Compressed Sensing - Questions from Forum Member

[fog37]

Hello,

Anyone on the forum using or familiar with the topic of compressed sensing? I have some related questions.

Thank you!

 

[Tom.G]

Not me, but just a few hours ago I ran across a recent article that may help in:

SPECTRUM magazine March 2022, pg. 44
(https://spectrum.ieee.org/robotic-foosball-table).

"Why we built a neuromorphic robot to play Foosball."
by Gregory Cohen of International Centre for Neuromorphic Systems located at Western Sydney University, Australia.

The pixels in a neuromorphic sensors - also called event based imagers - report only changes in illumination and only in the instant when changes happen. They don't produce any data when nothing is changing in front of them.
.
.
Startups Prophesee and IniVation already have brands of event-based imagers on the market.

Hope it helps at least a little bit!
Tom

 

[Jarvis323]

Hello,

Anyone on the forum using or familiar with the topic of compressed sensing? I have some related questions.

Thank you!

I am basically familiar with it from a high level (basically I've read the Wikipedia articles, done a small amount of literature review, but have never used it, and don't have a complete understanding of the math).

Just ask the questions I guess.

Although, maybe the people that can give good answers are in another sub-forum though (depending on the question), since compressed sensing is more of a topic in theoretical and applied mathematics. When it comes to using it, it will depend on what you will use it for. In some cases applying compressed sensing theory to an application domain is non-trivial, or not yet mature enough. It's a major topic of ongoing research, with lots of funding being put into it currently to help address big data challenges in various science domains.

 

[fog37]

Hello jarvis323! Thank you for your help.

My basic understanding is that we can sub-sampled a signal (i.e. capture less digital samples than Nyquist theorem requires) and still be able to reconstruct the original signal (a very good approximation of it), if the signal has structure, is compressible, and sparse in some domain (i.e. under some basis like the Fourier basis, the cosine basis, the wavelet basis, etc.)
In general, we have a continuous signal $s(t)$ and we sample it to obtain its discrete version $x[n]$. To reconstruct $x(t)$, we need $N$ samples by sampling at the frequency $$f=\frac {1}{2BW}$$. We then use interpolation to reconstruct $x(t)$ from its collected discrete samples.

In the case of compressible signals (lossy compression), we later discard the data that is less relevant and still reconstruct the original signal $x(t)$. That is what happens jpeg, mp3, etc.
In compressed sensing, we directly capture the signal information that matters. That is cool.
This leads to solving an under-determined linear system of equations: $$ y= \Phi x$$ where $x$ is the original discrete signal, $\Phi$ is the random sampling matrix, $y$ is a vector with the measured samples. The signal $x$ is equal to $x = \Psi \times s$ where $\Psi$ is a matrix containing basis vector and $s$ is a sparse vector...The goal is to find $s$! Do we need to know the basis $\Psi$ under which the signal $x(t)$ is sparse a priori?
Eventually, the problem to solve is $$y = \Phi \Psi s$$ The matrix $\Phi$ is a random matrix...What kind of randomness are we taking about? We are essentially randomly subsampling the signal $x[n]$...

Am I on the right track?

 

[Jarvis323]

Hi fog37. I'm afraid you're probably beyond me already in the mathematical understanding of compressed sensing. I might be able to help, but I'd have to do my own learning first and don't have the time now. I think the math subforums might be a better bet for now unless anyone esle here can answer your questions.

 

[fog37]

No worries! Thanks anyway.