Improved time bounds for near-optimal sparse Fourier representations
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Summary
A significantly improved algorithm for the problem of finding a Fourier representation R of m terms for a given discrete signal A of length N and a quadratic-in-m algorithm that works for any values of Ni's is given.
- Type
- article
- Published
- 2005-09-21
- Cited by
- 235
- References
- 31
- OpenAlex
- https://openalex.org/W1986545790
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:12622592
Keywords
Combinatorics, Fast Fourier transform, Binary logarithm, Sublinear function, Mathematics
References
- Fast algorithms for structured matrices : theory and applications : AMS-IMS-SIAM Joint Summer Research Conference on Fast Algorithms in Mathematics, Computer Science and Engineering, August 5-9, 2001, Mount Holyoke College, South Hadley, Massachusetts
- Numerical analysis of spectral methods
- Randomized Interpolation and Approximation of Sparse Polynomials
- I and i
- CBMS-NSF REGIONAL CONFERENCE SERIES IN APPLIED MATHEMATICS
- Approximate factorizations of Fourier matrices with nonequispaced knots
- Rapid Computation of the Discrete Fourier Transform
- On Wavelet-Based Numerical Homogenization
- Fast Fourier Transforms for Nonequispaced Data
- Near-optimal sparse fourier representations via sampling
- Asymptotic analysis for periodic structures
- A Multiresolution Strategy for Numerical Homogenization
- Applications of Discrete and Continuous Fourier Analysis
- Fast, small-space algorithms for approximate histogram maintenance
- An adaptive treecode for computing nonbonded potential energy in classical molecular systems
- Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
- Proving hard-core predicates using list decoding
- Constructing Small Sets that are Uniform in Arithmetic Progressions
- Theoretical and experimental analysis of a randomized algorithm for Sparse Fourier transform analysis
- Time Series Analysis: Forecasting and Control
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- An Introduction To Compressive Sampling
- Combinatorial compressive sampling with applications
- Efficient sparse approximation methods for medical imaging
- Deterministic Sparse Fourier Approximation via Fooling Arithmetic Progressions.
- On the computational power of quantum computers
- The Dantzig selector: Statistical estimation when P is much larger than n
- Methods of Music Classification and Transcription
- Sparse fourier transform in any constant dimension with nearly-optimal sample complexity in sublinear time
- Images compressive sensing reconstruction by inpainting
- Simple and practical algorithm for sparse Fourier transform
- Colocated MIMO radars using the Sparse Fourier Transform
- Improved Approximation Guarantees for Sublinear-Time Fourier Algorithms
- Adaptive sub-linear Fourier algorithms
- Sparse Fast Fourier Transform for Exactly and Generally K-Sparse Signals by Downsampling and Sparse Recovery
- BigBand: GHz-Wide Sensing and Decoding on Commodity Radios
- Efficient Software Implementation of the Nearly Optimal Sparse Fast Fourier Transform for the Noisy Case
- Manifold-Based Signal Recovery and Parameter Estimation from Compressive Measurements
- Sublinear Time, Approximate Model-based Sparse Recovery For All
- SPRIGHT: A Fast and Robust Framework for Sparse Walsh-Hadamard Transform
- Rapidly computing sparse Legendre expansions via sparse Fourier transforms
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