title: Analysis of correlation coefficient filtering in elasticity imaging.
abstract: Correlation-based speckle tracking methods are commonly used in elasticity imaging to estimate displacements. In the presence of local strain, a larger window size results in larger displacement error. To reduce tracking error, we proposed a short correlation window followed by a correlation coefficient filter. Although simulation and experimental results demonstrated the efficacy of the method, it was not clear why correlation coefficient filtering reduces tracking error since tracking error increases if normalization before filtering is not applied. In this paper, we analyzed tracking errors by estimating phase variances of the cross-correlation function and the correlation coefficient at the true time lag based on statistical properties of these functions' real and imaginary parts. The role of normalization is clarified by identifying the effect of the cross-correlation function's amplitude fluctuation on the function's imaginary part. Furthermore, we present analytic forms for predicting axial displacement error as a function of strain, system parameters (signal-to-noise ratio, center frequency, and signal and noise bandwidths), and tracking parameters (window and filter sizes) for cases with and without normalization before filtering. Simulation results correspond to theory well for both noise-free cases and general cases with an empirical correction term included for strains up to 4%.
authors.affiliation: Department of Biomedical Engineering, University of Michigan, Ann Arbor, MI, USA. shengwen@umich.edu
authors.forename: Sheng-Wen
authors.initials: SW
authors.lastname: Huang
authors.forename: Jonathan M
authors.initials: JM
authors.lastname: Rubin
authors.forename: Hua
authors.initials: H
authors.lastname: Xie
authors.forename: Russell S
authors.initials: RS
authors.lastname: Witte
authors.forename: Congxian
authors.initials: C
authors.lastname: Jia
authors.forename: Ragnar
authors.initials: R
authors.lastname: Olafsson
authors.forename: Matthew
authors.initials: M
authors.lastname: O'Donnell
mesh_terms: D000465:Algorithms; D055119:Elastic Modulus; D054459:Elasticity Imaging Techniques / Q000379:methods*; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013223:Statistics as Topic