Picking up where the last post left off, I mentioned the idea of using a selective smoothing approach.
Since the variance of differences is already computed after each line (as mentioned in the previous post), this quantity can be used to implement selective smoothing. We've noticed that after smoothing an image, the variance of differences decreases. Therefore, when implementing selective smoothing I attempt to reduce the current variance. The condition for smoothing is that the relative difference between the current variance and the variance updated with |tCurrent - tPrev| be less than some threshold value.
Applying selective smoothing directly did not yield better results (discontinuities vanish, but the image is still blurry). I've proceeded to run some more tests to better determine the sources of both discontinuities and the blurriness. While discontinuities seem to originate from both t values and means, the blurriness seems to be mostly due to means.
Faking a 0 mean for each line in the transform yield this:
What's interesting to note is that even though discontinuities are present, the image is not as blurry as it is after smoothing the means as well (in this image the t values were smoothed).
To sum up, this week was mostly concerned with implementing the selective smoothing and testing various approaches to see how they affect the image. I will now try study the transformed image (right after applying POT) to see, in each band, what discontinuities appear and where in each case (without faking a 0 mean, with 0 mean).