The problem of image reconstruction with Compton-scattering spectral data is an ill-posed problem, and the measurement error may be seriously amplified in the reconstruction result. For a stable solution, some kinds of a priori models of the problem should be incorporated into the process of reconstruction. Lee et al. [IEEE. Trans. Nucl. Sci. 40, 2049 (1993)] have proposed a continuous model with binary line processes. Owing to the coexistence of the continuous variable and the binary variable, the commonly used optimization methods for problems with continuous variables cannot be used in this case, and therefore a coupled-gradient artificial neural network was proposed for this mixed-integer problem. By introducing two interacting parts (with one part for the continuous variable and the other for the binary line processes) into the network, and by defining the appropriate energy function and dynamics, high-quality solutions were obtained upon convergence of the dynamics. Some simulated results are presented.
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