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Image registration and motion estimation play central roles in many fields, including RADAR, SONAR, light microscopy, and medical imaging. Because of its central significance, estimator accuracy, precision, and computational cost are of critical importance. We have previously presented a highly accurate, spline-based time delay estimator that directly determines sub-sample time delay estimates from sampled data. The algorithm uses cubic splines to produce a continuous representation of a reference signal and then computes an analytical matching function between this reference and a delayed signal. The location of the minima of this function yields estimates of the time delay. In this paper we describe the MUlti-dimensional Spline-based Estimator (MUSE) that allows accurate and precise estimation of multidimensional displacements/strain components from multidimensional data sets. We describe the mathematical formulation for two-and three-dimensional motion/strain estimation and present simulation results to assess the intrinsic bias and standard deviation of this algorithm and compare it to currently available multi-dimensional estimators. In 1000 noise-free simulations of ultrasound data we found that 2D MUSE exhibits maximum bias of 2.6 × 10 −4 samples in range and 2.2 × 10 −3 samples in azimuth (corresponding to 4.8 and 297 nm, respectively). The maximum simulated standard deviation of estimates in both dimensions was comparable at roughly 2.8 × 10 −3 samples (corresponding to 54 nm axially and 378 nm laterally). These results are between two and three orders of magnitude better than currently used 2D tracking methods. Simulation of performance in 3D yielded similar results to those observed in 2D. We also present experimental results obtained using 2D MUSE on data acquired by an Ultrasonix Sonix RP imaging system with an L14-5/38 linear array transducer operating at 6.6 MHz. While our validation of the algorithm was performed using ultrasound data, MUSE is broadly applicable across imaging applications.

Existing methods for characterizing the imaging performance of ultrasound systems do not clearly quantify the impact of contrast, spatial resolution, and signal-to-noise ratio (SNR). Although the beamplot, contrast resolution metrics, SNR measurements, ideal observer methods, and contrastdetail analysis provide useful information, it remains difficult to discern how changes in system parameters affect these metrics and clinical imaging performance. In this paper, we present a rigorous methodology for characterizing the pulse-echo imaging performance of arbitrary ultrasound systems. Our metric incorporates the 4-D spatio-temporal system response, which is defined as a function of the individual beamformer channel weights. The metric also incorporates the individual beamformer channel electronic SNR. Whereas earlier performance measures dealt solely with contrast resolution or echo signal-to-noise ratio, our metric combines them so that tradeoffs between these parameters are easily distinguishable. The new metric quantifies an arbitrary system's contrast resolution and SNR performance as a function of cyst size, beamformer channel weights, and beamformer channel SNR.We present a theoretical derivation of the unified performance metric and provide simulation and experimental results highlighting the metric's utility. We compare the fundamental performance limits of 2 beamforming strategies: the dynamic focus finite impulse response (FIR) filter beamformer and the spatial matched filter (SMF) beamformer to the performance of the conventional delay-and-sum (DAS) beamformer. Results from this study show that the SMF beamformer and the FIR beamformer offer significant gains in beamformer SNR and contrast resolution compared with the DAS beamformer, respectively. The metric clearly distinguishes the performance of the SMF beamformer, which enhances system sensitivity, from the FIR beamformer, which optimizes system contrast resolution. Finally, the metric provides one quantitative goal for optimizing a broadband beamformer's contrast resolution performance.