Papers › The L1-Potts functional for robust jump-sparse reconstruction
The L1-Potts functional for robust jump-sparse reconstruction
Andreas Weinmann, Martin Storath, Laurent Demaret
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We investigate the non-smooth and non-convex L¹-Potts functional in discrete and continuous time. We show Γ-convergence of discrete L¹-Potts functionals towards their continuous counterpart and obtain a convergence statement for the corresponding minimizers as the discretization gets finer. For the discrete L¹-Potts problem, we introduce an O(n²) time and O(n) space algorithm to compute an exact minimizer. We apply L¹-Potts minimization to the problem of recovering piecewise constant signals from noisy measurements f. It turns out that the L¹-Potts functional has a quite interesting blind deconvolution property. In fact, we show that mildly blurred jump-sparse signals are reconstructed by minimizing the L¹-Potts functional. Furthermore, for strongly blurred signals and known blurring operator, we derive an iterative reconstruction algorithm.
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