Emerging ultrasound phased-array technologies will soon enable the acquisition of high-resolution 3D+T images for medical applications. Processing the huge amount of spatiotemporal measurements remains a practical challenge. In this work, dynamic ultrasound images are sparsely represented by a mixture of moving speckles. We model the shape of a speckle and its locally linear motion with a weighted multivariate Gaussian kernel. Parameters of the model are estimated with online Bayesian learning from a stream of random measurements. In our preliminary experiments with a simulated phantom of a moving cylindrical structure, the optical flow of speckles is estimated for a vertical line profile and compared to the ground truth. The mean accuracy of the linear motion estimate is of 93.53%, using only a statistically sufficient random subset of the data.