scholarly journals A Nonuniform Fast Fourier Transform Based on Low Rank Approximation

2018 ◽  
Vol 40 (1) ◽  
pp. A529-A547 ◽  
Author(s):  
Diego Ruiz-Antolín ◽  
Alex Townsend
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Low Rank ◽  
Low Rank Approximation ◽  
Nonuniform Fast Fourier Transform ◽  
Rank Approximation

A Novel Compression Method of Spectral Data Matrix Based on the Low-Rank Approximation and the Fast Fourier Transform of the Singular Vectors

2021 ◽  
pp. 000370282110447
Author(s):  
Joseph Dubrovkin
Keyword(s):  
Fourier Transform ◽  
Fast Fourier Transform ◽  
Spectral Data ◽  
Compression Ratio ◽  
Low Rank ◽  
Data Matrix ◽  
Compression Method ◽  
Low Rank Approximation ◽  
Singular Vectors ◽  
Rank Approximation

Storage, processing, and transfer of huge matrices are becoming challenging tasks in the process analytical technology and scientific research. Matrix compression can solve these problems successfully. We developed a novel compression method of spectral data matrix based on its low-rank approximation and the fast Fourier transform of the singular vectors. This method differs from the known ones in that it does not require restoring the low-rank approximated matrix for further Fourier processing. Therefore, the compression ratio increases. A compromise between the losses of the accuracy of the data matrix restoring and the compression ratio was achieved by selecting the processing parameters. The method was applied to multivariate chemometrics analysis of the cow milk for determining fat and protein content using two data matrices (the file sizes were 5.7 and 12.0 MB) restored from their compressed form. The corresponding compression ratios were about 52 and 114, while the loss of accuracy of the analysis was less than 1% compared with processing of the non-compressed matrix. A huge, simulated matrix, compressed from 400 MB to 1.9 MB, was successfully used for multivariate calibration and segment cross-validation. The data set simulated a large matrix of 10 000 low-noise infrared spectra, measured in the range 4000–400 cm−1 with a resolution of 0.5 cm−1. The corresponding file was compressed from 262.8 MB to 19.8 MB. The discrepancies between original and restored spectra were less than the standard deviation of the noise. The method developed in the article clearly demonstrated its potential for future applications to chemometrics-enhanced spectrometric analysis with limited options of memory size and data transfer rate. The algorithm used the standard routines of Matlab software.

scholarly journals Coherent Integration Method Based on Radon-NUFFT for Moving Target Detection Using Frequency Agile Radar

Sensors ◽  
2020 ◽  
Vol 20 (8) ◽  
pp. 2176
Author(s):  
Jiameng Pan ◽  
Qian Zhu ◽  
Qinglong Bao ◽  
Zengping Chen
Keyword(s):  
Fourier Transform ◽  
Target Detection ◽  
Integration Method ◽  
Phase Fluctuation ◽  
Low Rank ◽  
Moving Target ◽  
Low Rank Approximation ◽  
Coherent Integration ◽  
Frequency Agile ◽  
Rank Approximation

This paper considers the coherent integration problem for moving target detection using frequency agile (FA) radar, involving range cell migration (RCM) and the nonuniform phase fluctuations among different pulses caused by range-agile frequency (R-AF) coupling and velocity-time-agile frequency (V-T-AF) coupling. After the analysis of the term corresponding to the phase fluctuation caused by V-T-AF coupling, the term can be regarded as related to an equivalent non-uniform slow time, and nonuniform fast Fourier transform (NUFFT) could be the solution. So a fast coherent integration method combining Radon Fourier transform (RFT) and NUFFT based on low-rank approximation, i.e., Radon-NUFFT, is proposed. In this method, the RCM is solved by Radon algorithm via target trajectory searching, the non-uniform phase fluctuation caused by R-AF coupling is compensated by constructing a compensation item corresponding to the range and agile frequency. In addition, the compensation of the non-uniform phase fluctuation caused by V-T-AF coupling is converted into a problem of spectral analysis of non-uniform sampling complex-valued signal, which is solved by the NUFFT based on low rank approximation. Compared with the existing methods, the proposed method can realize the coherent integration for FA radar accurately and quickly. The effectiveness of the proposed method is verified by simulation experiments.

Improved MR image denoising via low- rank approximation and Laplacian-of-Gaussian edge detector

2020 ◽  
Vol 14 (12) ◽  
pp. 2791-2798
Author(s):  
Xiaoqun Qiu ◽  
Zhen Chen ◽  
Saifullah Adnan ◽  
Hongwei He
Keyword(s):  
Image Denoising ◽  
Low Rank ◽  
Edge Detector ◽  
Low Rank Approximation ◽  
Mr Image ◽  
Rank Approximation

scholarly journals Fast Joint Multiband Reconstruction From Wideband Images Based on Low-Rank Approximation

2020 ◽  
Vol 6 ◽  
pp. 922-933
Author(s):  
M. Amine Hadj-Youcef ◽  
Francois Orieux ◽  
Alain Abergel ◽  
Aurelia Fraysse
Keyword(s):  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation
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