Parametric Spline Models

Abstract

We know from points (i) and (ii) of Section 1.1.2 that an inverse problem can be solved by constraining the solution either implicitly, via a prior energy U₁ (x) as in Chapter 2, or explicitly by dimensionality reduction of the space containing x. The latter approach is the subject of this chapter. It is completely different from regularization with a prior energy. Dimensionality reduction has two advantages: It produces a simple exogenous model, and it is easy to handle when used as a component of a more complicated model.