Abstract
Satellite images can be corrupted by an optical blur and electronic noise. Blurring is modeled by convolution, with a known linear operator H, and the noise is supposed to be additive, white and Gaussian, with a known variance. The recovery problem is ill-posed and therefore must be regularized. Herein, we use a regularization model which introduces a ϕ-function, avoiding noise amplification while preserving image discontinuities (i.e. edges) of the restored image. This model involves two hyperparameters. Our goal is to estimate the optimal parameters in order to reconstruct images automatically.
In this paper, we propose to use the Maximum Likelihood estimator, applied to the observed image. To evaluate the derivatives of this criterion, we must estimate expectations by sampling (samples are extracted from a Markov chain). These samples are images whose probability takes into account the convolution operator. Thus, it is very difficult to obtain them directly by using a standard sampler. We have developed a new algorithm for sampling, using an auxiliary variable based on Geman-Yang algorithm, and a cosine transform. We also present a new reconstruction method based on this sampling algorithm. We detail the Markov Chain Monte Carlo Maximum Likelihood (MCMCML) algorithm which ables to simultaneously estimate the parameters, and to reconstruct the eled by convolution, with a known linear operator corrupted image.
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Jalobeanu, A., Blanc-Féraud, L., Zerubia, J. (1999). Hyperparameter Estimation for Satellite Image Restoration by a MCMCML Method. In: Hancock, E.R., Pelillo, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 1999. Lecture Notes in Computer Science, vol 1654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48432-9_9
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DOI: https://doi.org/10.1007/3-540-48432-9_9
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