Fitting Smooth Curves to Noisy Indicator-dilution and Other Unimodal Data

A linear least squares method for fitting noisy unimodal functions such as indicator-dilution curves with piecewise stretched exponential functions is described. Stretched exponential functions have the form z(t) = alpha t beta e gamma t, where alpha, beta, and gamma are constants. These functions are particularly useful for fitting experimental data that spans several orders of magnitude is non-Gaussian, high skewed, and long tailed. In addition, the method allows for specifying external restrictions on the smooth curve that might be required by physical constraints on the data. These constraints can take the form of restrictions on the value of the fitting function at certain points or the value of the derivatives in certain regions. To determine the necessary constants in the fitting functions, a linear least squares problem with linear equality and inequality constraints is solved.