A Low Complexity Scheme for Accurate 3D Velocity Estimation in Ultrasound Systems ‡ Siyuan Wei, Ming Yang, Chaitali Chakrabarti SECEE, Arizona State University, Tempe, AZ 85287 {siyuan.wei, m.yang, chaitali}@asu.edu Richard Sampson, Thomas F. Wenisch EECS, University of Michigan, Ann Arbor, MI 48109 {rsamp, twenisch}@umich.edu Oliver Kripfgans and J. Brian Fowlkes Dept. of Radiology, University of Michigan, Ann Arbor, MI 48109 {greentom, fowlkes}@umich.edu Abstract—Vector flow imaging is a critical component in the clinical diagnosis of cardiovascular diseases; however, most current methods are too computationally expensive to scale well to 3D. Less complex techniques, such as Doppler-based imaging (which cannot provide lateral flow measurements) and basic speckle tracking algorithms (which have poor lateral accuracy), are incapable of producing high quality 3D measurements. In this paper, we first extend a technique designed to improve lateral flow accuracy for 2D velocity vector estimation, the synthetic lateral phase method, to 3D (SLP-3D). We then show that a straight- forward implementation of this algorithm is too computationally complex for modern systems. Instead, we propose a two-tiered method that uses low complexity sum-of-absolute differences (SAD) for coarse-grained search and an optimized version of SLP- 3D to fine tune the search for sub-pixel accuracy. We show that the proposed method (SAD+SLP-3Dopt) achieves a 9× reduction in computational complexity compared to the naive SLP-3D. Field II simulations for plug and parabolic flow using our method show a fairly high degree of accuracy in both the axial and the lateral components. Finally, we show our technique can support accurate flow imaging with up to 130 velocity estimations/sec within the power constraints of a handheld device. I. I NTRODUCTION Ultrasound-based vector flow imaging is a critical modality for diagnosing numerous cardiovascular conditions, such as stenosis. The advent of 3D vector flow imaging has the po- tential to further enhance diagnostic capabilities, for example, by facilitating precise calculation of volumetric flow across an arbitrary plane through a vessel [1]. Furthermore, collecting a complete velocity vector field within a 3D region of interest enables derivation of other important flow parameters, such as pressure drops associated with flow restrictions [2]–[4]. While 3D flow imaging presents great promise, high computational complexity (and, correspondingly, high power consumption) makes it difficult to scale existing methods for 2D flow imaging into the third dimension, particularly for a hand-held ultrasound platform with tight power and thermal constraints. In addition to the already high complexity of beam- forming for 3D images [5]–[8], 3D velocity estimation typical- ly requires many more firings and an order of magnitude more computation than a comparable 2D system. Low-complexity flow imaging techniques, such as Doppler-based imaging and basic speckle tracking algorithms, are incapable of producing high quality 3D measurements. For instance, Doppler methods are unable to measure lateral velocity components [9]. Basic speckle tracking schemes often employ time-delay estimators, such as sum of absolute difference (SAD), sum of squared ‡ This work was supported in part by NSF CCF-1406739, CCF-1406810, CCF-0815457 and CSR-0910699. difference (SSD) and normalized cross correlation (NCC). Although these estimators provide excellent accuracy in the axial dimension, they are much less accurate in lateral dimen- sions due to the comparatively poor lateral resolution in 3D ultrasound. Many efforts have been made to improve lateral veloci- ty estimation accuracy, including 3D interpolation based on polynomial fitting [10] and transverse oscillation that utilizes lateral modulation created by superposition of multiple ultra- sound waves firing from multiple angles [3]. The synthetic lateral phase (SLP) method for 2D speckle tracking [11] has been shown to significantly improve the accuracy of lateral displacement estimations in elastography by enabling sub-pixel lateral resolution. In this work, we demonstrate how to extend SLP to three dimensions (SLP-3D). Whereas the SLP algorithm is both efficient and accurate in 2D, a naive extension to the 3D case results in an enormous computational burden; therefore, we also present optimizations that make SLP-3D computa- tionally tractable. We propose a two-tiered method that uses low complexity sum-of-absolute differences (SAD) for coarse- grained search and an optimized version of SLP-3D for fine tuning the search to achieve sub-pixel accuracy. We focus on 3D flow tracking for plane wave 3D imaging since such a system enables high frame rates (up to 6,000 3D frames/sec [8]) for tracking high velocity motion. The proposed method (SAD+SLP-3Dopt) achieves a 9× reduction in computation- al complexity (measured as a weighted sum of arithmetic operations) compared to the naive SLP-3D. We validate the image quality using Field II simulations for plug flow and parabolic flow, demonstrating a fairly high degree of accuracy in both the axial and the lateral components. Finally, we show our technique can support accurate flow imaging with up to 130 velocity estimations/sec within the power constraints of a handheld device. The rest of the paper is organized as follows. In Section II, we introduce the plane wave system used in this paper and the basic time-delay estimators (TDE) used for speckle tracking. In Section III, we compare the performance and computational complexity of the basic TDEs. In Section IV, we propose to use the extension of synthetic lateral phase in 3D for flow estimation. In Section V, we introduce our proposed method and the techniques to reduce its computational complexity. In Section VI, we present the simulation results. We conclude the paper in Section VII. U.S. Government work not protected by U.S. copyright