Regularized cubic B-spline approximation for processing laser Doppler anemometry data

We consider the application of Tikhonov type regularization methods for computing a cubic spline approximation to the solution of a particular Fredholm integral equation of the first kind which arises in laser Doppler anemometry experiments. The method of generalized cross validation is used to calculate an unbiased estimate to the value of the regularization parameter controlling the trade-off between the smoothness of the approximation and the fidelity of the transformed approximation to the data, which are assumed to be contaminated by 'white noise' error. Numerical results are presented, for zero order regularization on simulated laser anemometry data, which demonstrate that the success of the method is dependent on the positioning of the knots of the spline. Proposed extensions to this work are discussed, which include techniques for incorporating cross validation with higher orders of regularization and the addition of an automatic knot selection algorithm.