Pottslab
Pottslab is a toolbox for jumpsparse reconstruction based on the Potts model.
The Potts model is given by
\[ u^* = \arg\min_u \gamma \ \nabla u\_0 + \ Au  f\_p^p,\] where \(f \) is noisy data and \(A\) a linear operator.
 the regularizing term \(\ \nabla u\_0 \) enforces jumpsparse minimizers,
 \(\gamma > 0\) is an empirical parameter which controls the balance between the regularizing term and the data term \(\ Au  f\_p^p\), (\(p = 1\) or \(p = 2\) )
 also known as piecewise constant MumfordShah model (recently also called l0gradient model)
Application examples
Application to segmentation of vectorvalued images
 Supports segmentation of vectorvalued images (e.g. multispectral images, feature images)
 Linear complexity in number of color channels
 No apriori label selection required
Left: A natural image; Right: Result using Potts model
Application to denoising of jumpsparse/piecewiseconstant signals, or step/changepoint detection
Top: Noisy signal; Bottom: Minimizer of Potts functional (ground truth in red)
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References
 A. Weinmann, M. Storath, L. Demaret. The L1Potts functional for robust jumpsparse reconstruction. SIAM Journal on Numerical Analysis, 53(1):644673, 2015
 M. Storath, A. Weinmann, J. Frikel, M. Unser. Joint image reconstruction and segmentation using the Potts model. Inverse Problems, 31(2):025003, 2015
 A. Weinmann, M. Storath. Iterative Potts and BlakeZisserman minimization for the recovery of functions with discontinuities from indirect measurements. Proceedings of The Royal Society A, 471(2176), 2015
 M. Storath, A. Weinmann. Fast partitioning of vectorvalued images. SIAM Journal on Imaging Sciences, 7(3):18261852, 2014
 M. Storath, A. Weinmann, L. Demaret. Jumpsparse and sparse recovery using Potts functionals. IEEE Transactions on Signal Processing, 62(14):36543666, 2014
Developers

Main developers: Martin Storath, Andreas Weinmann

Contributors: Vasileios Angelopoulos,
Laurent Demaret, Jürgen Frikel, Kilian Hohm, Michael Kaul