相关论文: Fundamental performance limits for ideal decoders …
In this paper, we address the question of information preservation in ill-posed, non-linear inverse problems, assuming that the measured data is close to a low-dimensional model set. We provide necessary and sufficient conditions for the…
Undersampled inverse problems occur everywhere in the sciences including medical imaging, radar, astronomy etc., yielding underdetermined linear or non-linear reconstruction problems. There are now a myriad of techniques to design decoders…
The problem of recovering the sparsity pattern of a fixed but unknown vector $\beta^* \in \real^p based on a set of $n$ noisy observations arises in a variety of settings, including subset selection in regression, graphical model selection,…
We investigate the reconstruction of multivariate functions from samples using sparse recovery techniques. For Square Root Lasso, Orthogonal Matching Pursuit, and Compressive Sampling Matching Pursuit, we demonstrate both theoretically and…
We look at continuum solutions in optimisation problems associated to linear inverse problems $y = Ax$ with non-negativity constraint $x \geq 0$. We focus on the case where the noise model leads to maximum likelihood estimation through…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
Departing from traditional communication theory where decoding algorithms are assumed to perform without error, a system where noise perturbs both computational devices and communication channels is considered here. This paper studies…
The objective of this work is to quantify the reconstruction error in sparse inverse problems with measures and stochastic noise, motivated by optimal sensor placement. To be useful in this context, the error quantities must be explicit in…
To model modern large-scale datasets, we need efficient algorithms to infer a set of $P$ unknown model parameters from $N$ noisy measurements. What are fundamental limits on the accuracy of parameter inference, given finite signal-to-noise…
Inverse optimal control (IOC) aims to estimate the underlying cost that governs the observed behavior of an expert system. However, in practical scenarios, the collected data is often corrupted by noise, which poses significant challenges…
We consider in this paper the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and…
The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…
In this paper, the problems of frequency-limited and time-limited H2-optimal model order reduction of linear time-invariant systems are considered within the oblique projection framework. It is shown that it is inherently not possible to…
Ill-posed linear inverse problems appear frequently in various signal processing applications. It can be very useful to have theoretical characterizations that quantify the level of ill-posedness for a given inverse problem and the degree…
The focusing operation inherent to the linear discrete inverse problem is formalised. The development is given in the context of sound-field reproduction where the source strengths are the inverse solution needed to recreate a prescribed…
The presence of label noise often misleads the training of deep neural networks. Departing from the recent literature which largely assumes the label noise rate is only determined by the true label class, the errors in human-annotated…
Demixing is the problem of identifying multiple structured signals from a superimposed, undersampled, and noisy observation. This work analyzes a general framework, based on convex optimization, for solving demixing problems. When the…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
In frequency-limited model order reduction, the objective is to maintain the frequency response of the original system within a specified frequency range in the reduced-order model. In this paper, a mathematical expression for the…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…