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The problem of recovering a sparse matrix X from its sketchAXB T is referred to as the matrix sketching problem. Typically, the sketch is a lower dimensional matrix compared to X, and the sketching matrices A and B are known. Matrix sketching algorithms have been developed in the past to recover matrices from a continuous valued vectorspace (e.g., R^N×N ). However, employing such algorithms to recover discrete valued matrices may not be optimal. In this paper, we propose two novel algorithms that can efficiently recover a discrete valued sparse matrix from its sketch.

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We present a primal-dual interior point method (IPM) with a novel preconditioner to solve the ℓ1-norm regularized least square problem for nonnegative sparse signal reconstruction. IPM is a second-order method that uses both gradient and Hessian information to compute effective search directions and achieve super-linear convergence rates. It therefore requires many fewer iterations than first-order methods such as iterative shrinkage/thresholding algorithms (ISTA) that only achieve sub-linear convergence rates.

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Non-regular sampling can reduce aliasing at the expense of noise.
Recently, it has been shown that non-regular sampling can be carried
out using a conventional regular imaging sensor when the surface of
its individual pixels is partially covered. This technique is called
quarter sampling (also 1/4 sampling), since only one quarter of each
pixel is sensitive to light. For this purpose, the choice of a proper
sampling mask is crucial to achieve a high reconstruction quality. In
the scope of this work, we present an iterative algorithm to improve

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Fourier Transform Interferometry (FTI) is an interferometric procedure for acquiring HyperSpectral (HS) data. Recently, it has been observed that the light source highlighting a (biologic) sample can be coded before the FTI acquisition in a procedure called Coded Illumination-FTI (CI-FTI). This turns HS data reconstruction into a Compressive Sensing (CS) problem regularized by the sparsity of the HS data. CI-FTI combines the high spectral resolution of FTI with the advantages of reduced-light-exposure imaging in biology.

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This paper investigates the delay-Doppler estimation problem of a pulse-Doppler radar which samples and quantizes the noisy echo signals to one-bit measurements.By applying a multichannel one-bit sampling scheme, we formulate the delay-Doppler estimation as a structured low-rank matrix recovery problem.Then the one-bit atomic norm soft-thresholding method is proposed to recover the low-rank matrix, in which a surrogate matrix is properly designed to evaluate the proximity of the recovered data to the sampled one.With the recovered low-rank matrix, the delays and Doppler frequencies can be d

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We consider the problem of localizing point sources on an interval from possibly noisy measurements. In the absence of noise, we show that measurements from Chebyshev sys- tems are an injective map for non-negative sparse measures, and therefore non-negativity is sufficient to ensure unique- ness for sparse measures. Moreover, we characterize non- negative solutions from inexact measurements and show that any non-negative solution consistent with the measurements is proportionally close to the solution of the system with ex- act measurements.

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In a recent paper [1], we introduced the concept of “Unlimited Sampling”. This unique approach circumvents the clipping or saturation problem in conventional analog-to-digital converters (ADCs) by considering a radically different ADC architecture which resets the input voltage before saturation. Such ADCs, also known as Self-Reset ADCs (SR-ADCs), allow for sensing modulo samples.

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Sampling of smooth spatiotemporally varying fields is a well studied topic in the literature. Classical approach assumes that the field is observed at known sampling locations and known timestamps ensuring field reconstruction. In a first, in this work the sampling and reconstruction of a spatiotemporal bandlimited field is addressed, where the samples are obtained by a location-unaware, time-unaware mobile sensor. The spatial and temporal order of samples is assumed to be known. It is assumed that the field samples are affected by measurement-noise.

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