An adaptive total variation regularization method for electrical resistance tomography

Total variation (TV) regularization method is widely used to solve the inverse problem of Electrical resistance tomography (ERT), which is ill-posed. However, TV regularization often suffers the staircases effect. To reduce those staircases effect, a modified TV regularization, called adaptive total variation (ATV) regularization, is proposed in this paper, which automatically adjusts the regularization term by distinguishing between edges and ramps according to the image gradients. With adaptive regularization term, at block edges it behaves more like the TV functional (∫_Ω|∇u|dΩ) to perverse the edges and in ramp regions it behaves more like the H¹ functional (∫_Ω|∇u|²dΩ) to avoid the staircase effect. Simulation and experimental results of ATV regularization and TV regularization are compared, which show that ATV regularization can avoid the staircase effect and endure a relatively high level of noise in the measured voltages.