Rl. Kashyap et S. Moni, USING THE RESIDUAL AREA CRITERION FOR SIGNAL RECONSTRUCTION FROM NOISELESS AND NOISY SAMPLES, IEEE transactions on signal processing, 44(3), 1996, pp. 732-738
We consider reconstruction of a signal from a univariate data set. A p
roblem that is often observed using existing techniques is overshoots
between data samples. We propose a criterion, called the residual area
criterion, which addresses this problem. The curve of minimum are len
gth that interpolates the data is the piecewise linear curve connectin
g the data points. Our criterion is to minimize the L(2) distance to t
his curve from the chosen set of functions. We discuss the use of this
criterion for both noisy and noiseless samples. The main point of our
paper is that a significant improvement is realized by minimizing our
criterion rather than requiring continuity of high order derivatives
(which is the usual method employed for noiseless data) or minimizing
curvature (which is the usual criterion for noisy data). A comparison
of our method to existing methods is included.