Linear adaptive noise-reduction filters for tomographic imaging: Optimizing for minimum mean square error

摘要

This thesis solves the problem of finding the optimal linear noise-reduction filter for linear tomographic image reconstruction. The optimization is data dependent and results in minimizing the mean-square error of the reconstructed image. The error is defined as the difference between the result and the best possible reconstruction. Applications for the optimal filter include reconstructions of positron emission tomographic (PET), X-ray computed tomographic, single-photon emission tomographic, and nuclear magnetic resonance imaging. Using high resolution PET as an example, the optimal filter is derived and presented for the convolution backprojection, Moore-Penrose pseudoinverse, and the natural-pixel basis set reconstruction methods. Simulations and experimental results are presented for the convolution backprojection method.