Thanks to Igor Carron I’ve watched a great videolecture by Stephane Mallat High dimensional classification by recursive interferometry. Actually I watched it twice, and I think I understand most of it now))). And it was not about compressed sensing, not even about manifold learning much . It was mostly about a new application of wavelets . How to use wavelets to produce low dimensional data (image descriptor if we are talking about computer vision) from high dimensional data(that is image). The idea is to transcend linear representation and use nonlinear operation – absolute value of wavelet. Absolute value – square root of wavelet square carry information of frequencies differences. It’s invert Fourier transform have new harmonics – differences of frequencies of original function. That interference of harmonics of original image. Now it was reminding me something. Yep – phase congruency (pdf). Phase congruency also use absolute value of wavelet(windowed Fourier). It seems to me it has perfect explanation. Interference pattern defined by how in-phase both wave are. That is it’s like a phase congruency taken into each point. Phase congruency edge-detector is in fact finding maximum of somehow normalized interference pattern. In that sense this Mallat’s method producing invariants from high-dimensional data is analogous to producing sketch from photo.
Ok, enough rambling for now.