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- W1550626790 abstract "In this paper we consider under-determined systems of linear equations that have sparse solutions. This subject attracted enormous amount of interest in recent years primarily due to influential works cite{CRT,DonohoPol}. In a statistical context it was rigorously established for the first time in cite{CRT,DonohoPol} that if the number of equations is smaller than but still linearly proportional to the number of unknowns then a sparse vector of sparsity also linearly proportional to the number of unknowns can be recovered through a polynomial $ell_1$-optimization algorithm (of course, this assuming that such a sparse solution vector exists). Moreover, the geometric approach of cite{DonohoPol} produced the exact values for the proportionalities in question. In our recent work cite{StojnicCSetam09} we introduced an alternative statistical approach that produced attainable values of the proportionalities. Those happened to be in an excellent numerical agreement with the ones of cite{DonohoPol}. In this paper we give a rigorous analytical confirmation that the results of cite{StojnicCSetam09} indeed match those from cite{DonohoPol}." @default.
- W1550626790 created "2016-06-24" @default.
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- W1550626790 date "2013-03-29" @default.
- W1550626790 modified "2023-09-27" @default.
- W1550626790 title "A rigorous geometry-probability equivalence in characterization of $ell_1$-optimization" @default.
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