相关论文: Geometry of error amplification in solving Prony s…
Image signals typically are defined on a rectangular two-dimensional grid. However, there exist scenarios where this is not fulfilled and where the image information only is available for a non-regular subset of pixel position. For…
In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of…
Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
We continue studying robustness of solving algebraic systems of Prony type (also known as the exponential fitting systems), which appear prominently in many areas of mathematics, in particular modern "sub-Nyquist" sampling theories. We show…
We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numerous applications. An especially challenging scenario occurs…
It has been proposed recently that topological A-model string amplitudes for toric Calabi-Yau 3-folds in non self-dual graviphoton background can be caluculated by a diagrammatic method that is called the ``refined topological vertex''. We…
We study the problem of reconstructing a signal from its projection on a subspace. The proposed signal reconstruction algorithms utilize a guiding subspace that represents desired properties of reconstructed signals. We show that optimal…
To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
Approximation properties of the expansions $\sum_{k\in{\mathbb z}^d}c_k\phi(M^jx+k)$, where $M$ is a matrix dilation, $c_k$ is either the sampled value of a signal $f$ at $M^{-j}k$ or the integral average of $f$ near $M^{-j}k$ (falsified…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
Magnetic resonance imaging (MRI) plays a vital role in clinical diagnostics, yet it remains hindered by long acquisition times and motion artifacts. Multi-contrast MRI reconstruction has emerged as a promising direction by leveraging…
We initiate the algorithmic study of the following "structured augmentation" question: is it possible to increase the connectivity of a given graph G by superposing it with another given graph H? More precisely, graph F is the superposition…
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…
Prony's method is a prototypical eigenvalue analysis based method for the reconstruction of a finitely supported complex measure on the unit circle from its moments up to a certain degree. In this note, we give a generalization of this…
Recognizing symmetries in data allows for significant boosts in neural network training. In many cases, however, the underlying symmetry is present only in an idealized dataset, and is broken in the training data, due to effects such as…
A natural requirement of many distributed structures is fault-tolerance: after some failures, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general…
We establish a generic form of hardness amplification for the approximability of constant-depth Boolean circuits by polynomials. Specifically, we show that if a Boolean circuit cannot be pointwise approximated by low-degree polynomials to…
We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…