Robust approaches to non - linear diffusion based compressed sensing in parallel MRI

Magnetic resonance imaging (MRI) is one of the most popular non-invasive imaging techniques used to look inside the human body and visually represent the physiology of various organs and tissues. One of its particularly notable features is the lack of ionizing radiation involved. However, a relatively high scanning time puts it at a
disadvantage. Therefore, a major component of the research in this field over the last four decades has been focused on improving the imaging speed while also trying to achieve better image quality. The demand for accelerated imaging is often met by restricting the amount of data collected from the scanner. Missing data would then be estimated offline to reconstruct an artifact-free image. In this thesis, a new approach to MRI reconstruction using robust non-linear (NL) diffusion-based compressed sensing (CS) is introduced and investigated in detail.
The signal processing technique of CS is widely popular due to its ability to
facilitate efficient acquisition and reconstruction of a sparse or compressible signal
like that of MRI, from relatively few measurements. Among the numerous sparse
approximation techniques available in CS, minimization of total variation (TV) has
been the key approach to sharply preserve the edges during the reconstruction process.
In the primary phase of this work, a Perona-Malik (PM) diffusion-based sparse approximation algorithm is developed as an alternative to TV to address its high sensitivity to regularization parameter. In the succeeding part, a mixed-order diffusion
the algorithm is developed that can prevent the formation of both staircase and speckle effects during reconstruction.
It is further observed that the direction of image gradient computation has a significant influence on the diffusion of both edges and artifacts. In the final part of the work, this critical aspect is addressed by developing a directionality guided diffusion reconstruction algorithm. This enables better preservation of the complex structural details in the image by adapting the direction of diffusion to local variations in the directionality of edges and employing a precise diffusion in the local regions of the image on a sub-pixel level.

PHD THESIS SEPTEMBER 2019 INT Prof. (Dr.) Joseph Suresh Paul,
Research Supervisor,
Indian Institute of Information Technology and Management-Kerala,