This study implements a direct reconstruction algorithm for two-dimensional linearized electrical impedance tomography (EIT) and tests it numerically. Originally designed for linearized scenarios, the algorithm proves functional with changes in the current-to-voltage boundary operator. The research includes both idealized models and practical complete electrode model measurements, focusing on domains like the unit disk and convex polygons. Emphasis is placed on regularizing the algorithm and examining its link to singular value decomposition and Zernike polynomial properties—critical for stable conductivity reconstruction in EIT.
The direct reconstruction algorithm showcased here displays efficacy even in a linearized setting, allowing for insights into conductivity variations from boundary current-voltage measurements.
Special focus on the regularization of the algorithm highlights its importance in addressing challenges associated with truncated systems and improving the stability of reconstructions.
Numerical experiments illustrate the algorithm's versatility across different geometries, such as the unit disk and convex polygons, demonstrating practical applications in EIT.
The use of Zernike polynomials not only facilitates the reconstruction process but also connects with the singular value decomposition to enhance algorithm robustness.
#electrical-impedance-tomography #direct-reconstruction-algorithm #numerical-analysis #zernike-polynomials #regularization-techniques
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