About this Dataset

Data For "Quadrature-Based Compressive Sensing Guarantees For Bounded Orthonormal Systems", To Be Submitted To IEEE Signal Processing Letters

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.
Organization: Department of Commerce
Last updated: 2025-09-30T05:25:20.208873
Tags: acoustic-fields-antenna-characterization-compressive-sampling-compressive-sensing-far-field-pat

Tables

Figure 1 Legendre Sample Timing

@usgov.doc_gov_data_for_quadrature_based_compressive_sensing__449bd9e9.figure_1_legendre_sample_timing

7.51 kB
20 rows
5 columns

CREATE TABLE figure_1_legendre_sample_timing (
  "size_of_legendre_polynomial_basis_n_no_relevant_units" DOUBLE  -- Size Of Legendre Polynomial Basis N (no Relevant Units).,
  "average_time_s_to_apply_the_legendre_polynomial_sampli_a9683e66" DOUBLE  -- 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_sampli_737f12bd" DOUBLE  -- 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_sampli_fe6f93c3" DOUBLE  -- 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_sampli_e1904ec7" DOUBLE  -- Average Time (s) To Apply The Legendre Polynomial Sampling Operator On The Gauss-Legendre Quadrature Nodes Using A Fast Sampling Algorithm.
);

Figure 2 Legendre Polynomial Recovery

@usgov.doc_gov_data_for_quadrature_based_compressive_sensing__449bd9e9.figure_2_legendre_polynomial_recovery

6.53 kB
400 rows
4 columns

CREATE TABLE figure_2_legendre_polynomial_recovery (
  "normalized_measurement_number_m_n_no_relevant_units_fo_0d9c0d21" DOUBLE  -- 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__4eae52f9" DOUBLE  -- 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_coeff_9b6267f2" DOUBLE  -- 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 Measurments Taken. Values Of The Coefficients On This Support Are Distributed According To The Standard Normal Distribution And The The Coefficeint Vector Is Renormalized To Have Unit 2-norm.,
  "average_success_rate_relative_error_of_recovered_coeff_c271cdff" DOUBLE  -- 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 Measurments Taken. Values Of The Coefficients On This Support Are Distributed According To The Standard Normal Distribution And The The Coefficeint Vector Is Renormalized To Have Unit 2-norm.
);

Figure 3 Wigner D Function Recovery

@usgov.doc_gov_data_for_quadrature_based_compressive_sensing__449bd9e9.figure_3_wigner_d_function_recovery

12.95 kB
400 rows
4 columns

CREATE TABLE figure_3_wigner_d_function_recovery (
  "normalized_measurement_number_m_n_d_no_relevant_units__cb6f0fec" DOUBLE  -- 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_unit_fe5ef325" DOUBLE  -- 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_wigne_69efd0ec" DOUBLE  -- 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 Measurments Taken. Values Of The Coefficients On This Support Are Distributed According To The Standard Complex Normal Distribution And The The Coefficeint Vector Is Renormalized To Have Unit 2-norm. Measurment 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_wigne_a1a48348" DOUBLE  -- 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 Measurments Taken. Values Of The Coefficients On This Support Are Distributed According To The Standard Complex Normal Distribution And The The Coefficeint Vector Is Renormalized To Have Unit 2-norm. Measurment Noise Is Based On Discrete Sample Positions And Such That Peak Signal To Noise Ratio Is 80 DB.
);

Figure 4 Adjoint Legendre Sample Timing

@usgov.doc_gov_data_for_quadrature_based_compressive_sensing__449bd9e9.figure_4_adjoint_legendre_sample_timing

7.51 kB
20 rows
5 columns

CREATE TABLE figure_4_adjoint_legendre_sample_timing (
  "size_of_legendre_polynomial_basis_n_no_relevant_units" DOUBLE  -- Size Of Legendre Polynomial Basis N (no Relevant Units).,
  "average_time_s_to_apply_the_adjoint_legendre_polynomia_577ed37f" DOUBLE  -- 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_polynomia_d44ba222" DOUBLE  -- 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_polynomia_5c6636b6" DOUBLE  -- 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_polynomia_a5789baa" DOUBLE  -- Average Time (s) To Apply The Adjoint Legendre Polynomial Sampling Operator On The Gauss-Legendre Quadrature Nodes Using A Fast Sampling Algorithm.
);