Continuous reconstruction of density image from Compton scattered energy spectra with neural network

Compton scattering can be used to determine the electron densities of tissues for medical applications and those of materials for industrial applications. The information on the flux and the energy of the scattered photons can both be used for the electron density evaluation. Owing to the attenuation for both the incident and the scattered photons, the singular values of the projection matrix decay very fast and the reconstruction problem becomes ill-posed. To obtain stable solutions from the energy spectral data, a prior model should be incorporated in the reconstruction process. The prior model adopted here is a continuous model with binary line processes, which was first introduced by Lee et al. (1993). This model is helpful for obtaining a smooth image while preserving the boundaries of the image. However, the introduction of binary line processes prevents the use of the traditional optimisation method. A coupled gradient neural network with two interaction parts (one for the continuous variable and one for the binary variable) is proposed for this problem. By defining an appropriate energy function and dynamics, high quality solutions have been obtained upon convergence of the dynamics