Software solutions for two computationally intensive problems: reconstruction of dynamic MRI and handling of alpha-stable distributions
The availability of ever higher computational power over the last years has changed the way in which multiple scientific and technical problems can be addressed. In this Thesis two computationally intensive problems of interest are faced, namely, the reconstruction of dynamic MR images from highly undersampled data and the numerical computations involved in handling alpha-stable distributions for statistical modeling.
About the former problem, MRI is nowadays the diagnostic imaging technique of first choice for numerous diseases. Its main benefits are its outstanding versatility and soft-tissues contrast. However, it is often limited by the long examination times needed to acquire all the data required to reconstruct the desired images. One way to reduce this time is to reduce the amount of data used for reconstruction, shortening the examination time consequently. However, artifacts arise in the reconstructions as the number of samples is reduced. In order to eliminate these artifacts, some knowledge or models can be introduced about the structure of the images of interest during reconstruction. One of the main objectives of this Thesis is to provide a better model for the images under reconstruction than those currently available. In particular the reconstruction of cine cardiac MR images is faced. In this modality the motion of the heart along the cardiac cycle is studied. A model that takes into account not only the structure of the images but also the specific motion of the heart is presented. The model is introduced in a MRI reconstruction scheme adapted for different applications such as breath-hold and free-breathing acquisitions. Results using both simulations and in-vivo measurements from healthy volunteers and patients are presented.
About the latter problem, alpha-stable distributions are a rich class of probability distribution functions of significance in many scientific fields. However, the lack of closed formulae for their PDF and CDF is a major drawback to use them in practice. Numerical methods have to be used to evaluate them, what involves a high computational demand and hinders, for example, the estimation of their parameters from a data sample. In this Thesis some tools needed for the use of these distributions as a useful statistical model are provided; specifically, we have developed methods for fast and accurate numerical computation of densities and distribution functions as well as for the estimation of alpha-stable parameters. These methods exploit the parallel computing capabilities of modern multi-core systems.
