Total least squares method for the purpose of noise reduction in low-cost MRI images

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MRI images are very useful for detecting diseases, as well as for the treatment of diseases. However, MRI scanners are usually too expensive for developing countries to purchase and maintain. Therefore, a less expensive scanner is being developed at Delft University of Technology and Leiden University Medical Center. Unfortunately, the images which are generated by this low-cost MRI scanner are contaminated by noise. The MRI images are determined by solving a system of equations of the form Ax= y, where x is the unknown image. As this system is perturbed, regression methods can be applied in order to find the best approximate value of x. The ordinary least squares method solves this system for perturbations in y. Whereas in the MRI case, it appears that both A and y are perturbed. The total least squares method is often used in order to solve these kind of perturbed systems of equations. The aim of this thesis is to investigate the abilities of this method for the purpose of noise reduction in MRI images. It appears that the total least squares method in combination with regularization operators is able to cancel out a certain amount of noise from the images. However, no significant advantages compared to the ordinary least squares method are found.