Using the residual area criterion for signal reconstruction from noiseless and noisy samples

We consider reconstruction of a signal from a univariate data set. A problem 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 arc length that interpolates the data is the piecewise linear curve connecting the data points. Our criterion is to minimize the L² distance to this 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