See also

[1] Artifact Free Signal Denoising With Wavelets
[2] Reconstruction of wavelet coefficients using total variation minimization

Those papers state the same subject but differ in the following way :
- [1] is a short paper (proceedings of ICASSP'01). The algorithm is presented and experiments are reported in an abridged mathematical framework.
- [2] is a long paper where the mathematical framework is fully developed. In particular, the convergence of the algorithm is established.