Sparse regularization for small objects imaging with electrical resistance tomography

Abstract

Electrical resistance tomography (ERT) is a technique for reconstructing internal conductivity distribution of the field from electrical measurements on the surface. It is a nonlinear and ill-posed inverse problem which is easily affected by measurement noise. In order to improve the image quality of ERT, regularization methods are used to treat this ill-posedness. The Tikhonov method, which is based on L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> regularization, is generally used to solve this problem. However, it is not suitable when the conductivity has a sharp transition because it puts smoothness to obtain stability in the image reconstruction process. Recently, sparse regularization method with L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> norm shows its powerful effects for dealing with problem that has sharp transition in conductivity distribution. Thus image reconstruction results for small objects will be discussed in this paper with L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization method and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> regularization method. Simulation results show that L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization method can effectively improve the image reconstruction results of small objects. It also shows L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> regularization method is less sensitive to measurement noise.