The electrical tomography (ET) enables non-invasive measurement of electrical parameter distributions, which has been applied to phase distribution detection in fluidized beds. The accuracy of detection depends on the accurate detection of the absolute electrical parameter distribution. This paper utilizes explicit nonlinear models applied in electrical resistance tomography (ERT) and tunneling magnetoresistance-based electromagnetic tomography (TMR-EMT) to achieve reconstruction of absolute conductivity and permeability distributions. A model based on the variational principle is used for gas-liquid-solid three-phase holdup calculations. The proposed method can obtain the non-uniform distribution of the holdup in the radial direction, such as the high solids holdup ring and the distribution of bubble clusters.