Non-Linear Reconstruction for ERT Inverse Problem Based on Homotopy Algorithm

Due to the non-linear and non-convex properties, classical electrical resistance tomography (ERT) image reconstruction algorithms are less effective and less accurate. In this article, a non-linear and non-convex image reconstruction algorithm based on the homotopy method was proposed. The proposed algorithm converted the ERT inverse problem to a multi-object non-convex optimization which promoted the reconstruction accuracy and avoid the local optimal. Experimental validations were conducted. The optimization process is studied which demonstrates its effectiveness. Moreover, the proposed algorithm is compared with six other representative algorithms (linear/non-linear and convex/non-convex) at the condition of different distributions and the number of objects. The image quality parameters of the proposed algorithms are studied which show that the homotopy algorithm can provide image reconstruction result with higher quality and better stability than the other conventional algorithms.