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Aurora Computed Tomography (ACT) is a method for retrieving the three-dimensional (3-D) distribution of the volume emission rate from monochromatic auroral images obtained simultaneously by a multi-point camera network. We extend this method to a Generalized-Aurora Computed Tomography (G-ACT) that reconstructs the energy and spatial distributions of precipitating electrons from multi-instrument data, such as ionospheric electron density from incoherent scatter radar, cosmic noise absorption (CNA) from imaging riometers, as well as the auroral images. The purpose of this paper is to describe the reconstruction algorithm involved in this method and to test its feasibility by numerical simulation. Based on a Bayesian model with prior information as the smoothness of the electron energy spectra, the inverse problem is formulated as a maximization of posterior probability. The relative weighting of each instrument data is determined by the cross-validation method. We apply this method to the simulated data from real instruments, the Auroral Large Imaging System (ALIS), the European Incoherent Scatter (EISCAT) radar at Tromsø, and the Imaging Riometer for Ionospheric Study (IRIS) at Kilpisjärvi. The results indicate that the differential flux of the precipitating electrons is well reconstructed from the ALIS images for the low-noise cases. Furthermore, we demonstrate in a case study that the ionospheric electron density from the EISCAT radar is useful for improving the reconstructed electron flux. On the other hand, the incorporation of CNA data into this method is difficult at this stage, because the extension of energy range to higher energy causes a difficulty in the reconstruction of the low-energy electron flux. Nevertheless, we expect that this method may be useful in analyzing multi-instrument data and, in particular, 3-D data, which will be obtained in the upcoming EISCAT_3D.