Andres Asensio Ramos from the Instituto de Astrofísica de Canarias mentioned to me his recent preprint entitled; Compressive Sensing for Spectroscopy and Polarimetry by Andres Asensio Ramos and Arturo Lopez Ariste. The abstract reads:We demonstrate through numerical simulations with real data the feasibility of using compressive sensing techniques for the acquisition of spectro-polarimetric data. This allows us to combine the measurement and the compression process into one consistent framework. Signals are recovered thanks to a sparse reconstruction scheme from projections of the signal of interest onto appropriately chosen vectors, typically noise-like vectors. The compressibility properties of spectral lines are analyzed in detail. The results shown in this paper demonstrate that, thanks to the compressibility properties of spectral lines, it is feasible to reconstruct the signals using only a small fraction of the information that is measured nowadays. We investigate in depth the quality of the reconstruction as a function of the amount of data measured and the influence of noise. This change of paradigm also allows us to define new instrumental strategies and to propose modifications to existing instruments in order to take advantage of compressive sensing techniques.
After reading his paper we started an impromptu discussion that I am editing and copying with permission. I initially asked:
...While you are discussing CS techniques as applied to spectrographs and spectropolarimeters, I did not see a deep discussion on the reason as to why a CS hardware would provide an edge as opposed to a simple hardware. Can you enlighten me on this ? Are you and your co-author currently designing hardware or is it just an exercise in evaluating potential CS technologies ?...
...It is true that there is not a deep discussion on why CS techniques can be of interest because I think it is clear in our community that going fast when acquiring data is good. So, any improvement leading to faster instruments without compromising too much (or even not compromising at all) spectral and spatial resolution will be welcomed (once they understand the maths behind CS techniques). At least in solar physics, it is impossible to measure 2D images with spectro-polarimetric information in each pixel with a spectral resolution of, say, 20 mA per pixel, and a polarimetric sensitivity of 10^-5 (detect one polarized photon per 100000). Either long integration times have to be used (very poor temporal resolution) or reduce the polarimetric sensitivity (weak magnetic fields cannot be detected). In my opinion, CS can lead to an improvement in this field because the acquisition times can be reduced by a large factor, thus leading to a boost in time resolution.
The main concern I have encountered in our community (I'm referring to solar and stellar physics) is more philosophical than practical. I have given some talks introducing to my colleagues the ideas of CS and how novel instruments can be built under this framework and I always find the same response: "I don't believe it. Of course, if you put a prior on the signal you measure, you will never find 'surprises' " (surprises in the sense of strange signals that do not follow the main trend). That's the main reason why my colleague and myself decided to publish a paper presenting the potential of CS for spectroscopy and spectropolarimetry, showing that signals are compressible and that 'surprises' can be, in principle, found if you measure enough times and propose a sufficiently complete basis set.
Concerning the development of the ideas we propose, we are now working on a modification to an instrument existing in the french telescope THEMIS (http://www.themis.iac.es/). This instrument is a high-spectral-resolution spectro-imager (it measures 2D images of the solar surface with each column of the image at a slightly different wavelength) but using multiplexing techniques. Our plans include doing l1 reconstructions of the multiplexed measurements and our first numerical tests indicate a good behavior. I'm discussing with other colleagues on applying CS techniques to the Fabry-Perot interferometer of Solar Orbiter, but this is still in a very initial phase. With our paper I hope to convince our instrumental colleagues that it is worth pushing towards this new measuring paradigm....
Igor:
Andres:...With regards to THEMIS, you said "..This instrument is a high-spectral-resolution spectro-imager (it measures 2D images of the solar surface with each column of the image at a slightly different wavelength) but using multiplexing techniques...". Does that mean that it doesn't use multiplexing right now but that you will try multiplexing, now that you interested in CS, to see if there is a better way of acquiring signals that way ?...
Igor:...At the moment, it is working in "single wavelength" mode, meaning that there is only one wavelength per column in the image. The wavelength information is recovered by scanning either moving a slit or moving a grating. Our idea is to multiplex many wavelengths in each column, so that, assuming sparsity, we can recover the signal with a reduced amount of scan steps as compared with the single wavelength mode....
Andres:...Have you considered instrumentation that could provide superresolution ?...
Igor:...Not in the CS framework. I have considered doing Bayesian superresolution taking advantage of the natural jittering of some telescopes (like the Sunrise balloon and some wind-exposed coelostats) or inducing this jittering mechanically. Unfortunately, I haven't had time to push this approach to an end and the analytical calculations are still in my notebooks and some working numerical codes in my laptop. Are you aware of applications of CS to superresolution?...
With regards to superresolution yes: check the blog for work by Roummel Marcia an Rebecca Willett at Duke on performing superresolution with coded aperture and also the work of Justin Romberg ... you should find trace of his imagers on the blog and the CS hardware page.... I am interested in hearing about how you guys would try to perform the (cheap) multiplexing in hardware so that you provide much better resolution than the current cameras you currently have. I think it is an extremely hard sell to say that CS can provide faster acquisition at the cost of some accuracy when most people publish papers with accuracy in mind. Hence, CS has to go beyond providing the same data in order to become something that people want as opposed to something would like to have because it is the new fad :-)
Andres:
Igor:I have to disagree :) For us doing solar physics time resolution is crucial for detecting events happening at very short timescales. If these events happen in less than 1 second, we cannot spend 5 seconds integrating to gain signal-to-noise. Therefore, reducing a factor 5-10 the integration time while maintaining the spectral resolution and the polarimetric sensitivity at similar levels opens up the possibility of studying very fast events.....Obviously, it would be great to be able to go beyond the resolution imposed by the cameras, although our resolution is almost always limited by the atmospheric stability. Some present telescopes are equipped with adaptive optics systems so that diffraction limited images can be obtained in some moments of good atmospheric stability. Of course, I can imagine systems that could carry out superresolution during these moments of good stability, but they also need to be fast and accurate doing spectroscopy at a resolution of 10 mA per pixel and polarimetry better than 10^-4, something that I doubt can be done presently. If you tell me to choose between superresolution and accuracy, I clearly prefer to see things at a lower spatial resolution (limited by my telescope) but be able to follow fast events with great precision. That's my opinion and I'm sure if you ask other colleagues, you'll find a panoply of different opinions :)
....Adaptive optics to me is like fighting nature not measuring with it....I have some views on this and this is why I recently mentioned this issue of imaging with nature...Andres:
Igor:Yes, I've read the[se entries]. I have been thinking on the possibility of taking advantage of the atmosphere to improve the quality of our solar images, but I find it difficult mainly because we don't know the "atmospheric sensing matrix".
Andres:Yes I absolutely agree but I think we need to be inventive on that front. Specifically:
- Right now some people are using turbulence to perform what they call Lucky imaging or Turbulence aided micro-lensing, can we used that phenomenon effect to our advantage especially in the context of time multiplexing ?
- Do we have the means of figuring out atmospheric turbulences using other instruments/cameras not used for that purpose (specifically cameras on-board current satellites)
- Since the Moon is a known object, can we probe the atmospheric turbulence by evaluating what the Moon should look like and what it looks like on the sensor of interest. What about doing that type of studies with inter star angles ?
- Should we use interrogative means such as laser beams as the ones used for computing the distance between the Moon and the earth.
- Others.....
Igor:....Some colleagues at the IAC have imaged stellar systems using lucky imaging cameras. Although the concept is simple, I have always considered that it is a waste of photons and something smarter can be found....The atmosphere's PSF varies typically on the order of milliseconds. Perhaps it's possible to estimate how good the atmosphere behaves for reconstructions of sparse signals... More things to do for the future...
The discussion went on a little further. Thank you very much Andres for this thoughful and insightful discussion!Absolutely, [in particular with regards to Lucky imaging], I think it is a waste to let the unfocused part of the image go to waste. Connecting lucky imaging and the atmospheric PSF lead back to something called blind deconvolution, I mentioned something about it recently...
For information, the Planetary Society blog has a small description of the difference between an image taken by the Hubble and adaptive optics on the Keck Observatory. If you want to know more about the Hubble, you may want to go to Rice University tomorrow for a presentation on "Servicing the Hubble Space Telescope" by Michael Massimino, one of the astronauts who did the recent retrofitting of the Space Telescope. Finally, Jean-Luc Starck tells me that unlike HIFI, PACS (IAC site)works wonderfully, that it is in a calibration mode and that the CS mode should be tried in October. Woohoo, thanks Jean-Luc !Finally, as an aside, I am glad that I am now on Andres' e-mail list because if the La Palma Volcano slides into the ocean and triggers a mega-tsunami, I am sure he'll send an e-mail to all his E-mail contacts warning them about not being anywhere near a coast in Africa, Europe, the U.S., the Carribean or South America.
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