Related papers: Separating signal from noise
We consider a statistical problem of detection of a signal with unknown energy in a multi-channel system, observed in a Gaussian noise. We assume that the signal can appear in the $k$-th channel with a known small prior probability…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
The problem of separation of an observed sum of chaotic signals into the individual components in the presence of noise on the path to the observer is considered. A noise threshold is found above which high-quality separation is impossible.…
We consider the problem of exact support recovery of sparse signals via noisy measurements. The main focus is the sufficient and necessary conditions on the number of measurements for support recovery to be reliable. By drawing an analogy…
We study detection methods for multivariable signals under dependent noise. The main focus is on three-dimensional signals, i.e. on signals in the space-time domain. Examples for such signals are multifaceted. They include geographic and…
The paper investigates recoverability of discrete time signals represented by infinite sequences from incomplte observations. It is shown that there exist wide classes of signals that are everywhere dense in the space of square-summable…
In many applications, the observations can be represented as a signal defined over the vertices of a graph. The analysis of such signals requires the extension of standard signal processing tools. In this work, first, we provide a class of…
We determine conditions for the presence of stochastic resonance in a lossy bosonic channel with a nonlinear, threshold decoding. The stochastic resonance effect occurs if and only if the detection threshold is outside of a "forbidden…
The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…
The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…
We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is…
In this paper, we consider the problem of detecting signals in multiple, sequentially observed data streams. For each stream, the exact distribution is unknown, but characterized by a parameter that takes values in either of two disjoint…
We analyze the asymptotic performance of sparse signal recovery from noisy measurements. In particular, we generalize some of the existing results for the Gaussian case to subgaussian and other ensembles. An achievable result is presented…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
Common problem in signal processing is reconstruction of the missing signal samples. Missing samples can occur by intentionally omitting signal coefficients to reduce memory requirements, or to speed up the transmission process. Also, noisy…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
We derive a method to reconstruct Gaussian signals from linear measurements with Gaussian noise. This new algorithm is intended for applications in astrophysics and other sciences. The starting point of our considerations is the principle…
We investigate the recovery of signals exhibiting a sparse representation in a general (i.e., possibly redundant or incomplete) dictionary that are corrupted by additive noise admitting a sparse representation in another general dictionary.…
We consider the problem of recovering a signal observed in Gaussian noise. If the set of signals is convex and compact, and can be specified beforehand, one can use classical linear estimators that achieve a risk within a constant factor of…