Module lib.generate_data

Helper functions to generate synthetic datasets such as those considered in [Abdulaziz2019, Thouvenin2021].

lib.generate_data.generate_cube(file_name, f, emission_lines)

Script to generate a fully synthetic image cube as in [Abdulaziz2019].

Parameters

  • file_name (string) – Name of a reference monochromatic image in .fits format.

  • f (double[:]) – Frequencies over which the wideband image is generated.

  • emission_lines (bool) – If set to true, insert emission lines in the synthetic wideband image.

Returns

  • x0 (double[:, :, :]) – Synthetic wideband image (3D) [N(1), N(2), L].

  • X0 (double[:, :]) – Synthetic wideband image (reshape in 2D format) [N(1)*N*(2), L].

lib.generate_data.generate_cube_W28(file_name, f, emission_lines)

Script to generate a fully synthetic image cube as in [Abdulaziz2019] tailored to W28.

Parameters

  • file_name (string) – Name of a reference monochromatic image in .fits format.

  • f (double[:]) – Frequencies over which the wideband image is generated.

  • emission_lines (bool) – If set to true, insert emission lines in the synthetic wideband image.

Returns

  • x0 (double[:, :, :]) – Synthetic wideband image (3D) [N(1), N(2), L].

  • X0 (double[:, :]) – Synthetic wideband image (reshape in 2D format) [N(1)*N*(2), L].

lib.generate_data.generate_undersampled_cube(x0, f, Ny, Nx, c, unds)

Function returning a spectrally undersampled version of an input wideband image cube.

Parameters

  • x0 (double[:, :, :]) – Synthetic wideband image (3D) [Ny, Nx, c].

  • f (double[:]) – Frequencies over which the wideband image x0 is defined.

  • Ny (int) – Spatial dimension of x0 along axis y.

  • Nx (int) – Spatial dimension of x0 along axis y.

  • c (int) – Spectrsl dimension of x0.

  • unds (int) – Spectral downsampling factor.

Returns

  • x0_new (double[:, :, :]) – Output wideband image.

  • X0_new (double[:, :, :]) – Matrix-format version of x0_new.

  • f_new (double[:]) – Frequencies over which x0_new is defined.

  • c_new (int) – Number of spectral channels after spectral downsmapling.

lib.generate_data.stationary_Gaussian_process(m, n, rho)

Draw a realization of a stationary random Gaussian field over an :math`m times n` grid, following [Kroese2015].

Parameters

  • m (int) – Image dimension (y axis).

  • n (int) – Image dimension (x axis).

  • rho (anonymous function) – Function handle, function of a matrix \(h\) such that \(\text{cov}(X_t, Y_s) = \rho(t-s)\) is the covariance of a 2-dimensional stationary Gaussian field.

Returns

  • field1, field2 (double[:, :]) – Two independent realization over the :math`m times n` grid considered.

  • tx, ty (double[:]) – Two vectors such that each field can be displayed using the command imagesc(tx, ty, field1) (idem for field2).

Example

Note

  • The size of covariance matrix is m^2*n^2.

  • By default, when the function is called without assigning the output, field1 is drectly display using the imagesc MATLAB function.

lib.generate_data.util_gen_measurements(x, G, W, A, input_snr)

Generate noisy visibilities over several spectral channels.

Parameters

  • x (double[:, :, :]) – Input wodeband image.

  • G (cell of cell of sparse complex[:, :]) – Degridding matrix (per channel, per block).

  • W (cell of cell of int[:]) – Selection vector to extract data blocks from the full Fourier plane.

  • A (anonymous function.) – Function handle implementing the NUFFT.

  • input_snr (double) – Target input SNR taken over all channels.

Returns

  • y0 (cell of cell of complex[:]) – Clean (i.e., noiseless) visibilities.

  • y (cell of cell of complex[:]) – Noisy visibilities.

  • Nm (int) – Total number of visbilities (across all data blocks and channels).

  • sigma_noise (double) – Overall noise level.

lib.generate_data.util_gen_measurements_sigma(x, G, W, A, sigma_noise, seed)

Generate noisy synthetic viasilities using a predefined noise level.

Parameters

  • x (double[:, :, :]) – Input wodeband image.

  • G (cell of cell of sparse complex[:, :]) – Degridding matrix (per channel, per block).

  • W (cell of cell of int[:]) – Selection vector to extract data blocks from the full Fourier plane.

  • A (anonymous function.) – Function handle implementing the NUFFT.

  • sigma_noise (double) – Overall noise level.

  • seed (int) – Seed to initialize the random number generator.

Returns

  • y0 (cell of cell of complex[:]) – Clean (i.e., noiseless) visibilities.

  • y (cell of cell of complex[:]) – Noisy visibilities.

  • Nm (int) – Total number of visbilities (across all data blocks and channels).

lib.generate_data.util_gen_measurements_snr(x, G, W, A, input_snr, rng_stream)

Generate noisy synthetic viasilities using a predefined per-channel input SNR.

Parameters

  • x (double[:, :, :]) – Input wodeband image.

  • G (cell of cell of sparse complex[:, :]) – Degridding matrix (per channel, per block).

  • W (cell of cell of int[:]) – Selection vector to extract data blocks from the full Fourier plane.

  • A (anonymous function.) – Function handle implementing the NUFFT.

  • input_snr (double[:]) – Input SNR for each spectral channel.

  • rng_stream (random number generator) – Random number generator.

Returns

  • y0 (cell of cell of complex[:]) – Clean (i.e., noiseless) visibilities.

  • y (cell of cell of complex[:]) – Noisy visibilities.

  • Ml (int[:]) – Number of data points in each spectral channel.

  • Nm (int) – Total number of visbilities (across all data blocks and channels).

  • sigma_noise (double[:]) – Noise level in each spectral channel.

  • norm_noise (double[:]) – Euclidean norm of the Gaussian noise affecting each data channel.

lib.generate_data.util_gen_measurements_snr_new(x, G, W, A, input_snr, rng_stream)

Generate noisy synthetic viasilities using a predefined per-channel input SNR.

Parameters

  • x (double[:, :, :]) – Input wodeband image.

  • G (cell of cell of sparse complex[:, :]) – Degridding matrix (per channel, per block).

  • W (cell of cell of int[:]) – Selection vector to extract data blocks from the full Fourier plane.

  • A (anonymous function.) – Function handle implementing the NUFFT.

  • input_snr (double[:]) – Input SNR for each spectral channel.

  • rng_stream (random number generator) – Random number generator.

Returns

  • y0 (cell of cell of complex[:]) – Clean (i.e., noiseless) visibilities.

  • y (cell of cell of complex[:]) – Noisy visibilities.

  • Ml (int[:]) – Number of data points in each spectral channel.

  • Nm (int) – Total number of visbilities (across all data blocks and channels).

  • sigma_noise (double[:]) – Noise level in each spectral channel.

  • norm_noise (double[:]) – Euclidean norm of the Gaussian noise affecting each data channel.

  • G (cell of cell of sparse complex[:, :]) – Degridding matrix (per channel, per block) including noise whitening contribution.

lib.generate_data.util_gen_sampling_pattern(pattern, param)

Function to generate a synthetic \(uv\)-coverage as in [Onose2017].

Parameters

  • pattern (string) – Type of \(uv\)-coverage. Available options are …

  • param (struct) – Configuration options for the generation of the synthetic sampling pattern (to be completed).

Returns

  • u – [description]

  • v – [description]

  • uw – [description]

  • vw – [description]

  • Nm – [description]