Related papers: Random phaseless sampling for causal signals in sh…
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…
Sampling in shift-invariant spaces is a realistic model for signals with smooth spectrum. In this paper, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements…
We study phaseless sampling in spline spaces generated by B-splines with arbitrary knots. For real spline spaces, we give a necessary and sufficient condition for a sequence of sampling points to admit a local phase retrieval of any…
Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert…
We consider random sampling in finitely generated shift-invariant spaces $V(\Phi) \subset {\rm L}^2(\mathbb{R}^n)$ generated by a vector $\Phi = (\varphi_1,\ldots,\varphi_r) \in {\rm L}^2(\mathbb{R}^n)^r$. Following the approach introduced…
This paper investigates signal prediction through the perfect reconstruction of signals from shift-invariant spaces using nonuniform samples of both the signal and its derivatives. The key advantage of derivative sampling is its ability to…
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…
We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on…
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…
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…
The goal of phaseless compressed sensing is to recover an unknown sparse or approximately sparse signal from the magnitude of its measurements. However, it does not take advantage of any support information of the original signal.…
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…
We consider the question of estimating a real low-complexity signal (such as a sparse vector or a low-rank matrix) from the phase of complex random measurements. We show that in this "phase-only compressive sensing" (PO-CS) scenario, we can…
We provide a rigorous random matrix theory analysis of spiked cross-covariance models where the signals across two high-dimensional data channels are partially aligned. These models are motivated by multi-modal learning and form the…
Methods based on partial least squares (PLS) regression, which has recently gained much attention in the analysis of high-dimensional genomic datasets, have been developed since the early 2000s for performing variable selection. Most of…
Sampling shift-invariant (SI) signals with a high dynamic range poses a notable challenge in the domain of analog-to-digital conversion (ADC). It is essential for the ADC's dynamic range to exceed that of the incoming analog signal to…
The conjugate phase retrieval problem concerns the determination of a complex-valued function, up to a unimodular constant and conjugation, from its magnitude observations. It can also be considered as a conjugate phaseless sampling and…
Entanglement swapping entangles two particles that have never interacted[1], which implicitly assumes that each particle carries an independent local hidden variable, i.e., the presence of bilocality[2]. Previous experimental studies of…
We present a high-precision temporal-spatial phase-demodulation algorithm for phase-shifting interferometry (PSI) affected by random/systematic phase-stepping errors. Laser interferometers in standard optical-shops suffer from several error…
Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…