## Signal Processing

## Systems and Methods for Communication Using Sparsity Based Pre-Compensation

October 9, 2018

A signal pre-compensation system analyzes one or more properties of a communication medium and, taking advantage of the locality of propagation, generates using sparse fast Fourier transform (sFFT) a sparse kernel based on the medium properties. The system models propagation of data signals through the medium as a fixed-point iteration based on the sparse kernel, and determines initial amplitudes for the data symbol(s) to be transmitted using different communication medium modes. Fixed-point iterations are performed using the sparse kernel to iteratively update the initial amplitudes. If the iterations converge, a subset of the finally updated amplitudes is used as launch amplitudes for the data symbol(s). The data symbol(s) can be modulated using these launch amplitudes such that upon propagation of the pre-compensated data symbol(s) through the communication medium, they would resemble the original data symbols at a receiver, despite any distortion and/or cross-mode interference in the communication medium.

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## A Sparse Multi-Dimensional Fast Fourier Transform with Stability to Noise in the Context of Image Processing and Change Detection

September 13, 2016

We present the sparse multidimensional FFT (sMFFT) for positive real vectors with application to image processing. Our algorithm works in any fixed dimension, requires an (almost) - optimal number of samples and runs in complexity (to first order) for unknowns and nonzeros. It is stable to noise and exhibits an exponentially small probability of failure. Numerical results show sMFFT’s large quantitative and qualitative strengths as compared to minimization for Compressive Sensing as well as advantages in the context of image processing and change detection.

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## A Sparse Multidimensional FFT for Real Positive Vectors

May 10, 2016

We present a sparse multidimensional FFT (sMFFT) randomized algorithm for positive real vectors. The algorithm works in any fixed dimension, requires an (almost)-optimal number of samples (O (R log (N))) and runs in O (R log (N)) complexity (where N is the total size of the vector in d dimensions and R is the number of nonzeros) which we claim is optimal (up to first order). It is stable to noise, exhibits an exponentially small probability of failure and is generalizable to general complex vectors.

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## Embedded Second-Order Cone Programming with Radar Applications

September 1, 2015

Second-order cone programming (SOCP) is required for the solution of underdetermined systems of linear equations with complex coefficients, subject to the minimization of a convex objective function. This type of computational problem appears in compressed radar sensing, where the goal is to reconstruct a sparse image in a generalized space of phase model parameters whose dimension is higher than the number of complex measurements.

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## Re-Introduction of Communication-Avoiding FMM-Accelerated FFTs with GPU Acceleration

September 1, 2013

As distributed memory systems grow larger, communication demands have increased. Unfortunately, while the costs of arithmetic operations continue to decrease rapidly, communication costs have not. As a result, there has been a growing interest in communication-avoiding algorithms for some of the classic problems in numerical computing, including communication-avoiding Fast Fourier Transforms (FFTs).

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