Joint Calibration and Tomography based on Separable Least Squares Approach with Constraints on Linear and Non-Linear Parameters

Most of the existing tomography techniques rely on accurate calibration to reconstruct the features of interest. In several industrial applications, the calibration is typically performed off-line and has to be repeated frequently to counter time varying perturbation caused by aging, operating conditions, and so on. In this paper, a novel online joint calibration and tomography method based on variable projection based separable least squares approach with constraints on linear and non-linear parameters is proposed. The constraints on the linear parameters improve the estimation accuracy of the ill-posed and under determined tomography problem. The constraints on the non-linear parameters restricts the proposed method from departing far away from the initial guess, especially when a good initial guess is available. The proposed method is used to reconstruct the temperature distribution inside a blast furnace and simultaneously to calibrate the positions of acoustic transducers based on simulated acoustic time of flight measurements.