Two-dimensional iterative projection method for subsample speckle tracking of ultrasound images
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ORIGINAL ARTICLE
Two-dimensional iterative projection method for subsample speckle tracking of ultrasound images Brandon Rebholz1
· Fei Zheng1 · Mohamed Almekkawy1
Received: 29 October 2019 / Accepted: 1 September 2020 © International Federation for Medical and Biological Engineering 2020
Abstract Speckle tracking provides robust motion estimation necessary to create accurate post-processed images. These methods are known to be less accurate in the lateral dimension compared with the axial dimension due to the limitations on the lateral resolution of ultrasound scanning. This paper proposes a two-dimensional iterative projection (TDIP) algorithm using the Riesz transform to generate the analytic signals. The TDIP is an improvement to an already accurate speckle tracking algorithm called the phase coupled (PC) method. The PC method projects the intersection of gradients on the correlation map to the zero phase contour to estimate displacement. The TDIP method performs iterative projections and uses the aggregate of these projected locations to estimate the motion, in addition to rejecting inaccurate projections by checking them against the aggregate projection location. The TDIP additionally adopts the Riesz transform to generate two-dimensional analytic signals to improve lateral accuracy. The Riesz transform is a multidimensional extension of the Hilbert transform into the nD Euclidean space and therefore can be used to include data in both axial and lateral dimensions as opposed to the commonly used Hilbert transform which is one dimensional. The accuracy of the TDIP is quantitatively proven on simulated datasets from the Field II simulation program and on experimental data from two flow phantoms. At all cases, the TDIP is more accurate than the PC algorithm at two-dimensional displacement estimation. Keywords Speckle tracking · Motion detection · Riesz transform
1 Introduction Speckle tracking is a prolific division of algorithms that track motion between image frames, and is extensively used on ultrasound images. In ultrasound imaging, these speckles result from the combinations of destructive and constructive interference of echoes from scatterers in the observed tissue [1]. Speckle tracking algorithms provide estimates for fine tissue displacement and are integral to the fields of elastography, since strain imaging often relies heavily on accurate displacement estimates. Various algorithms have been developed to produce displacement estimates via speckle tracking [2–5]. In addition to speckle tracking algorithms, which track motion by some measure of similarity like cross
Brandon Rebholz
[email protected] 1
School of Electrical Engineering and Computer Science, The Pennsylvania State University, University Park, PA, USA
correlation, there are other methods of estimating motion in ultrasound. Optical flow methods [6, 7] are one of these alternatives for speckle tracking. Optical flow methods estimate displacement by a function of the gradients in either the spatial or temporal domain; however, the res
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