Restoration of Digital Multiplane Tomosynthesis by a Constrained Iteration Method

Tomosynthetic reconstructions suffer from the disadvantage that blurred images of object detail lying outside the plane of interest are superimposed over the desired image of structures in the tomosynthetic plane. It is proposed to selectively reduce these undesired superimpositions by a constrained iterative restoration method, suitably generalized to permit simultaneous deconvolution of multiple planes. Sufficient conditions are derived ensuring the convergence of the iterations to the exact solution in the absence of noise and constraints. Although in practice the restoration process must be left incomplete because of inescapable noise and quantization artifacts, the experimental results demonstrate that for reasons of stability the convergence conditions derived for the noise-free, unconstrained case should be satisfied. In order to establish a basis for a formal stopping criterion of the iteration procedure, the buildup of noise in the sequence of iterative restorations arising from white noise in the original radiographs is investigated theoretically and experimentally. This results in the derivation of an approximation to the limiting noise variance in the reconstructions which is verified experimentally.