I am interested in removing oscillations from a signal to capture the lower-frequency variations, similar to the objective of this problem. The oscillations vary in frequency in the time domain, so wavelet shrinkage seems to be a reasonable option, but most of the literature on wavelet shrinkage is applied to denoising, where the noise to be shrunk is i.i.d. Gaussian. Low-frequency oscillations are generally autocorrelated.
Is it still technically sound to apply wavelet shrinkage for removing higher frequency components even though they are not noise? Is there a better method? I am not aware of too many spatially-adaptive low-pass filters which have a convenient interpretation as wavelets.
Below are examples of two of such signals. As you can see, the oscillations occur with different frequencies along the space/time domain (x-axis). I have tried Fourier smoothing, but it does not seem to leave any relevant features. (I have also tried truncated SVD, but it also does a horrible job removing the oscillations.)