When reconstructing a measured spectrum to enhance its signal-to-noise ratio (SNR), the objective is to minimize the variance between the smooth reconstructed spectrum and the original measured spectrum, hence to attain an acceptably small χ<sup>2</sup> value. The χ<sup>2</sup> value thus measures the fidelity of the reconstruction to the original. Smoothness can be conceived as attenuated variation between adjacent points in a spectrum. Thus, a conceptual change in the application of the χ<sup>2</sup> function to the difference between adjacent points of the reconstructed spectrum permits its use, in principle, as both a measure of smoothness and a measure of fidelity. We show here that implementations of this concept produce results superior to Savitzky–Golay filters.
Vol. 3, Iss. 9 Virtual Journal for Biomedical Optics
H. Georg Schulze, Rod B. Foist, Andre Ivanov, and Robin F. B. Turner, "Chi-Squared-Based Filters for High-Fidelity Signal-to-Noise Ratio Enhancement of Spectra," Appl. Spectrosc. 62, 847-853 (2008)