Related papers: On recoverability of discrete time signals from sp…

The paper investigates recoverability of sequences from their periodic subsequences and offers some modification of the approach suggested in papers arXiv:1605.00414 and arXiv:1803.02233. It is shown that there exists a class of sequences…

In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…

This paper reports an effort to consolidate numerous coherence-based sparse signal recovery results available in the literature. We present a single theory that applies to general Hilbert spaces with the sparsity of a signal defined as the…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

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…

Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from…

The paper considers recovery of signals from incomplete observations and a problem of determination of the allowed quantity of missed observations, i.e. the problem of determination of the size of the uniqueness sets for a given data…

This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…

The paper studies spectral representation as well as predictability and recoverability problems for non-vanishing discrete time signals from $\ell_\infty$, i.e. for bounded discrete time signals, including signals that do not vanish at…

This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex…

Modeling multivariate time series as temporal signals over a (possibly dynamic) graph is an effective representational framework that allows for developing models for time series analysis. In fact, discrete sequences of graphs can be…

Recovering sparse signals from linear measurements has demonstrated outstanding utility in a vast variety of real-world applications. Compressive sensing is the topic that studies the associated raised questions for the possibility of a…

The paper suggests a frequency criterion of error-free recoverability of a missing value for sequences, i.e. discrete time processes, in a pathwise setting without probabilistic assumptions. The paper establishes error-free recoverability…

In many applications sampled data are collected in irregular fashion or are partly lost or unavailable. In these cases it is required to convert irregularly sampled signals to regularly sampled ones or to restore missing data. In this…

Suppose that a sequence of numbers $x_n$ (a `signal') is transmitted through a noisy channel. The receiver observes a noisy version of the signal with additive random fluctuations, $x_n + \xi_n$, where $\xi_n$ is a sequence of independent…

In this work, sample-based observability of linear discrete-time systems is studied. That is, we consider the case where the system output measurements are not available at every time instance. It is shown that some discrete-time systems…

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…

Compressed sensing investigates the recovery of sparse signals from linear measurements. But often, in a wide range of applications, one is given only the absolute values (squared) of the linear measurements. Recovering such signals (not…

A host of problems involve the recovery of structured signals from a dimensionality reduced representation such as a random projection; examples include sparse signals (compressive sensing) and low-rank matrices (matrix completion). Given…

Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…