I am working on a problem where I'm analysing a signal and trying to find a measure of whether a roughly Gaussian shape appears or oscillations - though the oscillations may not be periodic.
For example, in these two images, I am plotting the first left and right singular vectors of an SVD decomposition of my image. From there I wish to detect the oscillatory behaviour on the left and the inverted Gaussian shape on the right, i.e. being able to return a metric that says yes, this images contains an oscillatory/single vertical streak(s).
I've tried things like autocorrelation, cross correlation but I'm not having very consistent results. I wonder if anyone can point me to a technique or literature that may help me here. Many thanks.
This looks like something which can be done with wavelets analysis. You can try a naive version, take some function whose integral is zero (seems like you can take a triangle) and calculate the convolution of your signals with scaled versions of the function, If there's an underlying oscillatory signal you'll see it when the proper scale is used. I did something similar once, and there are some delicate normalization issues you'll have to take into account, but I think this might be a good direction.