## 1 Introduction  
Ultrasound strain elastography (USE) [1] can provide new information than that contained in B-Mode ultrasound images, which display only the amplitudes of envelope detected and decimated echo signals. USE has been successfully used for breast lesion differentiation [2; 3; 4] because it is capable of visualizing elevated tissue hardness. The strain/modulus nonlinearity has been also exploredby others in order to better characterize breast lesions [5; 6; 7]. Furthermore, a number of studies in the literature has been devoted to understanding signal quality [8], image resolution [9; 10] and contrast [11; 12] in USE. In this study, we solely focus on ultrasound-based motion tracking, because it plays a critically important role in USE. Among all motion tracking algorithms [13], the block-matching algorithm is one of the most used correlation-based methods and has been adopted by several prototype USE systems [14; 15; 16; 17; 18; 19; 20; 21] due to its simplicity. Furthermore, the block-matching algorithm can also be easily extended to include motion regularization or multi-scale tracking to deal with large tissue deformation. In the framework of block matching algorithm, similarity or correlation evaluation influences both motion tracking accuracy and computational efficiency [22]. The commonly used similarity/correlation evaluation metrics include sum absolute error, sum square error and (SSD), entropy, and normalized cross-correlation (NCC). NCC has been proved to be one of the best similarity matching criteria in block matching methods [22] and therefore, has been widely used in various ultrasound-based motion tracking algorithms. One drawback of using the NCC as a correlation metric is that calculating NCC following the standard protocol is computationally intensive, thereby limiting its use in many ultrasound techniques requiring real-time performance. [PERSON] proposed to use a pre-computed table in conjunction with a fast Fourier Transform (FFT) to calculate NCC values. His method is often referred as to Sum-Table (ST) method now [23]. [PERSON] et al. further modified [PERSON] approach [22] by replacing the requirement of using FFT with another ST. Both methods [22; 23] have demonstrated that they can achieve almost the same accuracy together with significantly faster calculation efficiency in a serial computing environment in which i.e., calculations are conducted by a central processing unit (CPU). Several major vendors (e.g., General Electric, Siemens, Philips, Hitachi, Toshiba, Samsung Medison, etc.) have released their commercially-available USE packages. However, those clinical USE systems all operate in 2D. However, continued efforts [16; 19; 24; 25; 26; 27; 28] are under the way to expand USE into 3-D because 3-D tracking can significantly improve quality of strain elastograms [16; 19]. Now FDA-approved 3-D automated breast ultrasound (ABUS) systems (e.g., GE InveniaTM; Siemens Acuson S2000 ABVS) have been released. It is our vision that with the availability of GPU-acceleration, bringing 3-D breast USE into the clinical workflow becomes possible. In the last decade, GPU-based parallel computing has been utilized to accelerate ultrasound-based motion tracking in several important applications including USE [21; 29; 30; 31], shear wave elastography [32] and color Doppler imaging [33]. In particular, the work by [PERSON] et al. [21] demonstrated that high quality strain data can be obtained for a reasonably large volume (e.g., \(2.5\times 2.5\times 2.5\) cm\({}^{3}\)) in 20 s. Consequently, investigating whether or not the concept of ST can be used to further improve 3-D motion tracking is a logical next step. To this end, our primary goal is to investigate the feasibility of using ST in conjunction with GPUs to further accelerate 3-D motion tracking. Thus, two above-mentioned ST methods (i.e., [PERSON] and [PERSON]'s methods) were analyzed and implemented for parallel (GPU) and serial (CPU) computing settings.