February 1, 2022

Channel Protection Using Random Modulation

February 1, 2022
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This 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 multiplication, and circular convolution, respectively.We […]

February 1, 2022
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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 modify the proposed approach to […]

Blind Deconvolutional Phase Retrieval via Convex Programming

February 1, 2022
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We 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 if the two signals belong […]

February 1, 2022
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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 the natural parameter space and […]

Compressive Multiplexing of Correlated Signals

February 1, 2022
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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 […]

February 1, 2022
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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 analog building blocks including analog […]

February 1, 2022
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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, and bias in the training […]

BranchHull: Convex Bilinear Inversion from the Entrywise Product of Signals with Known Signs

February 1, 2022
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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 […]

A convex approach to blind deconvolution with diverse inputs

February 1, 2022
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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 […]