Speckle coherence of piecewise-stationary stochastic targets.

Journal Article (Journal Article)

The van Cittert-Zernike (VCZ) theorem describes the propagation of spatial covariance from an incoherent source distribution, such as backscatter from stochastic targets in pulse-echo imaging. These stochastic targets are typically assumed statistically stationary and spatially incoherent with uniform scattering strength. In this work, the VCZ theorem is applied to a piecewise-stationary scattering model. Under this framework, the spatial covariance of the received echo data is demonstrated as the linear superposition of covariances from distinct spatial regions. This theory is analytically derived from fundamental physical principles, and validated through simulation studies demonstrating superposition and scaling. Simulations show that linearity is preserved over various depths and transmit apodizations, and in the presence of noise. These results provide a general framework to decompose spatial covariance into contributions from distinct regions of interest, which may be applied to advanced imaging methods. While the simulation tools used for validation are specific to ultrasound, this analysis is generally applicable to other coherent imaging applications involving stochastic targets. This covariance decomposition provides the physical basis for a recently described imaging method, Multi-covariate Imaging of Sub-resolution Targets.

Full Text

Duke Authors

Cited Authors

  • Morgan, MR; Trahey, GE; Walker, WF

Published Date

  • September 2019

Published In

Volume / Issue

  • 146 / 3

Start / End Page

  • 1721 -

PubMed ID

  • 31590494

Pubmed Central ID

  • PMC6760971

Electronic International Standard Serial Number (EISSN)

  • 1520-8524

International Standard Serial Number (ISSN)

  • 0001-4966

Digital Object Identifier (DOI)

  • 10.1121/1.5126686


  • eng