A genetic approach to shape reconstruction in limited data tomography

The paper proposes a new method for shape reconstruction in computerized tomography. Unlike nuclear medicine applications, in physical science problems we are often confronted with limited data sets: constraints in the number of projections or limited view angles . The problem of image reconstruction from projection may be considered as a problem of finding an image (solution) having projections that match the experimental ones. In our approach, we choose a statistical correlation coefficient to evaluate the fitness of any potential solution. The optimization process is carried out by a genetic algorithm. The algorithm has some features common to all genetic algorithms but also some problem-oriented characteristics. One of them is that a chromosome, representing a potential solution, is not linear but coded as a matrix of pixels corresponding to a two-dimensional image. This kind of internal representation reflects the genuine manifestation and slight differences between two points situated in the original problem space give rise to similar differences once they become coded. Another particular feature is a newly built crossover operator: the grid-based crossover, suitable for high dimension two-dimensional chromosomes. Except for the population size and the dimension of the cutting grid for the grid-based crossover, all the other parameters of the algorithm are independent of the geometry of the tomographic reconstruction. The performances of the method are evaluated on a phantom typical for an application with limited data sets: the determination of the neutron energy spectra with time resolution in case of short-pulsed neutron emission. A genetic reconstruction is presented. The qualitative judgement and also the quantitative one, based on some figures of merit, point out that the proposed method ensures an improved reconstruction of shapes, sizes and resolution in the image, even in the presence of noise. (authors)