Tikhonov regularization-based extended Kalman filter technique for robust and accurate reconstruction in diffuse optical tomography

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).