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Compressible distributions and Compressed Sensing

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We consider the problem of compressed sensing when the signal is drawn from a statistical signal model and identify probability distributions whose independent and identically distributed (iid) realizations are compressible or incompressible, i.e., can/cannot be approximated as sparse. Within this setting we consider some sample-distortion functions for i.i.d. distributions and derive a simple sample distortion lower bound. Via this we will argue that Lapace distribution associated with the MAP interpretation of the popular L1 reconstruction algorithm is really not compressible. We then extend the compressible model to consider a stochastic multi-resolution image model. Using empirical sample distortion functions we are able to compute an optimal bandwise sampling strategy and to accurately predict the compressed sensing possible performance gains available in compressive imaging.

This talk is part of the Signal Processing and Communications Lab Seminars series.

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