Pink noise and spectral distortions affect the demodulation accuracies of fiber Bragg gratings (FBGs). A noise reduction algorithm with Savitzky-Golay filtering on each intrinsic mode function component decomposed by CEEMDAN, followed by signal reconstruction from the filtered components, is presented herein. Simulations show that the algorithm retains FBG signal details while reducing noise, avoids measurement errors from excessive smoothing, and suppresses white and pink noises adequately. A resolution-enhanced peak detection algorithm with distortion spectrum correction is also proposed with high accuracy and simple calculation. The experimental results show that the goodness of fit of the FBG temperature-wavelength curve R2 improves from 0.9826 to 0.9999.