CS: Questions and Answers

In These Technologies Do Not Exist, I mentioned the possibility of performing some type of time modulation on a PMT.. A commenter, David, pointed out to me that I might be mistaken and that this technology possibly already exists:

....If this was a passive detection would it not be described as an analogue lock-in amplifier?

http://en.wikipedia.org/wiki/Lock-in_amplifier

Or if active, a heterodyne or homodyne detection scheme?

http://en.wikipedia.org/wiki/Heterodyne_detection

Our community routinely uses active non-linear detection with PMTs to measure phase and amplitude of time-modulated photon density waves in biological tissues. For example:

http://www.lrsm.upenn.edu/pmi/papers/AGYgroup/XingdeLi/YYang97OptEng36.pdf

http://dx.doi.org/10.1117/1.1331561

David

I am not sure this is the same thing, but I need to check on this further. Thanks David, whoever you are :)

A while back, on the Linedkin Compressed Sensing Group Discussion, Robert Kosut asked

Do any of you know what the largest signal sizes are that have benefited from CS? And what are is the computational time associated with that? And is any of this in papers.

Emil Sidky answered with:

The application to image reconstruction in X-ray computed tomography might be the one with the largest signal sizes. I know at least that we have reconstructed images with 10^8 -10^9 voxels from ~10^7 transmission measurements. But there are a couple of points to keep in mind:
(1) It's not clear whether or not the system matrix for CT admits exact reconstruction under ideal conditions, because we're not doing random sampling.
(2) For these large systems, we do not solve the constrained, TV-minimization problem to numerical accuracy of the computer. We typically truncate the iterative algorithm at 10-20 iterations, well short of convergence. Nevertheless, the CS-style optimization problems appear to lead to effective recon. algorithms for CT with sparsely sampled view angles.

As for recon. time: with the truncated algorithms and using GPU acceleration we have achieved decent results in 10 min. for problems of the size mentioned above.

A couple of our references:
http://arxiv.org/abs/0904.4495
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2630711/
http://arxiv.org/abs/0904.1016

Emil

While Eric Tramel answered:

Oh, also, if you consider them as a single problem, decoding of CS encoded video might be one of the largest problems, depending on video length :P

You're looking at 4-5*10^8 pixels per minute of video (and far sub HD at that).

Hao Shen just asked a new question on the LinkedIn compressed sensing group discussions.


Thank you all for asking and answering questions publicly. It will go a long way toward making CS more mainstream. The Theoretical Computer Science Q&A will become public on Monday, outstanding!