As demonstrated in Chapter , B-splines provide an exceptionally accurate method of forward interpolation. In this section, I discuss how this choice of the forward operator affects the regularization part of the problem. In the case of B-spline interpolation, the forward operator is a cascade of two operators: recursive deconvolution , which converts the model vector to the vector of spline coefficients , and a spline basis construction operator .System (-) transforms to

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The inconvenient part of system (-) is the complex regularization operator . Is it possible to avoid the cascade of and and to construct a regularization operator directly applicable to the spline coefficients ? The answer is positive. In the following subsection, I develop a method for constructing spline regularization operators from differential equations.

12/28/2000