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Nowadays ultrasound (US) examinations are typically performed with conventional machines providing two dimensional imagery. However, there exist a multitude of applications where doctors could benefit from three dimensional ultrasound providing better judgment, due to the extended spatial view. 3D freehand US allows acquisition of images by means of a tracking device attached to the ultrasound transducer. Unfortunately, view dependency makes the 3D representation of ultrasound a non-trivial task. To address this we model speckle statistics, in envelope-detected radio frequency (RF) data, using a finite mixture model (FMM), assuming a parametric representation of data, in which the multiple views are treated as components of the FMM. The proposed model is show-cased with registration, using an ultrasound specific distribution based pseudo-distance, and reconstruction tasks, performed on the manifold of Gamma model parameters. Example field of application is neurology using transcranial US, as this domain requires high accuracy and data systematically features low SNR, making intensity based registration difficult. In particular, 3D US can be specifically used to improve differential diagnosis of Parkinson's disease (PD) compared to conventional approaches and is therefore of high relevance for future application.

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