A Study of Methods of Choosing the Smoothing Parameter in Image Restoration by Regularization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms
IEEE Transactions on Image Processing
Comparison of Image Restoration Methods for Bioluminescence Imaging
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models
Journal of Mathematical Imaging and Vision
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We consider the problem of restoring astronomical images acquired with charge coupled device cameras. The astronomical object is first blurred by the point spread function of the instrument-atmosphere set. The resulting convolved image is corrupted by a Poissonian noise due to low light intensity, then, a Gaussian white noise is added during the electronic read-out operation. We show first that the split gradient method (SGM) previously proposed can be used to obtain maximum likelihood (ML) iterative algorithms adapted in such noise combinations. However, when ML algorithms are used for image restoration, whatever the noise process is, instabilities due to noise amplification appear when the iteration number increases. To avoid this drawback and to obtain physically meaningful solutions, we introduce various classical penalization-regularization terms to impose a smoothness property on the solution. We show that the SGM can be extended to such penalized ML objective functions, allowing us to obtain new algorithms leading to maximum a posteriori stable solutions. The proposed algorithms are checked on typical astronomical images and the choice of the penalty function is discussed following the kind of object.