EE Seminar: Over-Parameterized Models for Vector Fields with Application to Phase-Contrast MRI Data
Speaker: Keren Rotker
M.Sc. student under the supervision of Prof. Alex Bronstein and Prof. Dafna Ben-Bashat
Wednesday, June 13th, 2018 at 15:00
Room 011, Kitot Bldg., Faculty of Engineering
Over-Parameterized Models for Vector Fields with Application to Phase-Contrast MRI Data
Abstract
Vector fields arise in a variety of quantity measure and visualization techniques such as fluid flow imaging, motion estimation, deformation measures and color imaging, leading to a better understanding of physical phenomena. Recent progress in vector field imaging technologies has emphasized the need for efficient noise removal and reconstruction algorithms. A key ingredient in the success of extracting signals from noisy measurements is prior information. This prior knowledge can often be represented as a parameterized model. In this work, we extend the over-parameterization variational framework in order to perform model-based noise removal of vector fields. The over-parameterization methodology combines local modeling of the data with global model parameter regularization. By considering the vector field as a linear combination of basis vector fields and appropriate scale and rotation coefficients, the denoising problem reduces to a simpler form of coefficient recovery. We introduce two versions of the over-parameterization framework: total variation-based method and sparsity-based method, relying on the cosparse analysis model. We first demonstrate the efficiency of the proposed frameworks for two-
and three-dimensional vector fields with linear over-parameterization models. We then consider color images as vector fields and illustrate denoising via the new techniques. Finally, we address the problem of denoising magnetic resonance imaging (MRI) vector field data. Advances in medical imaging technologies have led to new modalities such as flow-sensitive magnetic resonance imaging (phase-contrast MRI) which allows the acquisition of blood flow velocities with a volumetric coverage in a time-resolved fashion. We adjust our model to suit several blood flow patterns and demonstrate the algorithm’s efficiency on two- and three-dimensional simulations.
