Limited Angle 3-D Reconstructions from Continuous and Pinhole Projections

The propagation of errors incurred in 3-D reconstructions with limited angular input performed by deconvolution and matrix inversion algorithms is analyzed. The convergence rate and noise properties of an iterative scheme that utilizes the finite extent of the object to recover the missing Fourier components in deconvolution are studied. Methods are developed to stabilize the performance of the reconstruction algorithms in the presence of noise. An analysis is given for the necessary condition for complete reconstruction in imaging situations involving a number of discrete inputs confined to limited angular range.