Reconstruction of volumes from imperfectly known transducer location for low-cost ultrasonic imaging

Reconstructing a three-dimensional ultrasound volume from freehand planar scans for low-cost applications requires the acquired planar data be placed in three-dimensional space. Placement is based on the reported position and orientation of the transducer from 6- or 9-degree of freedom sensors. While the literature reports adequate resolution and accuracy for reconstruction from expensive electromagnetic sensors, low-cost inertial sensors typically have poor position estimates due to drift in accelerometer readings. We formulate this problem as one of estimation of the parameters of position and orientation for ultrasound signals in the complex signal domain, wherein the “new” pose of the transducer is a Euclidean transform of the “prior” pose. It can be shown that this transform can be estimated from calibrated correlation functions from one cartesian translation and two rotations in combination with the low-cost sensor. Ideal cartesian translation of a Verasonics L12-3v transducer were used to validate the proposed method and demonstrated mean errors of −4.7 and 6.0 microns for translations of λ and 2λ with respective standard deviations of ±10.3 and ±20.2 microns and error ranges (min,max) of 33.7 (−22.8,10.9) and 76.9 (−31.1,45.8) microns. We further demonstrate the validity of the approach in simulations and experiments in tissue mimicking phantoms.