21 citations · 35 across the 10 of their papers we have counts for
12 papers
Implicit Regularization for Tubal Tensor Factorizations via Gradient Descent
Santhosh Karnik, Anna Veselovska, Mark Iwen +1
We provide a rigorous analysis of implicit regularization in an overparametrized tensor factorization problem beyond the lazy training regime. For matrix factorization problems, th…
Tensor Deli: Tensor Completion for Low CP-Rank Tensors via Random Sampling
Cullen Haselby, Mark Iwen, Santhosh Karnik +1
We propose two provably accurate methods for low CP-rank tensor completion - one using adaptive sampling and one using nonadaptive sampling. Both of our algorithms combine matrix c…
Tensor Sandwich: Tensor Completion for Low CP-Rank Tensors via Adaptive Random Sampling
Cullen Haselby, Santhosh Karnik, Mark Iwen
We propose an adaptive and provably accurate tensor completion approach based on combining matrix completion techniques (see, e.g., arXiv:0805.4471, arXiv:1407.3619, arXiv:1306.297…
Iterative Broadband Source Localization
Coleman DeLude, Rakshith Sharma, Santhosh Karnik +3
In this paper we consider the problem of localizing a set of broadband sources from a finite window of measurements. In the case of narrowband sources this can be reduced to the pr…
Neural Network Approximation of Continuous Functions in High Dimensions with Applications to Inverse Problems
Santhosh Karnik, Rongrong Wang, Mark Iwen
The remarkable successes of neural networks in a huge variety of inverse problems have fueled their adoption in disciplines ranging from medical imaging to seismic analysis over th…
Broadband Beamforming via Linear Embedding
Coleman DeLude, Santhosh Karnik, Mark Davenport +1
In modern applications multi-sensor arrays are subject to an ever-present demand to accommodate signals with higher bandwidths. Standard methods for broadband beamforming, namely d…
Harmless interpolation in regression and classification with structured features
Andrew D. McRae, Santhosh Karnik, Mark A. Davenport +1
Overparametrized neural networks tend to perfectly fit noisy training data yet generalize well on test data. Inspired by this empirical observation, recent work has sought to under…
Thomson's Multitaper Method Revisited
Santhosh Karnik, Justin Romberg, Mark A. Davenport
Thomson's multitaper method estimates the power spectrum of a signal from equally spaced samples by averaging tapered periodograms. Discrete prolate spheroidal sequences (D…
Improved bounds for the eigenvalues of prolate spheroidal wave functions and discrete prolate spheroidal sequences
Santhosh Karnik, Justin Romberg, Mark A. Davenport
The discrete prolate spheroidal sequences (DPSSs) are a set of orthonormal sequences in which are strictly bandlimited to a frequency band and maximal…
ROAST: Rapid Orthogonal Approximate Slepian Transform
Zhihui Zhu, Santhosh Karnik, Michael B. Wakin +2
In this paper, we provide a Rapid Orthogonal Approximate Slepian Transform (ROAST) for the discrete vector that one obtains when collecting a finite set of uniform samples from a b…
The Eigenvalue Distribution of Discrete Periodic Time-Frequency Limiting Operators
Zhihui Zhu, Santhosh Karnik, Mark A. Davenport +2
Bandlimiting and timelimiting operators play a fundamental role in analyzing bandlimited signals that are approximately timelimited (or vice versa). In this paper, we consider a ti…
The Fast Slepian Transform
Santhosh Karnik, Zhihui Zhu, Michael B. Wakin +2
The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high c…