Blind deconvolution refers to recovering signals by observing only their convolution. Blind deconvolution is a fundamental problem in signal processing, wireless communication, and systems theory. This problem arises in the context of blind channel estimation in wireless communications, passive imaging; for example, to estimate earth layer prole for oil exploration,…
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This letter considers the blind separation of convolutive mixtures in a multi-in-multi-out (MIMO) communication system. Multiple source signals are transmitted simultaneously over a shared communication medium (modeled as linear convolutive channels) to multiple receivers. We recast the joint recovery of the source signals, and the channel impulse responses as a…
Read moreThis paper considers recovering L-dimensional vectors w, and x 1 , x 2 , ? , x N from their circular convolutions y_{n} = w * x_{n} , n = 1, 2, 3, ? , N. The vector wis assumed to be S-sparse in a known basis that is spread…
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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…
Read moreWe 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…
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Trained 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,…
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…
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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…
Read moreWe consider the task of recovering two real or complex -vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a nontrivial convex relaxation of the bilinear measurements from convolution. We prove that…
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This paper proposes a novel framework to regularize the highly ill-posed and non-linear Fourier ptychography problem using generative models. We demonstrate experimentally that our proposed algorithm, Deep Ptych, outperforms the existing Fourier ptychography techniques, in terms of quality of reconstruction and robustness against noise, using far fewer samples. We further…
Read moreThis paper shows that modulation protects a bandlimited signal against convolutive interference. A signal?, bandlimited to BHz, is modulated (pointwise multiplied) with a known random sign sequence?, alternating at a rate?, and the resultant spread spectrum signal??is convolved against an M-tap channel impulse response??to yield the observed signal?, where??and??denote pointwise…
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This letter presents a framework for the compressive acquisition of correlated signals. We propose an implementable sampling architecture for the acquisition of ensembles of correlated (lying in an a priori unknown subspace) signals at a sub-Nyquist rate. The sampling architecture acquires structured compressive samples of the signals after preprocessing them…
Read moreThis paper considers the blind deconvolution of multiple modulated signals/filters, and an arbitrary filter/signal. Multiple inputs??are modulated (pointwise multiplied) with random sign sequences?, respectively, and the resultant inputs??are convolved against an arbitrary input??to yield the measurements?, where??and??denote pointwise multiplication, and circular convolution. Given?, we want to recover the unknowns??and?. We…
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The 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…
Read moreThis article proposes a novel approach to regularize the ill-posed and non-linear blind image deconvolution (blind deblurring) using deep generative networks as priors. We employ two separate pretrained generative networks given lower-dimensional Gaussian vectors as input, one of the generative models samples from the distribution of sharp images, while…
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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…
Read moreWe consider the task of recovering two real or complexm-vectors from phase less Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows a non-trivial convex relaxation of the bilinear measurements from convolution. We prove that…
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Recommendation systems are becoming increasingly important, as evidenced by the popularity of the Netflix prize and the sophistication of various online shopping systems. With this increase in interest, a new problem of nefarious or false rankings that compromise a recommendation systems integrity has surfaced. We consider such purposefully erroneous rankings…
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