A reconstruction method for transillumination laser CT using optical heterodyne detection is proposed. Laser CT does not obey the Radon transform due to surface effects, which occur as a result of refractive index mismatch and bring about an annulus artifact. Optical attenuation with surface effects is described using an affine model. In addition, the constraint derived from the quantitative relationship between projections is introduced in order to obtain a stable solution to the system of equations. This reconstruction produces a least squares problem with the above-mentioned constraint, which is solved via the conjugate gradient method. The method is applied to data from a physical phantom.

This paper introduces a two-dimensional alternating Turing machine (2-ATM) which is an extension of an alternating Turing machine to two-dimensions. This paper also introduces a three-way two-dimensional alternating Turing machine (TR2-ATM) which is an alternating version of a three-way two-dimensional Turing machine. We first investigate a relationship between the accepting powers of space-bounded 2-ATM's (or TR2-ATM's) and ordinary space-bounded two-dimensional Turing machines (or three-way two-dimensional Turing machines). We then introduce a simple, natural complexity measure for 2-ATM's (or TR2-ATM's), called “leaf-size”, and provides a spectrum of complexity classes based on leaf-size bounded computations. We finally investigate the recognizability of connected patterns by 2-ATM's (or TR2-ATM's).