Limited-data computed tomography algorithms for the physical sciences.

Five limited-data computed tomography algorithms are compared. The algorithms used are adapted versions of the algebraic reconstruction technique, the multiplicative algebraic reconstruction technique, the Gerchberg-Papoulis algorithm, a spectral extrapolation algorithm descended from that of Harris [J. Opt. Soc. Am. 54, 931-936 (1964)], and an algorithm based on the singular value decomposition technique. These algorithms were used to reconstruct phantom data with realistic levels of noise from a number of different imaging geometries. The phantoms, the imaging geometries, and the noise were chosen to simulate the conditions encountered in typical computed tomography applications in the physical sciences, and the implementations of the algorithms were optimized for these applications. The multiplicative algebraic reconstruction technique algorithm gave the best results overall; the algebraic reconstruction technique gave the best results for very smooth objects or very noisy (20-dB signal-to-noise ratio) data. My implementations of both of these algorithms incorporate apriori knowledge of the sign of the object, its extent, and its smoothness. The smoothness of the reconstruction is enforced through the use of an appropriate object model (by use of cubic B-spline basis functions and a number of object coefficients appropriate to the object being reconstructed). The average reconstruction error was 1.7% of the maximum phantom value with the multiplicative algebraic reconstruction technique of a phantom with moderate-to-steep gradients by use of data from five viewing angles with a 30-dB signal-to-noise ratio.