Fast sparse 2-D DFT computation using sparse-graph alias codes

We present a novel algorithm, named the 2D-FFAST (Two-dimensional Fast Fourier Aliasing-based Sparse Transform), to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample and computational complexity. The proposed algorithm is based on diverse concepts from signal processi...

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Vydané v:Proceedings of the ... IEEE International Conference on Acoustics, Speech and Signal Processing (1998) s. 4059 - 4063
Hlavní autori: Ong, Frank, Pawar, Sameer, Ramchandran, Kannan
Médium: Konferenčný príspevok.. Journal Article
Jazyk:English
Vydavateľské údaje: IEEE 01.03.2016
Predmet:
Algorithm design and analysis
Algorithms
Compressed sensing
Computation
Computational complexity
Computer architecture
Computing time
Decoding
Delays
Discrete Fourier transforms
Electronics
Fast Fourier Transform
Fourier analysis
Multi-dimensional Signal Processing
Reconstruction
Signal processing
Signal processing algorithms
Sparse graph code
Two dimensional
ISSN:2379-190X
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Shrnutí:We present a novel algorithm, named the 2D-FFAST (Two-dimensional Fast Fourier Aliasing-based Sparse Transform), to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample and computational complexity. The proposed algorithm is based on diverse concepts from signal processing (sub-sampling and aliasing), coding theory (sparse-graph codes) and number theory (Chinese-remainder-theorem) and generalizes the 1D-FFAST algorithm recently proposed by Pawar and Ramchandran to the 2D setting. Concretely, our proposed 2D-FFAST algorithm computes a k-sparse 2D-DFT, with a uniformly random support, of size N = N x × N y using O(k) noiseless spatial-domain measurements in O(k log k) computational time. Our results are attractive when the sparsity is sub-linear with respect to the signal dimension, that is, when k → ∞ and k/N → 0. For the case when the spatial-domain measurements are corrupted by additive noise, our 2D-FFAST framework extends to a noise-robust version of computing a 2D-DFT using O(k log 3 N) measurements in sub-linear time of O(k log 4 N). Empirically, we show that the 2D-FFAST can compute a k = 3509 sparse 2D-DFT of a 508 × 508-size phantom image using only 4.75k measurements. We also empirically evaluate the 2D-FFAST algorithm on a real-world magnetic resonance brain image using a total of 60.18% of Fourier measurements to provide an almost instant reconstruction with SNR=4.5 dB. This provides empirical evidence that the 2D-FFAST architecture is applicable to a wider class of input signals than analyzed theoretically in the paper.
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SourceType-Conference Papers & Proceedings-2
ISSN:2379-190X
DOI:10.1109/ICASSP.2016.7472440