A Special Solution-Selection Principle in Using a Tikhonov Regularizing Algorithm for Processing Multiwave Lidar Data

An algorithm is considered for recovering the aerosol size distribution and complex refractive index from optical data measured with a certain error δ. The size distribution and the optical data are related by a linear integral Fredholm equation of the first kind with an inaccurately specified kernel, which is solved by Tikhonov regularization. A new principle is proposed for selecting solutions, which is based on not one solution but a certain set of them. Averaging on that set results in a stable conclusion on the recovery of the aerosol parameters. __________ Translated from Izmeritel'naya Tekhnika, No. 10, pp. 14–19, October, 2005.     

A new numerical method for the inverse source problem from a Bayesian perspective

In this work, a new numerical method for the inverse problem of determining a spacewise‐dependent heat source for a parabolic heat equation is developed. We reconstruct the unknown heat source by an augmented Tikhonov regularization (a‐TR) method derived from a Bayesian perspective. The a‐TR method could determine the regularization parameter and detect the noise level automatically. Numerical results for several benchmark test problems indicate that the a‐TR method is an accurate and flexible method to determine the unknown spacewise‐dependent heat source. Copyright © 2010 John Wiley & Sons, Ltd.     

Waveband selection for NIR spectroscopy analysis of soil organic matter based on SG smoothing and MWPLS methods

Savitzky-Golay (SG) smoothing and moving window partial least square (MWPLS) methods were applied to the model optimization and the waveband selection for near-infrared (NIR) spectroscopy analysis of soil organic matter. The optimal single wavelength prediction bias (OSWPB) was used to evaluate the similarity of calibration set and prediction set, and a new division method for calibration set and prediction set was proposed. SG smoothing modes were expanded to 540 kinds. The specific computer algorithm platforms for optimization of SG smoothing mode combined with PLS factor and for MWPLS method with changeable parameters were built up. The optimal waveband for soil organic matter was 1926-2032 nm, the optimal smoothing mode was the 2nd order derivative, 6th degree polynomial, 45 smoothing points, the PLS factor, RMSEP and R_P were 8, 0.260 (%) and 0.877 respectively. The prediction effect was obviously better than that in the whole spectral collecting region. To get stable results, all the optimization processes were based on the average prediction effect on 50 different divisions of calibration set and prediction set.