It has been recently demonstrated that the local BOLD signals in resting-state fMRI (rs-fMRI) can be captured for the white matter (WM) by functional correlation tensors (FCTs). FCTs provide similar orientation information as diffusion tensors (DTs), and also functional information concerning brain dynamics. However, FCTs are susceptible to noise due to the low signal-to-noise ratio nature of WM BOLD signals. Here we introduce a robust FCT estimation method to facilitate individualized diagnosis. First, we develop a noise-tolerating patch-based approach to measure spatiotemporal correlations of local BOLD signals. Second, it is also enhanced by DTs predicted from the input rs-fMRI using a learning-based regression model. We evaluate our trained regressor using the high-resolution HCP dataset. The regressor is then applied to estimate the robust FCTs for subjects in the ADNI2 dataset. We demonstrate for the first time the disease diagnostic value of robust FCTs.