We consider the bilinear inverse problem of recovering two vectors,??and?, from their entrywise product. We consider the case where??and??have known signs and are sparse with respect to known dictionaries of size??and?, respectively. Here,??and??may be larger than, smaller than, or equal to?. We introduce?-BranchHull, which is a convex program posed in the natural parameter space and […]
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We propose two compressive multiplexers for the efficient sampling of ensembles of correlated signals. We show that we can acquire correlated ensembles, taking advantage of their (a priori-unknown) correlation structure, at a sub-Nyquist rate using simple modulation and filtering architectures. We recast the reconstruction of the ensemble as a low-rank matrix recovery problem from generalized […]
Read MoreThe recently developed theory of Compressive sensing (CS) has shown that sparse signals can be reconstructed from a much smaller number of measurements than their bandwidth suggests. In this paper we present a sampling scheme to acquire ensembles of correlated signals at a sub-Nyquist rate. The sampling architecture uses simple analog building blocks including analog […]
Read MoreTrained generative models have shown remark-able performance as priors for inverse problems in imaging for example, Generative Adversarial Network priors permit recovery of test images from 5-10x fewer measurements than sparsity priors. Unfortunately, these models may be unable to represent any particular image because of architectural choices, mode collapse, and bias in the training […]
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We consider the bilinear inverse problem of recovering two vectors,??and?, in??from their entrywise product. For the case where the vectors have known signs and belong to known subspaces, we introduce the convex program BranchHull, which is posed in the natural parameter space and does not require an approximate solution or initialization in order to be […]
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This note considers the problem of blind identification of a linear, time-invariant (LTI) system when the input signals are unknown, but belong to sufficiently diverse, known subspaces. This problem can be recast as the recovery of a rank-1 matrix, and is effectively relaxed using a semidefinite program (SDP). We show that exact recovery of both […]
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