$1/f$ Noise in Diffuse Optical Imaging and Wavelet-Based Response Estimation

In diffuse optical imaging (DOI) data analysis, the functional response is contaminated with physiological noise as in functional magnetic resonance imaging (fMRI). In this work we extend a previously proposed method for fMRI to estimate the parameters of a linear model of DOI time series. The regression is performed in the wavelet domain to infer drift coefficients at different scales and to estimate the strength of the hemodynamic response function (HRF). This multiresolution approach benefits from the whitening property of the discrete wavelet transform (DWT), which approximately decorrelates long-memory noise processes. We also show that a more accurate estimation is obtained by removing some regressors correlating with the protocol. Moreover, we observe that this improvement is related to a quantitative measure of 1/f noise. The performances of the method are first evaluated against a standard spline-cosine drift approach with simulated HRF and real background physiology. Lastly, the technique is applied to experimental event-related data acquired by near-infrared spectroscopy (NIRS).