Abstract:
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Magnetic Resonance Imaging (MRI) is widely used in medicine and other sciences. Currently, images obtained from MRI are reconstructed using the discrete inverse Fourier transform. This method has three serious shortcomings. First, it gives a highly discretized approximation to a naturally continuous function. Second, it requires the data sampling space to be an equally-spaced grid. Third, its approach to reconstruction of three-dimensional objects is two-dimensional because the image is reconstructed as a sequence of independent two-dimensional slices. We propose an alternative reconstruction method, using a penalized likelihood approach, that honors the continuous nature of the data, relaxes the requirements on the structure of the data sampling space, and makes a three-dimensional use of the data possible. This approach combines Kimeldorf-Wahba penalized likelihood methodology with computationally convenient bais functions, such as the Haar wavelets, and can be easily reformulated in a Bayesian context.
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