Recovery of Discontinuous Signals Using Group Sparse Higher Degree Total Variation


We tend to introduce a family of novel regularization penalties to enable the recovery of discrete discontinuous piecewise polynomial signals from undersampled or degraded linear measurements. The penalties promote the group sparsity of the signal analyzed below a $n$th order derivative. We have a tendency to introduce an efficient alternating minimization algorithm to unravel linear inverse problems regularized with the proposed penalties. Our experiments show that promoting cluster sparsity of derivatives enhances the compressed sensing recovery of discontinuous piecewise linear signals compared with an unstructured sparse prior. We have a tendency to also propose an extension to 2-D, which can be viewed as a group sparse version of upper degree total variation, and illustrate its effectiveness in denoising experiments.

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