Figure 2.

Reconstruction of a piecewise constant signal. Total variation minimization tends to produce transitional points at the jumps and to decrease the contrast. The iterative thresholding approach to the Potts problem gets stuck in a constant result. The result of the thresholding approach to the J-jump sparsity problem is satisfactory. Iterative Potts minimization and the iterative J-jump sparsity algorithm recover the piecewise constant signal almost perfectly. (a) Blurred and noisy data. (b) Iterative thresholding algorithm for (${\mathcal{P}}_{\gamma }$), γ=0.7. (c) Iterative thresholding algorithm for (${\mathcal{S}}_J$), J=8. (d) Total variation solution, λ=1.5. (e) Iterative Potts algorithm for (${\mathcal{P}}_{\gamma }$) (proposed method), γ=0.7. (f) Iterative J-jump sparsity algorithm for (${\mathcal{S}}_J$) (proposed method), J=8. (Online version in colour.)