267 research outputs found

    Uncertainty Relations and Sparse Signal Recovery for Pairs of General Signal Sets

    Full text link
    We present an uncertainty relation for the representation of signals in two different general (possibly redundant or incomplete) signal sets. This uncertainty relation is relevant for the analysis of signals containing two distinct features each of which can be described sparsely in a suitable general signal set. Furthermore, the new uncertainty relation is shown to lead to improved sparsity thresholds for recovery of signals that are sparse in general dictionaries. Specifically, our results improve on the well-known (1+1/d)/2(1+1/d)/2-threshold for dictionaries with coherence dd by up to a factor of two. Furthermore, we provide probabilistic recovery guarantees for pairs of general dictionaries that also allow us to understand which parts of a general dictionary one needs to randomize over to "weed out" the sparsity patterns that prohibit breaking the square-root bottleneck.Comment: submitted to IEEE Trans. Inf. Theor

    Almost Lossless Analog Signal Separation

    Full text link
    We propose an information-theoretic framework for analog signal separation. Specifically, we consider the problem of recovering two analog signals from a noiseless sum of linear measurements of the signals. Our framework is inspired by the groundbreaking work of Wu and Verd\'u (2010) on almost lossless analog compression. The main results of the present paper are a general achievability bound for the compression rate in the analog signal separation problem, an exact expression for the optimal compression rate in the case of signals that have mixed discrete-continuous distributions, and a new technique for showing that the intersection of generic subspaces with subsets of sufficiently small Minkowski dimension is empty. This technique can also be applied to obtain a simplified proof of a key result in Wu and Verd\'u (2010).Comment: To be presented at IEEE Int. Symp. Inf. Theory 2013, Istanbul, Turke

    Recovery of Sparsely Corrupted Signals

    Full text link
    • …
    corecore