torchbp.interferometry module

torchbp.interferometry.elevation_to_phase_slant_polar(z, origin1, origin2, fcenter, grid)[source]

Compute traditional (slant-range) interferometric phase at given elevation.

For scatterers at height z above the imaging plane:

phi = (4pi fcenter/c0)*(r1 − r2)

where r_n = slant range in nth image

Traditional slant-range model with a single physical wavelength. Its z = 0 value is the flat-earth phase of that model, which is not the flat-earth phase of a dealiased backprojection interferogram (flat_earth_phase_polar() evaluated with the image fc); only the topographic difference phi(z) - phi(0) is used by phase_to_elevation_slant_polar().

Parameters:

  • z (Tensor or float) – Elevation map [nr, ntheta] or scalar height.

  • origin1 (Tensor) – Master APC [x, y, z].

  • origin2 (Tensor) – Slave APC [x, y, z].

  • fcenter (float) – Center frequency of the transmitted spectrum in Hz, sets the wavelength. Not necessarily the same as the backprojection fc, which is a phase reference (see Choosing fc for backprojection).

  • grid (PolarGrid or dict) – Polar grid definition.

Returns:

phase – Interferometric phase [nr, ntheta].

Return type:

Tensor

torchbp.interferometry.flat_earth_phase_cart(origin1, origin2, fc, grid)[source]

Compute flat earth interferometric phase for a Cartesian grid.

See flat_earth_phase_polar(): only images dealiased with their own origins carry this phase, with the opposite sign.

Parameters:

  • origin1 (Tensor) – 3D antenna phase center of the master image [x, y, z].

  • origin2 (Tensor) – 3D antenna phase center of the slave image [x, y, z].

  • fc (float) – Phase reference frequency the images were dealiased with, i.e. the fc given to torchbp.util.bp_polar_range_dealias(). This is the backprojection phase reference, not the transmitted center frequency (see Choosing fc for backprojection).

  • grid (CartesianGrid or dict) – Cartesian grid definition.

Returns:

phase – Flat earth phase tensor. Shape: [nx, ny].

Return type:

Tensor

torchbp.interferometry.flat_earth_phase_polar(origin1, origin2, fc, grid)[source]

Compute flat earth interferometric phase for a polar grid.

Images backprojected onto the flat (z=0) grid without dealiasing have no flat-earth phase: the phase compensation of each image already removes the range to its own origin, so the interferogram img1 * conj(img2) of flat terrain is zero and only the topographic signal remains. Images dealiased with torchbp.util.bp_polar_range_dealias(), each with its own origin, carry the dealias ramps and their interferogram over flat terrain is -flat_earth_phase_polar(origin1, origin2, fc, grid); add the returned phase to flatten it. Dealiasing both images with the same origin also leaves no flat-earth phase.

The sign is the traditional convention, opposite to the backprojection interferogram, consistent with the negation in phase_to_elevation().

Parameters:

  • origin1 (Tensor) – 3D antenna phase center of the master image [x, y, z].

  • origin2 (Tensor) – 3D antenna phase center of the slave image [x, y, z].

  • fc (float) – Phase reference frequency the images were dealiased with, i.e. the fc given to torchbp.util.bp_polar_range_dealias(). This is the backprojection phase reference, not the transmitted center frequency (see Choosing fc for backprojection).

  • grid (PolarGrid or dict) – Polar grid definition.

Returns:

phase – Flat earth phase tensor. Shape: [nr, ntheta].

Return type:

Tensor

torchbp.interferometry.goldstein_filter(igram, patch_size=64, w=3, alpha=1, overlap=0.75)[source]

Goldstein phase filter. [1]

Parameters:

  • igram (Tensor) – Complex interferogram.

  • patch_size (int) – Patch side-length.

  • w (int) – Smoothing window size. Must be odd.

  • alpha (float) – Smoothing exponent.

  • overlap (float) – Overlap between patches as fraction of patch_size.

Return type:

Tensor

References

[1]

R. M. Goldstein and C. L. Werner, “Radar interferogram filtering for geophysical applications,” in Geophysical Research Letters, vol. 25, no. 21, pp 4035-4038, 1998

Returns:

filtered – Filtered interferogram.

Return type:

Tensor

Parameters:

  • igram (Tensor)

  • patch_size (int)

  • w (int)

  • alpha (float)

  • overlap (float)

torchbp.interferometry.phase_to_elevation(unw, coords, origin1, origin2, fcenter, model='layover')[source]

Convert phase unwrapped interferogram to elevation.

Parameters:

  • unw (Tensor) – Unwrapped phase tensor. Shape: [Nx, Ny].

  • coords (Tensor) – Coordinates for each position in image. Shape: [3, Nx, Ny].

  • origin1 (Tensor) – 3D antenna phase center location of the master image.

  • origin2 (Tensor) – 3D antenna phase center location of the slave image.

  • fcenter (float) – Center frequency of the transmitted spectrum in Hz, sets the wavelength. Not necessarily the same as the backprojection fc, which is a phase reference (see Choosing fc for backprojection).

  • model (str) – Height-sensitivity model. "layover" (default): the scatterer imaged at a ground-plane pixel is the one whose master range equals the pixel’s. "point": the point-phase-center form (z2/r2 - z1/r1), which assumes the scatterer sits directly above the pixel. Not as accurate with layover.

Returns:

z – Elevation tensor with the same shape as unw.

Return type:

Tensor

torchbp.interferometry.phase_to_elevation_cart(unw, origin1, origin2, fcenter, grid, model='layover')[source]

Convert phase unwrapped interferogram to elevation.

Parameters:

  • unw (Tensor) – Unwrapped phase tensor. Shape: [Nx, Ny].

  • origin1 (Tensor) – 3D antenna phase center location of the master image.

  • origin2 (Tensor) – 3D antenna phase center location of the slave image.

  • fcenter (float) – Center frequency of the transmitted spectrum in Hz, sets the wavelength. Not necessarily the same as the backprojection fc, which is a phase reference (see Choosing fc for backprojection).

  • grid (CartesianGrid or dict) – Image grid definition. CartesianGrid object or dictionary.

  • model (str) – Height-sensitivity model. "layover" (default): the scatterer imaged at a ground-plane pixel is the one whose master range equals the pixel’s. "point": the point-phase-center form (z2/r2 - z1/r1), which assumes the scatterer sits directly above the pixel. Not as accurate with layover.

Returns:

z – Elevation tensor with the same shape as unw.

Return type:

Tensor

torchbp.interferometry.phase_to_elevation_polar(unw, origin1, origin2, fcenter, grid, model='layover')[source]

Convert phase unwrapped interferogram to elevation.

Parameters:

  • unw (Tensor) – Unwrapped phase tensor. Shape: [Nx, Ny].

  • origin1 (Tensor) – 3D antenna phase center location of the master image.

  • origin2 (Tensor) – 3D antenna phase center location of the slave image.

  • fcenter (float) – Center frequency of the transmitted spectrum in Hz, sets the wavelength. Not necessarily the same as the backprojection fc, which is a phase reference (see Choosing fc for backprojection).

  • grid (PolarGrid or dict) – Image grid definition. PolarGrid object or dictionary.

  • model (str) – Height-sensitivity model. "layover" (default): the scatterer imaged at a ground-plane pixel is the one whose master range equals the pixel’s. "point": the point-phase-center form (z2/r2 - z1/r1), which assumes the scatterer sits directly above the pixel. Not as accurate with layover.

Returns:

z – Elevation tensor with the same shape as unw.

Return type:

Tensor

torchbp.interferometry.phase_to_elevation_slant_polar(unw, origin1, origin2, fcenter, grid, n_iter=5)[source]

Convert unwrapped topographic phase to elevation via Newton iteration.

Inverts the traditional interferometric relationship:

phi_topo(z) = elevation_to_phase_slant_polar(z, ...)
           − elevation_to_phase_slant_polar(0, ...)

Starts from the linearised BP-interferometry estimate and refines with Newton’s method.

Parameters:

  • unw (Tensor) – Unwrapped topographic phase (flat-earth removed) [nr, ntheta].

  • origin1 (Tensor) – Master APC [x, y, z].

  • origin2 (Tensor) – Slave APC [x, y, z].

  • fcenter (float) – Center frequency of the transmitted spectrum in Hz, sets the wavelength. Not necessarily the same as the backprojection fc, which is a phase reference (see Choosing fc for backprojection).

  • grid (PolarGrid or dict) – Polar grid definition.

  • n_iter (int) – Number of Newton iterations (default 5).

Returns:

z – Estimated elevation [nr, ntheta].

Return type:

Tensor

torchbp.interferometry.subpixel_correlation(im_m, im_s)[source]

Solve for subpixel offset that maximize coherent correlation between the two input images. [1]

Parameters:

  • im_m (Tensor) – Master image.

  • im_s (Tensor) – Slave image.

Return type:

tuple[Tensor, Tensor]

References

[1]

D. Li and Y. Zhang, “A Fast Offset Estimation Approach for InSAR Image Subpixel Registration,” in IEEE Geoscience and Remote Sensing Letters, vol. 9, no. 2, pp. 267-271, March 2012.

Returns:

  • offsets (Tensor) – Solved X and Y subpixel offsets.

  • corrs (Tensor) – Correlation at the best subpixel offset.

Parameters:

  • im_m (Tensor)

  • im_s (Tensor)

Return type:

tuple[Tensor, Tensor]