds to a subband is given as a function of the noise and the image energy in the subband. Results of numerical experiments on multiresolution image restoration using one and nine constraints, respectively, are presented and compared against image restoration results obtained from a conventional regularized image restoration algorithm that is based on generalized cross validation and uses the Laplacian operator as the smoothing filter. The experimental results obtained by the proposed method indicate that the restored image is closer to the original if one solves the restoration problem using more than one smoothing filter.
Ioannis M. Stephanakis, "Regularized image restoration in multiresolution spaces," Optical Engineering 36(6), (1 June 1997). http://dx.doi.org/10.1117/1.601368
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KEYWORDS
Image restoration

Wavelets

Image filtering

Signal to noise ratio

Optical engineering

Smoothing

Autoregressive models

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