Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography.

The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations.

Neural network algorithm for image reconstruction using the "grid-friendly" projections.

The presented paper describes a development of original approach to the reconstruction problem using a recurrent neural network. Particularly, the "grid-friendly" angles of performed projections are selected according to the discrete Radon transform (DRT) concept to decrease the number of projections required. The methodology of our approach is consistent with analytical reconstruction algorithms.

A 2D approach to tomographic image reconstruction using a Hopfield-type neural network.

Objective: In this paper a new approach to tomographic image reconstruction from projections is developed and investigated.

Method: To solve the reconstruction problem a special neural network which resembles a Hopfield net is proposed. The reconstruction process is performed during the minimizing of the energy function in this network.