Tex-MEMS: it keeps on going. Tex-MEMS IX at Texas Tech

Tex-MEMS IX will take place in Lubbock at Texas Tech on September 17th. You can still register. It is a very relaxed type of a meeting. The nice thing about it is that most of the time you get to see the work of people you would not be talking to on campus or in other areas not related to your research. It's a great eye opener and, unlike other professional meetings, there is very little competition between the speakers which makes it a pretty unique place to actually share your thoughts and imagine other ways of doing things. The list of talks is here. Thank you Tim for making it happen.

When Ali Beskok and I started this series of meeting, we had no idea that it would continue for more than 8 years. wow.

How does the Rice one pixel camera work ?

I have been asked this question several times by colleagues and friends, so I decided to use my talents in Microsoft Paint to try to provide an explanation with some beautifully handcrafted pictures.

The problem to solve is the following: Let's say you have only one sensitive pixel/photodetector/radiation detector/Teraherz detector at your disposal but you need to take a 10 Megapixel image like the one you can get from a Best Buy or an Amazon point-and-shoot cameras how would you go about it ? There are many ways to do this but let us also imagine that you can also put your hands on a DMD chip that is made of 10 million oscillating mirrors (an example include the famous Texas Instrument DMD) like the ones you can find in digital projectors and you can command the action of each and everyone of these tiny (15 micrometer by 15 micrometer) mirrors. In other words, with a proper set-up, every milliseconds, you can decide to shine each of these mirrors on your detector .... or not. There are now two options for obtaining this 10MP image.

First option (the raster mode):

The raster mode is simple. Just shine one mirror at a time onto the detector and let all the other mirros shine elsewhere. Do this once

twice (with another mirror)

thrice (with yet another mirror)
four times (....)
five times (...)
....5 millions times (...)
until you reach the last 10 millionth mirror.

After doing all this, you now have ten million information which put together piece by piece provides you with a 10 MP image. Generally, you then use a small CPU to perform the Discrete Cosine Transform so that eventually you are now the proprietor of a JPEG image (i.e. a compressed version of this 10MP image).

Second option (the Compressive Sensing mode):

You tell the set of mirrors, on that DMD chip, to display a set of random tilings. That way, a random set of mirrors are shining the incoming light unto the detector.

You do this once with an initial random tiling and obtain your first CS measurement

then you do this again with a second random tiling,  in order to obtain your second CS measurement

then you do this again with a third random tiling,  this is your third CS measurement
and so on.

Compressed sensing tells you that with very high probability, you will get the same result as the raster mode (first method) above but with many fewer CS measurements than the 10 million raster mode measurements obtained in the first method. In fact, instead of taking 10 million raster mode measurements, you are likely to need only 20 percent of that in the form of CS measurements, maybe even less.

The reason this second method works stems from the idea that most natural images are sparse in bases ranging from cosines, wavelets to curvelets (this is also why JPEG does a tremendous job in decreasing the size of most images). Functions that represent random tilings of reflective and non reflective mirrors (0s and 1s) are said to be mathematically "incoherent" with these bases thereby allowing an automatic compression at the detector level (here in the second mode, there is no need for compression with JPEG at the very end since the CS measurements are already compressed version of the image). A computational steps is required to obtain a human viewable image from these CS measurements. That step uses these solvers.

What are the pros and cons of the second option compared to the first one ?
Pros:

1. The overall sensor requires very low power because there is no CPU/GPU/FPGA trying to perform the compression stage at the very end (JPEG).
2. The sensor is dedicated to acquiring information. Information processing can be done somewhere else ( think on some other planet)
   
3. Compared to raw images (raster mode output), the information to be transmitted is very much compressed albeit not optimally (compared to JPEG).
4. Instead you can spend all your money designing the very best sensitive pixel you want, it may even act as a spectrometer (looking at many different energy bands), radiation detector and so forth.
5. Last but not least, the amount of light that goes to the detector is about half of the 10 million mirrors, which is quite high compared to the single mirror exposure in the raster mode (first method). In other words, the signal to noise ratio is pretty high (a good thing) in the CS mode as opposed to the raster mode.

Cons:

1. Faint signals could be submerged in the CS measurements. You first need to have a high signal to noise ratio signal to detect small signals.
2. Your sensor has to have a much larger dynamic range than in the raster mode in order for the A/D quantization algorithm to not mess with the CS measurements.
3. The number of CS measurements will be higher than the number of bits required to store the JPEG of the raster mode (about 4 to 5 times higher). Then again (and this is a pro-argument, the transformation from raster mode to JPEG is the power hungry stage of your camera and the reason you always need to recharge it, memory on the other hand is cheap.)

Terry Tao provides a much clearer mathematical explanation albeit with no beautifully hand crafted images such as the ones found here. All information about this single pixel camera system can be found at Rice University.

[ Update 2013: Inview Corporation develops single pixel cameras using the intellectual property from Rice University ]

Thermodynamics of Muscle

In the unpublished work of E.T Jaynes I came accross an interesting statement on muscle and thermodynamics, namely:

Jaynes, E. T. 1983, `The Muscle As An Engine ,' an unpublished manuscript

Jaynes, E. T., 1989, `Clearing up Mysteries - The Original Goal,' in Maximum-Entropy and Bayesian Methods, J. Skilling (ed.), Kluwer, Dordrecht, p. 1;

whereby Jaynes shows that in effect, the muscle is not violating the Second Law of thermodynamics because the work in a muscle is being performed on a very small scale using only one (in any event few) degree of freedom from a large molecule. Jaynes passed away in 1998 but he made a statement that his views on biology and thermodynamics would not be acknowledged until 20 years from the time he wrote his paper. This would be 2009.

Fuel powered muscles have already made the headlines (here) but they do not use large molecules to produce work. It is also interesting to note that some shape memory alloys metals (Ti-Ni) are considered for devising muscles . However since they are conductors, they are not, according to Jaynes' statement, optimal to provide the highest efficiency (since heat gets to spread easily). All this should point to a MEMS based solution.

Tex-MEMS VIII or Tex-MEMS 2006 website is up and running

Following on a previous entry, the website for Tex-MEMS VIII or Tex-MEMS 2006 is now open at: http://texmems.utdallas.edu. One of the keynote speaker will be Amit Lal, DARPA Program Manager.

Tex-MEMS VIII (or Tex-MEMS 2006) will take place in Dallas

It looks like a fire that occured in San Antonio is precluding the organizers to have tex-mems VIII in San Antonio this year. The folks at UT Dallas have decided to organize it instead. The web site will be up shortly.

Tex-Mems now has a web site

Tim Dallas just set up a web site for the whole Tex-MEMS network Ali Beskok and I started six years ago. Check it out at: http://www.texmems.org/

Tex-MEMS VI is on

The dreadful aspect of organizing a meeting like this is that you eventually seldom enjoy it. By that I mean you don't really get to see the good presentations or at least the ones you want because there is always something for the organizers to do. Case in point, I still don't have a title for my presentation yet, with the meeting on thursday, this is not good. At least being an organizer allows one to have a place holder. Most abstracts can be found here.