Mathematical Sciences: RUI:A Dynamic Programming Approach toImage Reconstruction from Projections
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt'}
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.
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