There are two major methods for image reconstruction from projections, transform and finite dimensional. The transform methods ultimately yield the picture pixel values as a convolution of the projection data with some weights (filter). Finite dimensional methods discretize at the very beginning by assuming a fixed set of basis pictures whose linear combination gives an approximation to the image. The choice of coefficients in the linear combination is determined by some optimization criterion. Current comercial CT-scan machines and NMR (Nuclear Magnetic Resonance) machines employ the transform methods in image reconstruction. The reason for this is that transform based algorithms are simpler and faster. Finite dimensional methods however, are more robust in data collection geometries, noisy data or small number of views. This project explores a finite dimensional method that is computationally competitive with the transform methods and enables one to express the picture pixel values in closed form. The essence of this approach is to use dynamic programming ideas to express the optimization criterion as recurrence relations. One then solves these recurrence relations and uses the solutions to obtain the pixel values of the picture.
