29 May 2013 Multichannel blind deconvolution using low rank recovery
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We introduce a new algorithm for multichannel blind deconvolution. Given the outputs of K linear time- invariant channels driven by a common source, we wish to recover their impulse responses without knowledge of the source signal. Abstractly, this problem amounts to finding a solution to an overdetermined system of quadratic equations. We show how we can recast the problem as solving a system of underdetermined linear equations with a rank constraint. Recent results in the area of low rank recovery have shown that there are effective convex relaxations to problems of this type that are also scalable computationally, allowing us to recover 100s of channel responses after a moderate observation time. We illustrate the effectiveness of our methodology with a numerical simulation of a passive noise imaging" experiment.
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Justin Romberg, Justin Romberg, Ning Tian, Ning Tian, Karim Sabra, Karim Sabra, "Multichannel blind deconvolution using low rank recovery", Proc. SPIE 8750, Independent Component Analyses, Compressive Sampling, Wavelets, Neural Net, Biosystems, and Nanoengineering XI, 87500E (29 May 2013); doi: 10.1117/12.2018550; https://doi.org/10.1117/12.2018550

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