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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.

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.

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

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.

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

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.

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.

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.