Image Reconstuction in MRI

The Possibilities of Portable Low-cost MRI Scanners

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Abstract

Hydrocephalus is one of the most common abnormalities affecting the nervous system of children around the globe. Especially in developing countries hydrocephalus is a large problem. It is often left untreated resulting in suffering, brain damage, developmental delays and ultimately death. This makes an early detection more opportune than ever. In standard MRI it is typical to adjust the hardware of the imager to minimise the effort needed in the reconstruction. MRI scanners are also heavy and expensive. Therefore a start is made in developing a sufficiently accurate image reconstruction algoritm that is able to effectively process signals produced by a low-cost MRI scanner. An analytic signal is set up for the new prototype magnetic resonance imager and a measurement model consisting of a set of linear equations is derived. For two dimensions, a new encoding method (rotating the magnet) is implemented in a Matlab program. The Matlab program constructs the signal with a Shepp-Logan phantom image and then solves the set of linear equations to reconstruct the original image. Care needs to be taken when it comes to several practical aspects as wel as theoretical issues. The model is analysed on its performance through tests on the Nyquist rate and its sensitivity to perturbations on the background magnetic flux density field. Satisfying the Nyquist rate is important when translating discrete signal samples in a continous signal. Perturbations due to human measurement errors have to be avoided where as perturbations due to limiting tools can be dealt with. Another study looks at the right balance between the number of rotations, the frequency bandwidth and the effective rank of the system matrix. The performance of iterative solvers CGLS and CGNE are tested. CGLS is the better choice when noise is included in the model. Which is the incentive for a short study about the p-norm. CGLS has been combined with Tikhonov regularisation and showed the best performance with regularisation matrix L=I and extra a-priori information compared to other regularisation matrices.