  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.
