Here is a follow up of our recent work on Compressive Sensing. I am not a co-author of this new paper so I feel freer to make a comment on it. In the previous approach, we defined the transmission matrix through measurements that required us to go through at least 4 different measurements with a phase difference of pi/4 in order to finally figure out each coefficient of the transmission matrix. Actually, this was the paper that originally used this technique. Our work put a spin on this by looking at it as a compressive sensing system (as opposed to using a reconstruction based on Tikhonov solver). But SLMs that produce those tiny phase shifts are expensive. For that reason, the authors of today's paper used a Texas Instrument DMD that loses this phase information. The paper shows that with enough of these phaseless information, we can recover the transmission matrix. In turn this knowledge is used to produce peaks through these media. Woohoo !
Reference-less measurement of the transmission matrix of a highly scattering material using a DMD and phase retrieval techniques by Angelique Dremeau, Antoine Liutkus, David Martina, Ori Katz, Christophe Schulke, Florent Krzakala, Sylvain Gigan, Laurent Daudet
This paper investigates experimental means of measuring the transmission matrix (TM) of a highly scattering medium, with the simplest optical setup. Spatial light modulation is performed by a digital micromirror device (DMD), allowing high rates and high pixel counts but only binary amplitude modulation. We used intensity measurement only, thus avoiding the need for a reference beam. Therefore, the phase of the TM has to be estimated through signal processing techniques of phase retrieval. Here, we compare four different phase retrieval principles on noisy experimental data. We validate our estimations of the TM on three criteria : quality of prediction, distribution of singular values, and quality of focusing. Results indicate that Bayesian phase retrieval algorithms with variational approaches provide a good tradeoff between the computational complexity and the precision of the estimates.
the solver is on Angelique's page under this paper:
- A. Drémeau, F. Krzakala - Phase recovery from a Bayesian point of view: the variational approach - Accepted at IEEE Int'l Conference on Acoustics, Speech and Signal Processing (ICASSP), (preprint) arXiv:1410.1368, Brisbane, Australia, April 2015.
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