Related papers: Signal Recovery from Time and Frequency Samples

In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a…

This thesis consists of original contributions in the area of digital signal processing. The reconstruction of signals sparse (highly concentrated) in various transform domains is the primary problem analyzed in the thesis. The considered…

We consider the problem of spectral compressed sensing in continuous domain, which aims to recover a 2-dimensional spectrally sparse signal from partially observed time samples. The signal is assumed to be a superposition of s complex…

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…

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…

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…

We consider the problem of ``algebraic reconstruction'' of linear combinations of shifts of several signals $f_1,\ldots,f_k$ from the Fourier samples. For each $r=1,\ldots,k$ we choose sampling set $S_r$ to be a subset of the common set of…

In many applications in compressed sensing, the measurement matrix is a Fourier matrix, i.e., it measures the Fourier transform of the underlying signal at some specified `base' frequencies $\{u_i\}_{i=1}^M$, where $M$ is the number of…

We investigate the problems of 1-D and 2-D signal recovery from subsampled Hadamard measurements using Haar wavelet sparsity prior. These problems are of interest in, e.g., computational imaging applications relying on optical multiplexing…

The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…

We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

Considering the ambiguousness of the discrete-time phase retrieval problem to recover a signal from its Fourier intensities, one can ask the question: what additional information about the unknown signal do we need to select the correct…

The problem of recovering a signal from its low frequency components occurs often in practical applications due to the lowpass behavior of many physical systems. Here we study in detail conditions under which a signal can be determined from…

The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…

As technology grows, higher frequency signals are required to be processed in various applications. In order to digitize such signals, conventional analog to digital convertors are facing implementation challenges due to the higher sampling…

Traditional sampling theories consider the problem of reconstructing an unknown signal $x$ from a series of samples. A prevalent assumption which often guarantees recovery from the given measurements is that $x$ lies in a known subspace.…

The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…

In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…

We consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…