Beginner's Guide to Compressed Sensing in Signal Processing

[maNoFchangE]

I hope this is the right place for this post.
I'm originally a physics student but my thesis supervisor assigned me a work in which the concept of compressed sensing (CS) becomes the underlying aspect. I have searched some sources online but, no good. I guess this is because this CS thing is already a very specific topic in signal processing which I have not been familiar with, given my background is physics. As I went further in those sources I came to come across completely new terms to me, so I think this subject is not something someone outside electronics/electrical engineering can quickly comprehend. That's why I would like to ask here if someone can give me direction I should follow and the related references, for instance what are the important concepts I need to possesses etc. I would really appreciate if you can suggest me references that a beginner like me can study for like one or two weeks. Also if you want to cite books, please specify the corresponding chapters.
Regards.

 

[berkeman]

I hope this is the right place for this post.
I'm originally a physics student but my thesis supervisor assigned me a work in which the concept of compressed sensing (CS) becomes the underlying aspect. I have searched some sources online but, no good. I guess this is because this CS thing is already a very specific topic in signal processing which I have not been familiar with, given my background is physics. As I went further in those sources I came to come across completely new terms to me, so I think this subject is not something someone outside electronics/electrical engineering can quickly comprehend. That's why I would like to ask here if someone can give me direction I should follow and the related references, for instance what are the important concepts I need to possesses etc. I would really appreciate if you can suggest me references that a beginner like me can study for like one or two weeks. Also if you want to cite books, please specify the corresponding chapters.
Regards.

Could you say a bit more about what you have found so far? Is this data compression of sensor data? Or something different?

If it's data compression of sensor data, then the general search term would be data compression, and in the context of sensors, you would look at the kind of data you get from different kinds of sensors, to pick the best compression algorithm to use for each. For example, many sensors are low bandwidth, with slowly varying data outputs. That would suggest one type of data compression. Other sensors jump in steps, which would suggest another type of data compression...

 

[maNoFchangE]

It is also known as compressive sampling and lies on the so called sparsity of the measured signal. According to the reference I found, using compressive sampling one can recover sparse signals with smaller sampling rate, which goes against the older established theory of Shannon's sampling. That's what I read from a reference, but I merely used the definitions there. I don't claim I understand most part of what I say. It's also said that CS is related to the "sparsity".

 

[meBigGuy]

Have you read the wikipedia article? Lots of references and associated technologies also.

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

 

[maNoFchangE]

meBigGuy, as I have written in my original post,

As I went further in those sources I came to come across completely new terms to me, so I think this subject is not something someone outside electronics/electrical engineering can quickly comprehend.

My problem is not only finding good references but also understanding the underlying concepts which I am completely new to. I don't want to just "know" what CS is, instead I feel like I need to get the understanding from the root. Finding the needed concepts might not be difficult if it had been a branch of physics but since it seems to belong to electrical engineering stuffs, I need the help from those more familiar with that field.
But actually after some readings one of those underlying concepts in CS is the optimization problem. I have made another thread under textbook forum asking about (preferably) undergrad textbook that contains optimization problem. If you want to give your recommendations here instead, it would also be welcome.

 

[sophiecentaur]

It is also known as compressive sampling and lies on the so called sparsity of the measured signal. According to the reference I found, using compressive sampling one can recover sparse signals with smaller sampling rate, which goes against the older established theory of Shannon's sampling. That's what I read from a reference, but I merely used the definitions there. I don't claim I understand most part of what I say. It's also said that CS is related to the "sparsity".

Sub-Nyquist sampling is a fairly common technique and you can get away with sub sampling as long as you take care that the alias frequency components do not coincide with the un aliased ones. You can eliminate the alias components with a subsequent comb filter. When the original signal is periodic and fairly unchanging then you have to choose the sampling frequency so that alias components interleave with the wanted ones. This is a technique that was used in digitising PAL TV signals and worked perfectly for stationary pictures but would introduce artefacts with movement. The more you know about the nature of the original signal, the better job you can do when sub-sampling.

It may help you to get more information if you search using the terms I have used, as well as "compressive sampling" which may be a bit more specific than you need when you are reading round the topic.

 

[meBigGuy]

sophie, have you bothered to read the wikipedia article on compressed sensing?
" is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems. "

maNoFchangE:

You are asking a question about a very complex signal processing technique that requires understanding of linear systems, sparsity, and incoherence.

Just understanding sparsity is a major learning process. http://en.wikipedia.org/wiki/Sparse_matrix

The references at the end of the wikipedia ( http://en.wikipedia.org/wiki/Compressed_sensing ) article might put you onto something that will present it in terms you can understand.

For example,
http://www.brainshark.com/brainshark/brainshark.net/portal/title.aspx?pid=zCdz10BfTRz0z0

BTW, I have done no reading on this and cannot personally recommend any references.

 

[sophiecentaur]

sophie, have you bothered to read the wikipedia article on compressed sensing?

I read it and I realize that it is a different approach but it still involves sub sampling of a signal and attempting to eliminate the resulting artefacts. That article has much more in common with practical systems than you seem to have spotted. Terminology may be different in places, of course. The OP clearly needs a broad input of references to work with if a PhD thesis is the final aim and the available specific information is 'sparse'. The parallels between apparently different systems that use sub sampling are well worth finding out about. It is never a bad thing to relate abstract Maths to more elementary (possibly) concrete applications.

 

[maNoFchangE]

You are asking a question about a very complex signal processing technique that requires understanding of linear systems, sparsity, and incoherence.

Yes, I have also read that those three become the main pillars of this sensing method.

The OP clearly needs a broad input of references to work with if a PhD thesis is the final aim and the available specific information is 'sparse'.

This has become kinda dilemma for me, first it's not for PhD thesis, instead a master thesis and for my PhD I already plan to switch topics so I will most likely never touch my current problem anymore in the future. And it's not that I hesitate to learn this CS thing all the way from the needed underlying concepts such as those three mentioned by meBigGuy and in additional the signal processing, which also turned out to be important given I have only shallow background on that subject, on the other hand my supervisor gave me one week to come to a conclusion whether using compressed sensing is applicable with the work I will be working on. If I were to study a subject that I'm very likely not going to use it again, I prefer to learn it all out and one week is obviously not enough. I can probably learn it in rush in a week, simply accepting everything that stands in the way without trying to get a proper understanding, but that way I don't think what I will have learned can stay in my memory for long enough time, that simply doesn't worth the time of one week learning. By the way I'm really sorry if I spit out too much of my personal problem, I'm really desperate of what to do, I wanted to consult to my supervisor but he is not around throughout this week.

 

[sophiecentaur]

Commiserations. Many supervisors do not give an awful lot of thought when they suggest projects and seldom match them to individual students.
One strategy I might suggest would be to get a couple of specific questions together, from that article, and see whether he can answer them OK. IF not, then you could say that there may just not be enough material for you to work with in that single paper and that you would need a lot of help from him/her. Now's the time to ask for help.

 

[maNoFchangE]

Thanks for your concern sophiecentaur.
Actually my supervisor is not that inconsiderate, I have been working with him for more than 5 months and up to now (before he gave me the papers about this CS thing) his tasks for me were all easily conceivable and were done well I would say. What happens this time is seemingly he looked into these papers which he suggested me to study from, and came to think that the contents of the papers might be applicable for my thesis (which I also think indeed applicable) but without having looked into the technical part which turned out to be something that I completely never learned about, which is this compressed sensing. That's why I'm waiting to have a talk with him next week and hopefully I can either have more time or have another different subject to work on.

 

[sophiecentaur]

You are lucky and your supervisor will, no doubt, help you here.