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W2099088889 abstract "It is well known that compressed sensing problems reduce to solving large under-determined systems of equations. If we choose the elements of the compressed measurement matrix according to some appropriate probability distribution and if the signal is sparse enough then the l 1 -optimization can recover it with overwhelming probability (see, e.g. [5], [9], [10]). In fact, [5], [9], [10] establish (in a statistical context) that if the number of measurements is proportional to the length of the signal then there is a sparsity of the unknown signal proportional to its length for which the success of the l 1 -optimization is guaranteed. In this paper we consider a modification of this standard setup, namely the case of the so-called approximately sparse unknown signals [7], [27]. We determine sharp lower bounds on the values of allowable approximate sparsity for any given number (proportional to the length of the unknown signal) of measurements. We introduce a novel, very simple technique which provides very good values for proportionality constants." @default.
W2099088889 created "2016-06-24" @default.
W2099088889 creator A5065505687 @default.
W2099088889 date "2009-06-01" @default.
W2099088889 modified "2023-10-14" @default.
W2099088889 title "Explicit thresholds for approximately sparse compressed sensing via ℓ<inf>1</inf>-optimization" @default.
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W2099088889 doi "https://doi.org/10.1109/isit.2009.5205715" @default.
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