A Bayesian approach for denoising one-dimensional data

A Bayesian technique to correct for Poisson noise in one-dimensional data, such as X-ray/neutron scattering curves, is presented. This 'denoising' method calculates a probability for any given curve to be the true underlying signal and generates the curves having the highest probabilities. Gaussian processes with a nonstationary squared-exponential covariance function are used to obtain smooth curves without needing to assume a particular functional form. Two benchmark denoising methods, adaptive weights smoothing and wavelet shrinkage, formed a basis for comparison. All three methods were tested on different types of X-ray scattering data. Besides producing quantitative uncertainty estimates, which the benchmarks lacked, the Bayesian technique met or exceeded their fidelity to the true signal, as measured by mean-square residuals. A free software implementation of the methods described in this paper has been developed.