A Log-Euclidean and Total Variation based Variational Framework for Computational Sonography

TL;DR

This paper introduces a novel variational framework for 3D ultrasound imaging that uses tensor estimation and log-Euclidean methods to improve image quality and enable flexible probe positioning.

Contribution

It presents a new log-Euclidean tensor-based variational method with total variation regularization for computational sonography, extending previous work with improved tensor positivity and image quality.

Findings

Enhanced ultrasound image quality demonstrated on in vivo data

Tensor field regularization preserves edges and details

Framework enables arbitrary probe position synthesis

Abstract

We propose a spatial compounding technique and variational framework to improve 3D ultrasound image quality by compositing multiple ultrasound volumes acquired from different probe orientations. In the composite volume, instead of intensity values, we estimate a tensor at every voxel. The resultant tensor image encapsulates the directional information of the underlying imaging data and can be used to generate ultrasound volumes from arbitrary, potentially unseen, probe positions. Extending the work of Hennersperger et al., we introduce a log-Euclidean framework to ensure that the tensors are positive-definite, eventually ensuring non-negative images. Additionally, we regularise the underpinning ill-posed variational problem while preserving edge information by relying on a total variation penalisation of the tensor field in the log domain. We present results on in vivo human data to show the efficacy of the approach.