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This is a great question but it's a little off-topic. I've been watching compressed sensing (CS) from the sidelines for the past decade, while wearing experime

This is a great question but it's a little off-topic. I've been watching compressed sensing (CS) from the sidelines for the past decade, while wearing experimental-cosmology, synthetic-aperture RADAR, and instrumentation/FPGA hats. (Not electrodynamics or optics, per your question, but nearby.) Here's my perspective. If you're doing compressed sensing correctly, it transforms the entire instrument from electrically complex and algorithmically simple, to algorithmically complex and electrically simple. Unfortunately this isn't a strategy you can bolt on to a traditional architecture and turn off as a de-risking strategy if it doesn't work. From the perspective of a team building a tool to accomplish a task, it's an all-or-nothing gamble. Consequently, the challenges to aggressive adoption of CS are both technical (can it work?) and programmatic (is it feasible given human, political, and financial constraints?) In the fields I've been exposed to, state-of-the-art instrumentation is complex enough that domain experts spend their entire careers understanding the quirks of a few established instrument topologies. Where CS is applicable, it would take a big leap of faith from an entire team to build an instrument around CS. Before that leap of faith is accessible, the team would have to be conversant in CS research and the implementation of CS algorithms in practice. And, after the leap of faith, a successful CS project requires secondary leaps of faith from funding agencies to get these instruments built. These barriers are highest for exactly the kind of complex, expensive projects where CS is supposed to shine. As an aside, the latest IEEE Signal Processing magazine (https://ieeexplore.ieee.org/document/8653526 https://ieeexplore.ieee.org/document/8653526) has an interesting article on hardware architectures for compressed sensing. As CS progresses, and as CS researchers transition from pure-CS research to applied-CS techniques, the use of CS in physics will probably grow.

billfruit 8y ago
So I gather that CS requires new types of instrument typologies and know-how, till we see it deployed more widely. I am though ever in awe of the hype that ML/NNs are getting for the past 2-3 years, where as Compressed-Sensing is likely to be a more fundamental shift in many fields.
- ChrisFoster 8y ago
  I'd argue the opposite. Vanilla CS theory assumes a very simple system model for the measurement process (ie, linear measurement) and shows that with a few assumptions you need far fewer measurements than you might expect. This by itself is a valuable observation. However, I'm less impressed with CS as a practical tool because in many realistic systems the measurement process is nonlinear and difficult to model. That is, the desired system state you're trying to infer is some nonlinear function of the experimentally measured quantities. I think the best instruments of the future will use CS ideas to motivate the use of an appropriate sensor domain to reduce the number of measurements required. But that actual computational reconstructions of system state (ie, inference) will be done with a nonlinear differentiable model which can be optimized using a data driven approach and with ML-like tools. In addition to the benefit of allowing nonlinearities, this approach gives you a lot of freedom to optimize the computational complexity of the reconstruction (ie, complexity of the system model) vs accuracy of the results.

billfruit 8y ago

So I gather that CS requires new types of instrument typologies and know-how, till we see it deployed more widely. I am though ever in awe of the hype that ML/NNs are getting for the past 2-3 years, where as Compressed-Sensing is likely to be a more fundamental shift in many fields.

ChrisFoster 8y ago
I'd argue the opposite. Vanilla CS theory assumes a very simple system model for the measurement process (ie, linear measurement) and shows that with a few assumptions you need far fewer measurements than you might expect. This by itself is a valuable observation. However, I'm less impressed with CS as a practical tool because in many realistic systems the measurement process is nonlinear and difficult to model. That is, the desired system state you're trying to infer is some nonlinear function of the experimentally measured quantities. I think the best instruments of the future will use CS ideas to motivate the use of an appropriate sensor domain to reduce the number of measurements required. But that actual computational reconstructions of system state (ie, inference) will be done with a nonlinear differentiable model which can be optimized using a data driven approach and with ML-like tools. In addition to the benefit of allowing nonlinearities, this approach gives you a lot of freedom to optimize the computational complexity of the reconstruction (ie, complexity of the system model) vs accuracy of the results.