Reconstrução de imagens a partir de projeções paralelas

Abstract

In medicine, there is a still growing interest in non-invasive examination techniques, that can depict anatomical structures. Among these methods, there are Magnetic Resonance Imaging (MRI), Positron Emission Tomography (PET) and Computerized Tomography (CT). All these methods are based on the same principie: for a choice of angles, one measures the line integrais in a plane. This procedure produces a set of profíles, which is called the Radon transform of the object. The next step is to reconstruct a two-dimensional image from its Radon transform. It is possible to obtain reconstruction algorithms from the so-called Fourier slice theorem. This theorem relates the one-dimensional Fourier transform of a given profile to the two-dimensional Fourier transform of the object which is to be reconstructed. In this work, one considers three different reconstruction methods based on this theorem. The fírst one is the filtered Backprojection method. The second one is the convolution Backprojection, and the last one is fíltering after Backprojection. This work compares the aforesaid transform reconstruction methods concerning accuracy and time. One analyzes three interpolation methods as well: linear, spline and the nearest neighbor required for the Backprojection. One concludes that the filtered Backprojection method be more suitable to the application in image reconstruction from projections concerning reconstruction time and accuracy among the three methods analyzed in this work.