Optical microscope tomography II Nonnegative constraint by a gradient-projection method

In part I of this series we proposed a new principle of tomographic imaging using an optical microscope devised with a support-constraint reconstruction algorithm [ J. Opt. Soc. Am. A4, 292 ( 1987)]. In this paper we describe a new reconstruction algorithm with a nonnegative constraint that utilizes a priori knowledge of nonnegativity of absorbance or optical density of three-dimensional sample distribution. This method drastically improves the longitudinal resolution in tomography reconstruction, which was the most serious problem with the developed microscope tomography principle. Compared with conventional nonnegative-constrained iterative reconstruction algorithms, the algorithm developed here essentially reduces computation-time and memory-capacity requirements because it includes conjugate directional searching and gradient projection based on the Kuhn–Tucker condition, guaranteeing the convergence of the algorithm within a finite (the smallest) number of iterations. Results of experiments with a biological specimen, using the proposed algorithm, demonstrate an evident improvement of longitudinal resolution with a computation time only three times longer than that of the fastest nonconstrained algorithm.