A measure of curve fitting error for noise filtering diffusion tensor MRI data

摘要

A parameter, χ_p~2, based on the fitting error was introduced as a measure of reliability of DT-MRI data, and its properties were investigated in simulations and human brain data. Its comparison with the classic χ~2 revealed its sensitivity to both the goodness of fit and the pixel signal-to-noise-ratio (SNR), unlike the classic χ~2, which is sensitive only to the goodness of fit. The new parameter was thus able to separate effectively pixels with coherent signals (having small fitting error and/or high SNR) from those with random signals (having inconsistent fitting and/or low SNR). A practical advantages of χ_p~2 over the classic χ~2 was that χ_p~2 is quantified directly from the data of each pixel, without requiring accurate estimation of data-dependent parameters (such as noise variance), which often makes application of the classic χ~2 problematic. Analytical approximations of χ_p~2 enabled an objective (data-independent) and automated calculation of a threshold value, used for internal scaling of the χ_p~2 map. Apart from assessing data reliability on a pixel-by-pixel basis, χ_p~2 was used to develop an objective and generic methodology for the exclusion of pixels with unreliable DT information by discarding pixels with χ_p~2 values exceeding the threshold. Pixels corresponding to very low SNR, and poorly fitted cerebrospinal fluid and surrounding brain tissue, had increased χ_p~2 values and were successfully excluded, providing DT anisotropy maps free from artifactual anisotropic appearance.