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07/03/2023
Tensor Sandwich: Tensor Completion for Low CP-Rank Tensors via Adaptive Random Sampling
We propose an adaptive and provably accurate tensor completion approach ...
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02/01/2023
Sparse Spectral Methods for Solving High-Dimensional and Multiscale Elliptic PDEs
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claim...
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08/28/2022
Neural Network Approximation of Lipschitz Functions in High Dimensions with Applications to Inverse Problems
The remarkable successes of neural networks in a huge variety of inverse...
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12/20/2021
Toward Fast and Provably Accurate Near-field Ptychographic Phase Retrieval
Ptychography is an imaging technique which involves a sample being illum...
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10/10/2021
A Hybrid Scattering Transform for Signals with Isolated Singularities
The scattering transform is a wavelet-based model of Convolutional Neura...
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06/04/2021
Phase Retrieval for L^2([-π,π]) via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements
In this paper, we focus on the approximation of smooth functions f: [-π,...
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05/28/2021
Lower Bounds on the Low-Distortion Embedding Dimension of Submanifolds of ℝ^n
Let ℳ be a smooth submanifold of ℝ^n equipped with the Euclidean (chorda...
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03/24/2021
On the ℓ^∞-norms of the Singular Vectors of Arbitrary Powers of a Difference Matrix with Applications to Sigma-Delta Quantization
Let A _max := max_i,j |A_i,j| denote the maximum magnitude of entries of...
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12/17/2020
Sparse Fourier Transforms on Rank-1 Lattices for the Rapid and Low-Memory Approximation of Functions of Many Variables
We consider fast, provably accurate algorithms for approximating functio...
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09/20/2019
Sparse Harmonic Transforms II: Best s-Term Approximation Guarantees for Bounded Orthonormal Product Bases in Sublinear-Time
In this paper, we develop a sublinear-time compressive sensing algorithm...
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07/24/2019
Inverting Spectrogram Measurements via Aliased Wigner Distribution Deconvolution and Angular Synchronization
We propose a two-step approach for reconstructing a signal x∈C^d from s...
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02/11/2019