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November 3 2011 5 03 /11 /November /2011 09:03

This page is dedicated to start discussions about the article "Sparse Recovery with Brownian Sensing". Feel free to post any comment, sugggestion, question, correction, extension... I will enjoy discussing this with you.

  • Abstract:

" We consider the problem of recovering the parameter α ∈ R^K of a sparse function f (i.e. the number of non-zero entries of α is small compared to the number K of features) given noisy evaluations of f at a set of well-chosen sampling points. We introduce an additional randomization process, called Brownian sensing, based on the computation of stochastic integrals, which produces a Gaussian sensing matrix, for which good recovery properties are proven, independently on the number of sampling points N , even when the features are arbitrarily non-orthogonal. Under the assumption that f is Hölder continuous with exponent at least 1/2, we provide an estimate â of the parameter such that ||α − â||_2 = O( ||η||_2/ sqrt(N)), where η is the observation noise. The method uses a set of sampling points uniformly distributed along a one-dimensional curve selected according to the features. We report numerical experiments illustrating our method."

  • Future work:

Find a systematic way to choose an appropriate curve to sample along.

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