Pottslab

Pottslab is a toolbox for jump-sparse 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.

Application examples

Segmentation of vector-valued images


Left: A natural image; Right: Result using Potts model


Texture segmentation using highdimensional curvelet-based feature vectors

Joint image reconstruction and segmentation


Left: Shepp-Logan phantom; Center: Filtered backprojection from 7 angular projections; Right: Joint reconstruction and segmentation using the Potts model from 7 angular projections


Left: Blurred noisy image; Right: Joint deconvolution and segmentation using the Potts model

Denoising of jump-sparse/piecewise-constant signals, or step detection/changepoint detection


Top: Noisy signal; Bottom: Minimizer of Potts functional (ground truth in red)

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References

Developers