Denoise Techniques When Clean Signal and Pure Noise Are Available I have the clean version of the signal.
I can obtain the environmental noise.
I want to apply an effective denoising technique on a noisy signal (i.e., clean plus environmental noise).

Some observations:


The noise to signal ratio is extremely low.
The noise is spread across all frequencies in the frequency domain.


Are there any techniques for possibly taking advantage the noise and the clean signal towards denoising the noisy signal?
If the data is stationary and the noise is white then you should use the Wiener Filter.  

If data isn't stationary you should look into the family of adaptive filters (LMS Filter and RLS Filter for starter).