Calibration Using Matrix Completion with Application to Ultrasound Tomography

TL;DR

This paper introduces a robust calibration method for ultrasound tomography sensors using low-rank matrix completion and multidimensional scaling, effectively handling missing and delayed measurements.

Contribution

The paper presents a novel calibration approach that leverages matrix completion and MDS to accurately estimate sensor positions despite missing and delayed ToF data.

Findings

The method accurately estimates sensor positions in simulated ultrasound tomography scenarios.

It provides analytic error bounds demonstrating robustness to noise.

Simulations confirm practical effectiveness of the proposed calibration technique.

Abstract

We study the calibration process in circular ultrasound tomography devices where the sensor positions deviate from the circumference of a perfect circle. This problem arises in a variety of applications in signal processing ranging from breast imaging to sensor network localization. We introduce a novel method of calibration/localization based on the time-of-flight (ToF) measurements between sensors when the enclosed medium is homogeneous. In the presence of all the pairwise ToFs, one can easily estimate the sensor positions using multi-dimensional scaling (MDS) method. In practice however, due to the transitional behaviour of the sensors and the beam form of the transducers, the ToF measurements for close-by sensors are unavailable. Further, random malfunctioning of the sensors leads to random missing ToF measurements. On top of the missing entries, in practice an unknown time delay is also added to the measurements. In this work, we incorporate the fact that a matrix defined from all the ToF measurements is of rank at most four. In order to estimate the missing ToFs, we apply a state-of-the-art low-rank matrix completion algorithm, OPTSPACE . To find the correct positions of the sensors (our ultimate goal) we then apply MDS. We show analytic bounds on the overall error of the whole process in the presence of noise and hence deduce its robustness. Finally, we confirm the functionality of our method in practice by simulations mimicking the measurements of a circular ultrasound tomography device.