AMS in orbit. Six months ago, I wondered when compressed sensing would be used in the context of weak lensing. A month ago, I then wondered how we could estimate the mass of the universe using similar techniques. Well, it looks like some folks have been wondering the same thing for a long time now. In particular, Adrienne Leonard will present the following work at Texas A&M next week:
Title: Compressed Sensing for Weak Lensing
Weak gravitational lensing allows us to map the distribution of matter in the universe by measuring the small distortions to galaxy images arising due to the gravitational potential along the line of sight. The measured shear is effectively a convolution of the matter overdensity with a broad radial kernel encoding geometrical information. Therefore, the weak lensing problem can be modeled as an instance of compressed sensing, as we know that the matter overdensity is mostly sparse in some wavelets domains. In this case, the sensing operator models an integration along each line of sight, from low redshift (i.e. close distance) to high redshift (i.e. far away distance). Then, we exploit current results on the compress sensing theory in order to build an efficient method for estimating the matter density along lines of sight using most of the theoretical knowledge available. More precisely, the reconstruction problem is cast as a constraints convex optimization problem, where we seek a sparse solution under data fidelity constraints. We also characterize the solution and prove the convergence of the global scheme. The results show that we are able to reconstruct the matter cluster in different redshifts without the smooth and shift issues that occur in the current state-of-art methods.
I can't wait to see the paper and/or presentation.