February 2022 – CACTUS

Cleaning up toxic waste: Removing nefarious contributions to recommendation systems

February 2, 2022
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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 to be a form of […]

Simultaneous Phase Retrieval and Blind Deconvolution via Convex Programming

February 2, 2022
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We 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 if the two signals belongto […]

Bilinear Compressed Sensing Under Known Signs via Convex Programming

February 2, 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 […]

February 2, 2022
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This 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 the other from that of […]

February 2, 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 […]

Blind Deconvolution Using Modulated Inputs

February 2, 2022
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This 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 make a structural assumption that […]

Compressive Acquisition and Least-Squares Reconstruction of Correlated Signals

February 2, 2022
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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 with easy-toimplement components. Quantitatively, we […]

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 […]