Multiscale optical flow computation from the monogenic signal

Two-dimensional iterative projection method for subsample speckle tracking of ultrasound images

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. Graphical Abstract The lateral estimates from the Phase Coupled algorithm. This method uses the Hilbert transform for the analytic signal. There is large estimated motion within the flow blockage bounded by the red, fin shape in the center of the flow channel. The flow channel itself is also bounded by dashed, red lines. Graphical Abstract The lateral estimates from the TDIP method. This method is not tracking motion within the blockage in the center of the flow channel. The channel and the blockage are both bounded by dashed, red lines.