Data for "Quadrature-Based Compressive Sensing Guarantees for Bounded Orthonormal Systems", to be submitted to IEEE Signal Processing Letters

Description

This dataset contains CSV files for the figures in the paper titled "Quadrature-Based Compressive Sensing Guarantees for Bounded Orthonormal Systems", to be submitted to the journal IEEE Signal Processing Letters. In this paper, we derive an approach to apply compressive sensing guarantees to linear inverse problems where measurements are samples of a function that can be expanded in a series of bounded orthonormal functions and require implementations using fast transform algorithms. In particular, we develop extensions of compressive sensing guarantees that can be used in the case described but where samples are taken on quadrature sample points instead of continuous sampling domains. This work has applications in antenna metrology, acoustic field measurements, astronomy, and more. The figures that this dataset is for are examples comparing transform algorithm times in continuous sample domains versus quadrature sample positions as well as comparisons of the performance of compressive sensing using continuous sampling versus quadrature-node-based sampling.

Resources

Name Format Description Link
8 Data contained in the columns of this file are given by the file header below (comma separated): Size of Legendre polynomial basis N (no relevant units).,Average time (s) to apply the Legendre polynomial sampling operator using continuously distributed measurements with a sample density of m/N = 0.25 using a recursive sampling algorithm.,Average time (s) to apply the Legendre polynomial sampling operator using continuously distributed measurements with a sample density of m/N = 0.5 using a recursive sampling algorithm.,Average time (s) to apply the Legendre polynomial sampling operator using continuously distributed measurements with a sample density of m/N = 0.75 using a recursive sampling algorithm.,Average time (s) to apply the Legendre polynomial sampling operator on the Gauss-Legendre quadrature nodes using a fast sampling algorithm. https://data.nist.gov/od/ds/mds2-3073/Figure_1_legendre_sample_timing.csv
0 This MATLAB script uses the above listed files to generate the figures used in the paper. https://data.nist.gov/od/ds/mds2-3073/paper_plot_script.m
0 A README file describing this dataset. https://data.nist.gov/od/ds/mds2-3073/README.txt
8 Data contained in the columns of this file are given by the file header below (comma separated):Normalized measurement number m/N (no relevant units) for compressive recovery of Legendre polynomial coefficients with N=100.,Normalized coefficient sparsity s/N (no relevant units) for compressive recovery of Legendre polynomial coefficients with N=100.,Average success rate (relative error of recovered coefficients < 0.001) for compressive recovery of Legendre polynomial coefficients using continuously random sample positions (distributed according to Chebyshev measure) with N=100. Averaging is over 50 trials where at each trial the coefficients have a randomly selected support of size s and m measurements taken. Values of the coefficients on this support are distributed according to the standard normal distribution and the the coefficient vector is renormalized to have unit 2-norm.,Average success rate (relative error of recovered coefficients < 0.001) for compressive recovery of Legendre polynomial coefficients using discrete random sample positions (see Corollary 4) with N=100. Averaging is over 5 trials where at each trial the coefficients have a randomly selected support of size s and m measurements taken. Values of the coefficients on this support are distributed according to the standard normal distribution and the the coefficient vector is renormalized to have unit 2-norm. https://data.nist.gov/od/ds/mds2-3073/Figure_2_legendre_polynomial_recovery.csv
8 Data contained in the columns of this file are given by the file header below (comma separated):Normalized measurement number m/N_D (no relevant units) for compressive recovery of Wigner D-function coefficients with n_max = 5 and noisy samples. Here N_D is the size of the Wigner D-function basis with n_max = 5.,Normalized coefficient sparsity s/N_D (no relevant units) for compressive recovery of Wigner D-function coefficients with n_max = 5 and noisy samples. Here N_D is the size of the Wigner D-function basis with n_max = 5.,Relative error in dB for compressive recovery of Wigner D-function coefficients with n_max = 5 and noisy samples that are continuously distributed (according to uniform measure on SO(3)). Averaging is over 50 trials where at each trial the coefficients have a randomly selected support of size s and m measurements taken. Values of the coefficients on this support are distributed according to the standard complex normal distribution and the the coefficient vector is renormalized to have unit 2-norm. Measurement noise is based on discrete sample positions and such that peak signal to noise ratio is 80 dB.,Relative error in dB for compressive recovery of Wigner D-function coefficients with n_max = 5 and noisy samples that are continuously distributed (see Corollary 5). Averaging is over 50 trials where at each trial the coefficients have a randomly selected support of size s and m measurements taken. Values of the coefficients on this support are distributed according to the standard complex normal distribution and the the coefficient vector is renormalized to have unit 2-norm. Measurement noise is based on discrete sample positions and such that peak signal to noise ratio is 80 dB. https://data.nist.gov/od/ds/mds2-3073/Figure_3_wigner_D_function_recovery.csv
8 Data contained in the columns of this file are given by the file header below (comma separated): Size of Legendre polynomial basis N (no relevant units).,Average time (s) to apply the adjoint Legendre polynomial sampling operator using continuously distributed measurements with a sample density of m/N = 0.25 using a recursive sampling algorithm.,Average time (s) to apply the adjoint Legendre polynomial sampling operator using continuously distributed measurements with a sample density of m/N = 0.5 using a recursive sampling algorithm.,Average time (s) to apply the adjoint Legendre polynomial sampling operator using continuously distributed measurements with a sample density of m/N = 0.75 using a recursive sampling algorithm.,Average time (s) to apply the adjoint Legendre polynomial sampling operator on the Gauss-Legendre quadrature nodes using a fast sampling algorithm. https://data.nist.gov/od/ds/mds2-3073/Figure_4_adjoint_legendre_sample_timing.csv

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  • acoustic-fields-antenna-characterization-compressive-sampling-compressive-sensing-far-field-pat

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