Malte Kuhlmann (MPI-IS) arrived in Heidelberg today. We looked at his results on reconstructing astronomical scenes from radio interferometry data. He has done both optimization with a regularized likelihood, and full sampling in image space using hybrid Monte Carlo. He is using an "L1" regularization, which is equivalent to a biexponential prior probability in pixel amplitudes. He finds that he can do a good job of reproducing the input scenes for fake data, when he samples, but that the optimization takes you to a strange place. This is a consequence of the point that in a very high dimensional space, with non-Gaussian priors, the posterior mode an be very far from the posterior mean. We discussed noise propagation for interferometry and also the advantages that a sampling system has over the conventional heuristic methods (such as CLEAN).
Melissa Ness (MPIA) and I worked on adding intrinsic scatter into her model of APOGEE spectra. We need the intrinsic scatter to be understood when we turn her model around and use it to label new spectra for which we don't know the temperature and metallicity. The results we got looked pretty bad, so we have work to do tomorrow.
That's pretty strange according to the results of Candès et al. who demonstrated that you get perfect recovery if the number of measurements in the Fourier domain is enough and the resulting image is sparse. Are the wrong reconstructions a result of not having enough measurements which biases the posterior mode?
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