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Electrical Impedance Tomography (EIT) reconstructs the conductivity distribution within a medium from electrical stimulation and measurements at the medium surface. Level set based reconstruction method (LSRM) has gained attention during the last decade as an effective solution to address the need of reconstructing structures with limited amount of available data. The classical LSRM is based on the quadratic formulations (L2 norms); however, the L2 norms are not robust to outliers and spatial noise. The L1 norm is a more solid alternative to produce high robustness against outliers and noise. The L1 norm is minimized by Primal dual-interior point method (PDIPM). In this paper, we derive a novel level set (LS) based regularization framework for using the L1 norm independently on the data and the regularization term of an inverse problem. The proposed LS based regularization method, called LS based PDIPM (LS-PDIPM), applies the PDIPM to minimize the L1 norms. We use the LS-PDIPM to reconstruct 2D images from EIT simulated data. The proposed LS-PDIPM with the L1 norms provides sharper and less noisy images, when comparing with the L2 norm based regularization method.

A Level Set based Regularization Framework for EIT Image Reconstruction