If you recall, I am a firm believer of phase transition curves as a means of actually judging reconstruction algorithms against others. This is one of the reasons, I mentioned that there was a problem with pre-publication peer-review.

I asked Thomas Arildsen about the availability of the enhanced version of SL0 they recently featured (see below), here is what he answered:

Hi Igor,

The paper is on its way to ICASSP in a shorter version also containing a link to the simulation framework. The ArXiv paper will be updated soon. The software can be found in our university's repository here: http://vbn.aau.dk/en/publications/compressive-sensing-simulation-framework%28d0595c3f-e050-48ce-8f47-3dc7f76620f5%29.html. It also has a repository on Bitbucket, allowing people to branch it etc.: https://bitbucket.org/ppeder08/cssf...Best,Thomas

Here is the new version of the paper: Improving Smoothed l0 Norm in Compressive Sensing Using Adaptive Parameter Selection by Chtistian Schou Oxvig, Patrick Steffen Pedersen, Thomas Arildsen, Torben Larsen. The abstract reads:

Signal reconstruction in compressive sensing involves finding a sparse solution that satisfies a set of linear constraints. Several approaches to this problem have been considered in existing reconstruction algorithms. They each provide a trade-off between reconstruction capabilities and required computation time. In an attempt to push the limits for this trade-off, we consider a smoothed l0 norm (SL0) algorithm in a noiseless setup. We argue that using a set of carefully chosen parameters in our proposed adaptive SL0 algorithm may result in significantly better reconstruction capabilities in terms of phase transition while retaining the same required computation time as existing SL0 algorithms. A large set of simulations further support this claim. Simulations even reveal that the theoretical l1 curve may be surpassed in major parts of the phase space.

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