Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography. (26th October 2016)

• Record Type: Journal Article
• Authors: Harrach, Bastian; Minh, Mach Nguyet
• Is Part Of: Inverse problems. Volume 32:Number 12(2016:Dec.)
• Publication Date: 2016-10-26
• Subjects: minimizing residual -- linearized equation -- global convergence -- shape reconstruction -- electrical impedance tomography; 35R30 -- 35J25; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/12/125002
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results are available in the literature yet, and reconstructions tend to contain ringing artifacts. In this work, we shall minimize the linearized residual functional under a linear constraint defined by a monotonicity test, which plays the role of a special regularizer. Global convergence is then established to guarantee that this method is stable under the effects of noise. Moreover, numerical results show that this method yields good shape reconstructions under high levels of noise without the appearance of artifacts.