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

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.