Signal Processing

Fast Large-Scale Algorithm for Electromagnetic Wave Propagation in 3D Media

Publication Source: IEEE High Performance Extreme Computing Conference (HPEC) 2019, Waltham, MA

We present a fast, large-scale algorithm for the simulation of electromagnetic waves (Maxwell’s equations) in three-dimensional inhomogeneous media. The algorithm has a complexity of O(N log(N)) and runs in parallel. Numerical simulations show the rapid treatment of problems with tens of millions of unknowns on a small shared-memory cluster ( 16 cores).

Systems and Methods for Communication Using Sparsity Based Pre-Compensation

Publication Source: Patent US10097280B2

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

Publication Source: 2016 IEEE High Performance Extreme Computing Conference (HPEC '16), Waltham, MA, USA.

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 Reservoir Labs and runs in Reservoir Labs complexity (to first order) for  Reservoir Labsunknowns and Reservoir Labs 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 toReservoir Labs 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

Publication Source: arXiv:1604.06682 [cs.DS]

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

Publication Source: The IEEE Conference on High Performance Extreme Computing (HPEC), Waltham, MA, USA, 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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