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• W2140867429 abstract "We consider the problem of recovering two unknown vectors, w and x, of length L from their circular convolution. We make the structural assumption that the two vectors are members of known subspaces, one with dimension N and the other with dimension K. Although the observed convolution is nonlinear in both w and x, it is linear in the rank-1 matrix formed by their outer product wx*. This observation allows us to recast the deconvolution problem as low-rank matrix recovery problem from linear measurements, whose natural convex relaxation is a nuclear norm minimization program. We prove the effectiveness of this relaxation by showing that, for “generic” signals, the program can deconvolve w and x exactly when the maximum of N and K is almost on the order of L. That is, we show that if x is drawn from a random subspace of dimension N, and w is a vector in a subspace of dimension K whose basis vectors are spread out in the frequency domain, then nuclear norm minimization recovers wx* without error. We discuss this result in the context of blind channel estimation in communications. If we have a message of length N, which we code using a random L x N coding matrix, and the encoded message travels through an unknown linear time-invariant channel of maximum length K, then the receiver can recover both the channel response and the message when L ≳ N + K, to within constant and log factors." @default.
• W2140867429 created "2016-06-24" @default.
• W2140867429 creator A5012870568 @default.
• W2140867429 creator A5041443633 @default.
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• W2140867429 date "2014-03-01" @default.
• W2140867429 modified "2023-10-10" @default.
• W2140867429 title "Blind Deconvolution Using Convex Programming" @default.
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• W2140867429 doi "https://doi.org/10.1109/tit.2013.2294644" @default.
• W2140867429 hasPublicationYear "2014" @default.
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