Avaliação comparativa de métodos de reconstrução inversa

Abstract

This dissertation compares tomographic reconstruction algorithms. Sixteen reconstruction algorithms from five classes, with different models and operating principles, were studied and compared using descriptive, quantitative, and qualitative criteria. Firstly, in the descriptive comparison, the algorithms were grouped according to their common elements. That is, the classes and their fundamental characteristics are presented. The data set used for the quantitative evaluation is generated from three (3) complete base images, which have different qualitative characteristics to consider application groups that are not correlated with each other: health, architecture, and industry. We obtain a group of 60 projection sets (sinograms) from the 03 base images through a simulated acquisition process with progressive corruption. Corruption occurs by directly adding Gaussian noise to a single part of the acquisition process at a time, either in the full image of the target object or in the full image of the sinogram. The first approach accommodates applications where the error is associated with propagation phenomena and the interaction of the probe beams with the target object. In contrast, the second approach accommodates applications where the error is associated with the measurement process. For each algorithm iteration, a reconstruction image corresponding to a sinogram of the set is obtained. When applicable to the algorithm, 50 iterations are used. The quantitative analysis uses different image quality measures to compare the reconstructions. An Aggregate Quality Index is proposed in order to condense the information obtained. We assess the computational cost of the reconstruction based on the processing time of one iteration (the first). Finally, the qualitative comparison evaluates sections of the reconstructions of the images obtained in the sequence of iterations of the algorithm. The discernment of structures (changes in values, speed or inclination, and oscillations when they occur) is evaluated by inspection and statistical indices: Mean, Standard Deviation, and Otsu threshold. The evaluation indicates that algorithms based on likelihood function maximization are more effective (quality) and stable (the quality trend as iterations progress and error is added shows to be monotonous), with a reasonable efficiency compromise (computational cost). The results also suggest criteria for choosing the appropriate reconstruction methods for different application scenarios and suggestions for improving some algorithms.