Image Restoration with Compound Regularization Using a Bregman Iterative Algorithm

Abstract : Some imaging inverse problems may require the solution to simultaneously exhibit properties that are not enforceable by a single regularizer. One way to attain this goal is to use a linear combinations of regu- larizers, thus encouraging the solution to simultaneously exhibit the characteristics enforced by each individual regularizer. In this paper, we address the optimization problem resulting from this type of compound regular- ization using the split Bregman iterative method. The resulting algorithm only requires the ability to e±ciently compute the denoising operator associated to each in- volved regularizer. Convergence is guaranteed by the theory behind the Bregman iterative approach to solving constrained optimization problems. In experiments with images that are simultaneously sparse and piece-wise smooth, the proposed algorithm successfully solves the deconvolution problem with a compound regularizer that is the linear combination of the 1 and total variation (TV) regularizers. The lowest MSE obtained with the (1+TV) regularizer is lower than that obtained with TV or `1 alone, for any value of the corresponding regularization parameters.
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https://hal.inria.fr/inria-00369598
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Submitted on : Friday, March 20, 2009 - 2:25:56 PM
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• HAL Id : inria-00369598, version 1

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Manya V. Afonso, José M. Bioucas-Dias, Mario A. T. Figueiredo. Image Restoration with Compound Regularization Using a Bregman Iterative Algorithm. SPARS'09 - Signal Processing with Adaptive Sparse Structured Representations, Inria Rennes - Bretagne Atlantique, Apr 2009, Saint Malo, France. ⟨inria-00369598⟩

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