Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography

Abstract

Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Image reconstruction in EIT is a nonlinear and ill-posed inverse problem. The Tikhonov method with L(2) regularization is always used to solve the EIT problem. However, the L(2) method always smoothes the sharp changes or discontinue areas of the reconstruction. Image reconstruction using the L(1) regularization allows addressing this difficulty. In this paper, a sum of absolute values is substituted for the sum of squares used in the L(2) regularization to form the L(1) regularization, the solution is obtained by the barrier method. However, the L(1) method often involves repeatedly solving large-dimensional matrix equations, which are computationally expensive. In this paper, the projection method is combined with the L(1) regularization method to reduce the computational cost. The L(1) problem is mainly solved in the coarse subspace. This paper also discusses the strategies of choosing parameters. Both simulation and experimental results of the L(1) regularization method were compared with the L(2) regularization method, indicating that the L(1) regularization method can improve the quality of image reconstruction and tolerate a relatively high level of noise in the measured voltages. Furthermore, the projected L(1) method can also effectively reduce the computational time without affecting the quality of reconstructed images.

Research on Three-Dimensional Imaging Method Using Tensor for Electrical Impedance Tomography (Eit)

“…In order to simulate the typical noise levels in real measurement systems, Gaussian, zero mean random noise was added to the simulated voltages. The amplitude of the noise was 0.5% of simulated voltage [28]. A conventional adjacent current injection and voltage measurement strategy based on the complete electrode model were chosen consisting of 16 current excitation configurations and 13 corresponding voltage measurement configurations for each current excitation, i.e., the number of measured data was 208 for the reconstruction of one EIT image.…”

“…At present, the traditional EIT image reconstruction algorithms [3,4] include sensitivity coefficient method [5][6][7], iterative algorithm [8], conjugate gradient method [9], and TV regularization [10,11]. The sensitivity coefficient method [5] is a simple image reconstruction algorithm, but the image reconstruction quality is not high because approximate substitution is used in the calculation process.…”

A review on image reconstruction algorithms for electrical capacitance/resistance tomography

“…The presence of the l 1 term is used to induce sparsity in the optimal solution of equation (20). Another important advantage of the l 1 -regularization over the l 2 -regularization is that as opposed to the latter, l 1 -regularization is less sensitive to outputs, which in image processing correspond to sharp edges (Wang et al , 2012a).…”

A novel deep neural network method for electrical impedance tomography

“…Artificial Neural Networks (ANN) are offering robust models and they are used in various branches of biomedical engineering (Prauzek et al, 2013). They have been widely employed in image reconstruction in Electrical Capacitance Tomography (ECT) (Chen et al, 2012) and in EIT (Wang et al, 2009a; Wang et al, 2009b; Wang et al, 2012). ANN are offering the current state of the art non-linear approach, towards image reconstruction for EIT.…”