The model is the following:
and is a sample path of a fractional diffusion with white noise
where and is the Caputo derivative so that the product rule holds. For the fractional diffusion equation have the solution where .
For denoising correlated fractional noise we can apply the thresholds discovered by Wang in wang-1996-thresholding-long-memory
We can approximately decorrelate the fractional Brownian motion by applying a wavelet transform : let so that (*) implies
Then we have various options to estimate from the wavelet transform.