相关论文: Prony's Method in Banach Modules

This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…

Phase retrieval problems occur in a wide range of applications in physics and engineering. Usually, these problems consist in the recovery of an unknown signal from the magnitudes of its Fourier transform. In some applications, however, the…

This is a survey paper discussing one specific (and classical) system of algebraic equations - the so called "Prony system". We provide a short overview of its unusually wide connections with many different fields of Mathematics, stressing…

We consider the recovery of sparse signals subject to sparse interference, as introduced in Studer et al., IEEE Trans. IT, 2012. We present novel probabilistic recovery guarantees for this framework, covering varying degrees of knowledge of…

It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…

For the first time, this paper investigates the phase retrieval problem with the assumption that the phase (of the complex signal) is sparse in contrast to the sparsity assumption on the signal itself as considered in the literature of…

The problem of recovering a signal from its power spectrum, called phase retrieval, arises in many scientific fields. One of many examples is ultra-short laser pulse characterization in which the electromagnetic field is oscillating with…

We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's…

Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…

It has been shown both experimentally and theoretically that sparse signal recovery can be significantly improved given that part of the signal's support is known \emph{a priori}. In practice, however, such prior knowledge is usually…

We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is…

To interpolate a supersparse polynomial with integer coefficients, two alternative approaches are the Prony-based "big prime" technique, which acts over a single large finite field, or the more recently-proposed "small primes" technique,…

We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…

The problem of how to find a sparse representation of a signal is an important one in applied and computational harmonic analysis. It is closely related to the problem of how to reconstruct a sparse vector from its projection in a much…

Recovering an unknown but structured signal from its measurements is a challenging problem with significant applications in fields such as imaging restoration, wireless communications, and signal processing. In this paper, we consider the…

Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a…

Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…

Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…

We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is…

In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…