# A sparse multidimensional FFT for real positive vectors

@article{Ltourneau2016ASM, title={A sparse multidimensional FFT for real positive vectors}, author={Pierre-David L{\'e}tourneau and Harper Langston and Beno{\^i}t Meister and Richard A. Lethin}, journal={ArXiv}, year={2016}, volume={abs/1604.06682} }

We present a sparse multidimensional FFT (sMFFT) randomized algorithm for real positive vectors. The algorithm works in any fixed dimension, requires (O(R log(R) log(N)) ) samples and runs in O( R log^2(R) log(N)) complexity (where N is the total size of the vector in d dimensions and R is the number of nonzeros). It is stable to low-level noise and exhibits an exponentially small probability of failure.

## 2 Citations

### A sparse multi-dimensional Fast Fourier Transform with stability to noise in the context of image processing and change detection

- Computer Science2016 IEEE High Performance Extreme Computing Conference (HPEC)
- 2016

Numerical results show the sparse multidimensional FFT (sMFFT)'s large quantitative and qualitative strengths as compared to ℓ1-minimization for Compressive Sensing as well as advantages in the context of image processing and change detection.

### Approximate Inverse Chain Preconditioner: Iteration Count Case Study for Spectral Support Solvers

- Computer Science2020 IEEE High Performance Extreme Computing Conference (HPEC)
- 2020

A new preconditioner for symmetric diagonally dominant systems of linear equations that is both algebraic in nature as well as hierarchically-constrained depending on the condition number of the system to be solved and accelerated by utilizing precomputations to simplify setup and multiplications in the context of an iterative Krylov-subspace solver.

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Numerical results show the sparse multidimensional FFT (sMFFT)'s large quantitative and qualitative strengths as compared to ℓ1-minimization for Compressive Sensing as well as advantages in the context of image processing and change detection.

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