Underdetermined systems and compressed sensing [Matlab]

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This video shows how to solve for the sparse solution of an underdetermined system of equations using compressed sensing (code in Matlab).
Original paper by Tibshirani (1996): statweb.stanfor...
Book Website: databookuw.com
Book PDF: databookuw.com/...
These lectures follow Chapter 3 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com...
Brunton Website: eigensteve.com
This video was produced at the University of Washington

Пікірлер: 25

@christopherrowley7601 2 жыл бұрын

Incredibly helpful series! Awesome work!

@hashirroshinvaliyaparambil70 3 жыл бұрын

You're priceless dear Mr Steve

@Eigensteve 3 жыл бұрын

Thanks so much!

@bulutosman 2 жыл бұрын

Can someone help me with the matlab code? At the line 12, minimize(norm(s_L1,1));, I'm getting an error which says "Unrecognized function or variable 'cvx_bcompress_mex'. " I've already downloaded and set up the cvx package. I didnt understand what this error means?

@orewabrt1106 5 ай бұрын

it would be cool to show how hermite transform work, it is popular as sparse domain. beside dft and dct or wavelet

@uralmutlu4320 Жыл бұрын

What about the next step? We have Theta=C*Phi, how do we get Phi to calculate x?

@yanhairen7293 3 жыл бұрын

Very informative video. Thank you so much. I am quite new to this area and have one question. Correct me if I am asking something silly: with the equation y = C * Phi * s , assume we have an image sensor + binary mask in front of image sensor(0: opaque, 1: transparent). The transparent part on the mask actually represents C. My question is how we design C. I know Phi is DCT related parameters, but how do we design the random binary mask C ?

@alegian7934 3 жыл бұрын

I was thinking, could we possibly use some norm other than 1? maybe (this is a complete guess) the naturally occuring signals tend to minimize the sqrt(2) norm. Maybe the l1 norm strips away too much

@ahmaddarawshi91 3 жыл бұрын

People do use other norms, p norms. p>=1 will maintain convexity. 0

@trikal8949 3 жыл бұрын

Sir ......can machine learning is also helpfull in solid mechanics...... If yes then please make a video on it...... I am about to do research in field of solid mechanics so please tell me

@anilkumar-kv4we 3 жыл бұрын

Thank you professor....

@bhanuprakashreddy 3 жыл бұрын

Thank you professor for presenting nice and useful information and can you please informe me how to compress an image by using compressive sensing Thanks in advance professor.

@Eigensteve 3 жыл бұрын

Here are videos for how to compress an image in Python (kzfaq.info/get/bejne/q6hjqZmfndqWlIU.html) and in Matlab (kzfaq.info/get/bejne/ga2ZicJjzp2VY30.html)

@AmirKhan_KnowTech 3 жыл бұрын

Actually, in compressed sensing we are not going to compress an existing captured image rather we are going to capture a compressed image. Compressive sensing is not a compression technique after capturing the image but it is before capturing.

@lhwadele 3 жыл бұрын

Thank you for the awesome video! I wonder in the case of the presence of noise (at 7:00 of the video), what happens if we use: subject to 'norm(y-theta*s, 1)', instead of 'norm(y-theta*s, 2)'? A more sparse solution?

@ben-z 2 жыл бұрын

Because it's placing a constraint on the distance between y and Theta*s, I think L1 and L2 would work similarly (exactly if we adjust the threshold properly). i.e. |x| < 0.001 and x^2 < 0.001^2 are exactly the same.

@hoaxuan7074 3 жыл бұрын

FFT, Walsh Hadamard are very tuned to the natural world and will concentrate that type of information down to a few dimensions. Which is unfair sharing. A random projection won't concentrate such information at all and gives fair sharing. At a price. The response to information at one part of an image will be completely different to the same information at different part of the image. A random pattern of sign flips before a FFT or Hadamard give a rough random projection. Repeat for better quality. What would be a better pattern of sign flips that still gave reasonable sharing with more regular response across say an image. I was kind of thinking the parity of an incrementing counter would be a good choice for generating such sign flips. I'll give it a try.

@hoaxuan7074 3 жыл бұрын

Of course the (Walsh) Hadamard transform is very tied up with parity and Gray codes. For a counter c running between 0 and say 255 the parity function parity(c and s) which outputs +1 or -1 depending on parity even or odd gives the different sequencies of the transform. The basis vectors. For s=0 you get the all 1's vector (sequency 0). For s=128 you get sequency 1 where the first half of the vector is +1's and the second half is -1's. There is one transition between values. The most complicated waveform (but not the highest sequency) is parity(c and 255). Which is very unlikely to occur in natural world data, yet is not random.

@hoaxuan7074 3 жыл бұрын

That's not going to work. It will just shift around the order of the sequencies. I'll have to think of some other pattern of sign flips that is sub-random and approximately orthogonal to the basis vectors of the Hadamard transform.

@charuvaza3807 3 жыл бұрын

Sir can u please make a video on restricted isometry property.

@taimurzaman7322 Жыл бұрын

How do you download cvx ?

@kristinacollins 3 жыл бұрын

Attempting to adapt this to an image, but my code does not go brrr so much as ker-chunk-chunk: stackoverflow.com/questions/66510827/compressed-sensing-why-does-my-convex-solver-fail-when-i-give-it-more-sample Any advice is most appreciated.

@nivithpmuraliNSR 3 жыл бұрын

SIR, I KNOW YOU HAVE MADE A VIDEO ABOUT KALMAN FILTER MORE THAN AN YEAR AGO SIR BUT THIS IS A SPECIAL REQUEST FROM ME SIR COULD YOU PLEASE MAKE A VIDEO ON HOW TO USE KALMAN FILTER WITH ARDUINO. SIR, PLEASE MAKE A VIDEO ON IT IF YOU CAN 👍👍

@Eigensteve 3 жыл бұрын

Thanks for the request. I would check out Brian Douglas's channel, as he has lots of great control+hardware videos.

@nivithpmuraliNSR 3 жыл бұрын

@@Eigensteve thankyou sir