Sparse Vector Distributions and Recovery from Compressed Sensing

It is well known that the performance of sparse vector recovery algorithms from compressive measurements can depend on the distribution underlying the non-zero elements of a sparse vector. However, the extent of these effects has yet to be explored, and formally presented. In this paper, I empirically investigate this dependence for seven distributions and fifteen recovery algorithms. The two morals of this work are: 1) any judgement of the recovery performance of one algorithm over that of another must be prefaced by the conditions for which this is observed to be true, including sparse vector distributions, and the criterion for exact recovery; and 2) a recovery algorithm must be selected carefully based on what distribution one expects to underlie the sensed sparse signal.Comment: Originally submitted to IEEE Signal Processing Letters in March 2011, but rejected June 2011. Revised, expanded, and submitted July 2011 to EURASIP Journal special issue on sparse signal processin

The GTZAN dataset: Its contents, its faults, their effects on evaluation, and its future use

The GTZAN dataset appears in at least 100 published works, and is the most-used public dataset for evaluation in machine listening research for music genre recognition (MGR). Our recent work, however, shows GTZAN has several faults (repetitions, mislabelings, and distortions), which challenge the interpretability of any result derived using it. In this article, we disprove the claims that all MGR systems are affected in the same ways by these faults, and that the performances of MGR systems in GTZAN are still meaningfully comparable since they all face the same faults. We identify and analyze the contents of GTZAN, and provide a catalog of its faults. We review how GTZAN has been used in MGR research, and find few indications that its faults have been known and considered. Finally, we rigorously study the effects of its faults on evaluating five different MGR systems. The lesson is not to banish GTZAN, but to use it with consideration of its contents.Comment: 29 pages, 7 figures, 6 tables, 128 reference

When 'exact recovery' is exact recovery in compressed sensing simulation

In a simulation of compressed sensing (CS), one must test whether the recovered solution \vax is the true solution \vx, i.e., ``exact recovery.''Most CS simulations employ one of two criteria: 1) the recovered support is the true support; or 2) the normalized squared error is less than $\epsilon^2$. We analyze these exact recovery criteria independent of any recovery algorithm, but with respect to signal distributions that are often used in CS simulations. That is, given a pair (\vax,\vx), when does ``exact recovery'' occur with respect to only one or both of these criteria for a given distribution of \vx? We show that, in a best case scenario, $\epsilon^2$ sets a maximum allowed missed detection ratein a majority sense