Related papers: Deconvolution with unknown noise distribution is p…
Shuffled regression and unlinked regression represent intriguing challenges that have garnered considerable attention in many fields, including but not limited to ecological regression, multi-target tracking problems, image denoising, etc.…
Blind deconvolution is an ubiquitous non-linear inverse problem in applications like wireless communications and image processing. This problem is generally ill-posed since signal identifiability is a key concern, and there have been…
Quantile estimation in deconvolution problems is studied comprehensively. In particular, the more realistic setup of unknown error distributions is covered. Our plug-in method is based on a deconvolution density estimator and is minimax…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
Blind deconvolution over graphs involves using (observed) output graph signals to obtain both the inputs (sources) as well as the filter that drives (models) the graph diffusion process. This is an ill-posed problem that requires additional…
We present a noise deconvolution technique for obtaining noiseless expectation values of noisy observables at the output of multiqubit quantum channels. For any number of qubits or in the presence of correlations, our protocol applies to…
In the blind deconvolution problem, we observe the convolution of an unknown filter and unknown signal and attempt to reconstruct the filter and signal. The problem seems impossible in general, since there are seemingly many more unknowns…
This work considers the multi-channel blind deconvolution problem under the assumption that the channels are short. First, we investigate the ill-posedness issues inherent to blind deconvolution problems and sufficient and necessary…
This paper discusses the recovery of an unknown signal $x\in \mathbb{R}^L$ through the result of its convolution with an unknown filter $h \in \mathbb{R}^L$. This problem, also known as blind deconvolution, has been studied extensively by…
This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructured sparse recovery problems. When the noise level is…
Accurate noise modelling is important for training of deep learning reconstruction algorithms. While noise models are well known for traditional imaging techniques, the noise distribution of a novel sensor may be difficult to determine a…
The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…
Subsampled blind deconvolution is the recovery of two unknown signals from samples of their convolution. To overcome the ill-posedness of this problem, solutions based on priors tailored to specific application have been developed in…
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…
We study a blind deconvolution problem on graphs, which arises in the context of localizing a few sources that diffuse over networks. While the observations are bilinear functions of the unknown graph filter coefficients and sparse input…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…
We refine and extend an earlier MDL denoising criterion for wavelet-based denoising. We start by showing that the denoising problem can be reformulated as a clustering problem, where the goal is to obtain separate clusters for informative…
We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…
We elaborate on a deconvolution method, used to estimate the empirical distribution of unknown parameters, as suggested recently by Efron (2013). It is applied to estimating the empirical distribution of the 'sampling probabilities' of m…