Wiener filtering/deconvolution for non-stationary noise
The Wiener Filter can written as a Least Squares problem (See How Is the Formula for the Wiener Deconvolution Derived?).
In you case, Since noise is basically with different STD per sample you may use the simple extension of Weighted Least Squares on top of the terms for the Wiener Filter.
Once you do that you'll have the optimal solution.