Related papers: Recovering Structured Data From Superimposed Non-L…
This paper considers the problem of estimating an unknown high dimensional signal from noisy linear measurements, {when} the signal is assumed to possess a \emph{group-sparse} structure in a {known,} fixed dictionary. We consider signals…
In this paper we study the reconstruction of binary sparse signals from partial random circulant measurements. We show that the reconstruction via the least-squares algorithm is as good as the reconstruction via the usually used program…
Single time-scale distributed estimation of dynamic systems via a network of sensors/estimators is addressed in this letter. In single time-scale distributed estimation, the two fusion steps, consensus and measurement exchange, are…
We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of…
We focus on a multidimensional field with uncorrelated spectrum, and study the quality of the reconstructed signal when the field samples are irregularly spaced and affected by independent and identically distributed noise. More…
We address the problem of reconstructing X-Ray tomographic images from scarce measurements by interpolating missing acquisitions using a self-supervised approach. To do so, we train shallow neural networks to combine two neighbouring…
The realisation of sensing modalities based on the principles of compressed sensing is often hindered by discrepancies between the mathematical model of its sensing operator, which is necessary during signal recovery, and its actual…
In this paper, we study the number of measurements required to recover a sparse signal in ${\mathbb C}^M$ with $L$ non-zero coefficients from compressed samples in the presence of noise. For a number of different recovery criteria, we prove…
In this paper, we study the recovery of a signal from a set of noisy linear projections (measurements), when such projections are unlabeled, that is, the correspondence between the measurements and the set of projection vectors (i.e., the…
Estimation of third-order statistics relies on the availability of a huge amount of data records, which can pose severe challenges on the data collecting hardware in terms of considerable storage costs, overwhelming energy consumption, and…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
We study the problem of recovering a structured signal $\mathbf{x}_0$ from high-dimensional data $\mathbf{y}_i=f(\mathbf{a}_i^T\mathbf{x}_0)$ for some nonlinear (and potentially unknown) link function $f$, when the regressors $\mathbf{a}_i$…
Extracting information from nonlinear measurements is a fundamental challenge in data analysis. In this work, we consider separable inverse problems, where the data are modeled as a linear combination of functions that depend nonlinearly on…
Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available…
Motivated by applications in unsourced random access, this paper develops a novel scheme for the problem of compressed sensing of binary signals. In this problem, the goal is to design a sensing matrix $A$ and a recovery algorithm, such…
We study the problem of modeling multiple symmetric, weighted networks defined on a common set of nodes, where networks arise from different groups or conditions. We propose a model in which each network is expressed as the sum of a shared…
Auto-Encoders are unsupervised models that aim to learn patterns from observed data by minimizing a reconstruction cost. The useful representations learned are often found to be sparse and distributed. On the other hand, compressed sensing…
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse…
The implementation of computational sensing strategies often faces calibration problems typically solved by means of multiple, accurately chosen training signals, an approach that can be resource-consuming and cumbersome. Conversely, blind…
A spatially distributed system contains a large amount of agents with limited sensing, data processing, and communication capabilities. Recent technological advances have opened up possibilities to deploy spatially distributed systems for…