AN ADAPTIVE SPLINE METHOD FOR SIGNAL RESTORATION

by Pierre Moulin

We consider the classical problem of estimating a signal $f$,
given noisy samples of a linear transformation of $f$.
A nonlinear regression method is proposed for estimating $f$
in the class of polynomial B-splines defined over nonuniform grids.
This type of approximation offers great flexibility, as the number of knots,
knot locations and knot coefficients are free parameters.
Estimates are obtained using a simple iterative algorithm derived
by application of a multistage hypothesis-testing procedure.