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Rational approximation schemes for reconstructing periodic signals from samples with poorly separated spectral content are described. These methods are automatic and adaptive, requiring no tuning or manual parameter selection. Collectively,…
We study the recovery of multiple high-dimensional signals from two noisy, correlated modalities: a spiked matrix and a spiked tensor sharing a common low-rank structure. This setting generalizes classical spiked matrix and tensor models,…
In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…
This note proposes a new algorithm for estimating spectral function from limited noisy Matsubara data. We consider both the molecule and condensed matter cases. In each case, the algorithm constructs an interpolant of the Matsubara data and…
Spiking Neural Networks (SNNs) are widely regarded as a biologically-inspired and energy-efficient alternative to classical artificial neural networks. Yet, their theoretical foundations remain only partially understood. In this work, we…
Phase retrieval in dynamical sampling is a novel research direction, where an unknown signal has to be recovered from the phaseless measurements with respect to a dynamical frame, i.e. a sequence of sampling vectors constructed by the…
Spiking Neural Networks (SNNs) provide biological plausibility and energy efficiency, yet systematic investigations of memory augmentation strategies remain limited. We conduct a five-model ablation study integrating Leaky…
The parameter reconstruction problem in a sum of Dirac measures from its low frequency trigonometric moments is well understood in the univariate case and has a sharp transition of identifiability with respect to the ratio of the separation…
Spiking neural networks (SNNs) that mimic information transmission in the brain can energy-efficiently process spatio-temporal information through discrete and sparse spikes, thereby receiving considerable attention. To improve accuracy and…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
The paper explores the capability of continuous-time recurrent neural networks to store and recall precisely timed scores of spike trains. We show (by numerical experiments) that this is indeed possible: within some range of parameters, any…
A unified view of sparse signal processing is presented in tutorial form by bringing together various fields. For each of these fields, various algorithms and techniques, which have been developed to leverage sparsity, are described…
We propose an algebraic framework generalizing several variants of Prony's method and explaining their relations. This includes Hankel and Toeplitz variants of Prony's method for the decomposition of multivariate exponential sums,…
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…
Skewed probit regression is but one example of a statistical model that generalizes a simpler model, like probit regression. All skew-symmetric distributions and link functions arise from symmetric distributions by incorporating a skewness…
The paper considers the problem of performing a task defined on a model parameter that is only observed indirectly through noisy data in an ill-posed inverse problem. A key aspect is to formalize the steps of reconstruction and task as…
We consider synthetic aperture radar imaging of a region containing point-like targets. Measurements are the set of frequency responses to scattering by the targets taken over a collection of individual spatial locations along the flight…
The basic inverse problem in spectral graph theory consists in determining the graph given its eigenvalue spectrum. In this paper, we are interested in a network of technological agents whose graph is unknown, communicating by means of a…
Spiking Neural Networks (SNNs) have been proposed as biologically plausible and energy-efficient alternatives to conventional Artificial Neural Networks (ANNs). However, the training of SNN usually relies on surrogate gradients due to the…
The problem of recovering a structured signal from its linear measurements in the presence of speckle noise is studied. This problem appears in many imaging systems such as synthetic aperture radar and optical coherence tomography. The…