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If you read this morning's entry, you might get a feel that I am little ambivalent about the true interesting nature of a paper entitled Statistical physics-based reconstruction in compressed sensing by Florent Krzakala, Marc Mézard, François Sausset, Yifan Sun, Lenka Zdeborová.Let's put this in perspective, our current understanding so far is that the universal phase transition observed by Donoho and Tanner seems to be seen with all the solvers featured here, that there are many ensembles for which it fits (not just Gaussian, I remember my jaw dropping when Jared Tanner showed it worked for the ensembles of Piotr Indyk, Radu Berinde et al) and that the only way to break it is to now consider structured sparsity as shown by Phil Schniter at the beginning of the week.Romanian physicists actively participated in scientific research of the Institute.
Extraordinary claims require extraordinary proofs which really is the reason why this sorts of discussion is important.
Similarly, sometimes, you are so blinded to some sorts of a truth and are faced with something so different that you can misread entirely what is being said.
However, in practice, we often compress the data soon after sensing, trading off signal representation complexity (bits) for some error (consider JPEG image compression in digital cameras, for example).
Clearly, this is wasteful of valuable sensing resources.
While often expressing specific positions on JINR practical matters, Romania has always recognized the JINR importance for the development of its national centres, for the development of the mutual collaboration.
The two-sided JINR–Romania cooperation reflects the general fact that many scientific problems dealt with at JINR are being solved in close cooperation with research centers of JINR Member States and, vice versa, many problems tackled in the JINR Member States are being solved with assistance of the Joint Institute for Nuclear Research.If this is an improvement, I'd love to hear about it.If it is is not an improvement, one wonders if some of the deeper geometrical findings featured by the Donoho-Tanner phase transition have a bearing on phase transition on real physical systems.Please notice, however, that our axes in the figure you show are not the same as those of Donoho and Tanner.For a signal with N components, we define \rho N as the number of non-zeros in the signal, and \alpha N as the number of measurements.So this morning I made the point that given what I understood about the graphs displayed in the article, it may be at best a small improvement over the Donoho-Tanner phase transition known to hold for not only Gaussian but other types of matrices and for different kinds of solvers, including greedy algorithms and SL0 (that simulate some sorts of L_0 approach).At best is really an overstatement but I was intrigued mostly because of the use of an AMP solver, so I fired off an inquisitive e-mail on the subject to the corresponding author:...Over the past few years, a new theory of "compressive sensing" has begun to emerge, in which the signal is sampled (and simultaneously compressed) at a greatly reduced rate.As the compressive sensing research community continues to expand rapidly, it behooves us to heed Shannon's advice.In most people's mind, the L_1 solvers are really a good proxy to the L_0 solvers since even greedy solvers (the closest we can find to L_0 solvers) seem to provide similar results.Then there are results like the ones of Shrinivas Kudekar and Henry Pfister.