IMPROVED BACKPROPAGATION ALGORITHMS BY EXPLOITING DATA REDUNDANCY IN LIMITED-ANGLE DIFFRACTION TOMOGRAPHY

Abstract

Filtered backpropagation (FBPP) is a well-known technique used in Diffraction Tomography (DT). For accurate reconstruction of a complex-valued image using FBPP, full 360 ◦ angular coverage is necessary. However, it has been shown that by exploiting inherent redundancies in the projection data, accurate reconstruction is possible with 270 ◦ coverage. This is called the minimal-scan angle range. This is done by applying weighting functions (or filters) on projection data of the object to eliminate the redundancies. There could be many general weight functions. These are all equivalent at 270 ◦ coverage but would perform differently at lower angular coverages and in presence of noise. This paper presents a generalized mathematical framework to generate weight functions for exploiting data redundancy. Further, a comparative analysis of different filters when angular coverage is lower than minimal-scan angle of 270 ◦ is presented. Simulation studies have been done to find optimum weight filters for sub-minimal angular coverage. The optimum weights generate images comparable to a full 360 ◦ coverage FBPP reconstruction. Performance of the filters in the presence of noise is also analyzed. These fast and deterministic algorithms are capable of correctly reconstructing complex valued images even at angular coverage of 200 ◦ while still under the FBPP regime.