zea.inverse¶
Inverse beamforming: recover channel data from beamformed images.
The zea.inverse subpackage inverts the delay-and-sum (DAS) beamformer: it
recovers pre-beamformed channel data from a post-beamformed image by
expressing the beamformer as a differentiable linear operator and solving a
least-squares problem — optionally regularized with a point-scatterer prior.
Modules¶
zea.inverse.operators– The DAS beamformer as a differentiable linear operator (DASOperator) and a time-domain point-scatterer simulator (ScattererSimulator).zea.inverse.solvers– Matrix-free solver primitives (cgls(),linear_adjoint()).zea.inverse.seeding– Scatterer seeding from a beamformed image (seed_scatterers()).zea.inverse.inversion– High-level inversion drivers (invert_direct(),invert_scatterers()).
The DAS beamformer sums on the order of n_el * n_tx samples into every
pixel, so inverting a single compounded image for the full channel-data cube
is well-posed for data fit but severely underdetermined for recovery.
invert_direct() makes this concrete by computing the minimum-norm
(pseudo-inverse) solution, while invert_scatterers() regularizes the
nullspace with a physical point-scatterer parameterization, which recovers
channel data far better on point-target scans.
The scatterer-prior inversion follows the off-grid stochastic-optimization scatterer model of van de Schaft et al., Off-Grid Ultrasound Imaging by Stochastic Optimization (arXiv:2407.02285).
Example
import zea
from zea.inverse import DASOperator, invert_scatterers
with zea.File("path/to/scan.hdf5") as file:
parameters = file.load_parameters(
xlims=(-0.018, 0.018), zlims=(0.003, 0.04), pixels_per_wavelength=2
)
raw_data = file.data.raw_data[0, ..., 0] # first frame, RF
operator = DASOperator(parameters)
image = operator.forward(raw_data)
result = invert_scatterers(operator, image, n_scatterers=15000, n_iter=70)
# result.channel_data is the recovered pre-beamformed data cube
For a walkthrough see the tutorials: Inverse beamforming: recovering channel data with zea.inverse (synthetic), Inverse beamforming on a CIRS phantom scan (recorded phantom scan), and Inverse beamforming on an in-vivo carotid scan (in-vivo).
Modules