Search Results for author: Santhosh Karnik

Found 5 papers, 0 papers with code

Iterative Broadband Source Localization

no code implementations21 Oct 2022 Coleman DeLude, Rakshith Sharma, Santhosh Karnik, Christopher Hood, Mark Davenport, Justin Romberg

We show that by using these models, our adapted algorithms can successfully localize broadband sources under a variety of adverse operating scenarios.

Neural Network Approximation of Continuous Functions in High Dimensions with Applications to Inverse Problems

no code implementations28 Aug 2022 Santhosh Karnik, Rongrong Wang, Mark Iwen

The approach is based on the observation that the existence of a Johnson-Lindenstrauss embedding $A\in\mathbb{R}^{d\times D}$ of a given high-dimensional set $S\subset\mathbb{R}^D$ into a low dimensional cube $[-M, M]^d$ implies that for any H\"older (or uniformly) continuous function $f:S\to\mathbb{R}^p$, there exists a H\"older (or uniformly) continuous function $g:[-M, M]^d\to\mathbb{R}^p$ such that $g(Ax)=f(x)$ for all $x\in S$.

Broadband Beamforming via Linear Embedding

no code implementations14 Jun 2022 Coleman DeLude, Santhosh Karnik, Mark Davenport, Justin Romberg

In modern applications multi-sensor arrays are subject to an ever-present demand to accommodate signals with higher bandwidths.

Dimensionality Reduction

Harmless interpolation in regression and classification with structured features

no code implementations9 Nov 2021 Andrew D. McRae, Santhosh Karnik, Mark A. Davenport, Vidya Muthukumar

Our results recover prior independent-features results (with a much simpler analysis), but they furthermore show that harmless interpolation can occur in more general settings such as features that are a bounded orthonormal system.

Classification regression

Thomson's Multitaper Method Revisited

no code implementations22 Mar 2021 Santhosh Karnik, Justin Romberg, Mark A. Davenport

This is useful in problems where many samples are taken, and thus, using many tapers is desirable.

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