Once again you are providing an excellent high level overview in very simple terms (for the mathematically trained). Really enjoy your videos.

I have never come across this...what a powerful idea! You are doing a great job covering it. Thx

@prashantsharmastunning

3 жыл бұрын

2 months ago how?

I'm currently studying a Phd and your work and videos really inspire. Thanks for this great video series!

You are a legend steve. I dont care about this method but still watch it because you make it interesting and understandable

Today is a GREAT day! Profesor Brunton upload a new vid :)

I've been reading up on compressive sensing literature (e.g. by Richard Baraniuk et al.), and they are really hard follow for a math lightweight like me. Your explanations are so much clearer. Looking forward to see more in this series.

Thank you for all your videos. This is how all professors should give a lecture at university.

Thanks a lot! Cant wait for next lecture! Greetings from México 🙂

Thank you so much for making this. This helped me a lot. Please make more videos on compressive sensing. 😊

great!!! cant wait for the next lecture.

Love this topic series

Love this guy!

Hi Professor, had a question regarding the equivalent formulation. Could we also reformulate the original convex problem as minimization of (L2 norm) ||Θs-y|| subject to constraint (L1 norm) ||s||

Hi Professor, I have a question about the measurement matrix C. I see in literature that most seem to portrait it as a dense random matrix, not a spiky one on each row as you show here. So I guess you show C as a spiky matrix, just because that it is incoherent with the Fourier basis so it would function as well as a dense random matrix? I think I was confused originally when I saw you (in one of the previous video) taking random data points in time domain for super-positioned sine-waves, rather than taking random "combination" of all data points in time domain (which a random matrix would do). So, hopefully my above understanding is correct. Thanks for all the videos!

is x here represents the compressed version of the original image since we are inferring the "active" Fourier coefficients? So it shouldn't be the high-resolution image. Am I correct?

Love it! Why Does anyone need Netflix :)

Is the sparsest solution to the underdetermined problem unique?

Good morning Professor, Thank you for the nice videos. I have one question though: why do we want "the sparsest" s to be our solution? Shouldn't we look just for the "right" s? How can we claim that the sparsest s is the right one? Thank you, Matteo

@Eigensteve

3 жыл бұрын

Great question. We want the sparsest vector because we have the observation that signals in nature are almost always very sparse. So solving for the sparsest vector is often a proxy for solving for the "natural" vector. This is extremely peculiar, and not at all obvious at first.

but what if we have s and we want to find the right fourier basis?

Extremely relevant insights into the topic, professor. Thank you for discussing these.

Is this somehow connected to LASSO and Ridge regressions? Love you videos! Thanks a lot!

@firemario876

3 жыл бұрын

yea, lasso is analogous to L1 regularization, which encourages sparse answers stats.stackexchange.com/questions/200416/is-regression-with-l1-regularization-the-same-as-lasso-and-with-l2-regularizati

Hello, thank you for this great lecture. I have a question, in the equation (y=C.x ) isn't possible that there are many xs that give the same y? Thank you in advance.

@weradsaoud2018

5 ай бұрын

does the sparsest s constraint is sufficient to determine the wanted x?

Thanks for this video ok

1:45 do you mean underdetermined or undetermined?

@Eigensteve

3 жыл бұрын

Underdetermined... I wrote it wrong on the board.

@dabulls1g

3 жыл бұрын

@Steve Brunton thanks! Great lecture!

SIR COULD MAKE VIDEO ON USING KALMAN FILTER WITH C++ LANGUAGE OR PYTHON

Hey please add the code for image compression using DCT,FFT,Wavelet

@Brainwizard.2

3 жыл бұрын

Do your homework

I appreciate you making videos on this topic for the not-so-bright people like me. I'm fine with utilizing math, but when that math is presented without context it drains all life out of me.

Thank you very much for your complete and helpful explanation. If possible, I would like to have your email and ask you some questions.

عاشت ايدك

I can't work out the transformation that he is using to write on the board 🤣. He's writing in reverse, right?!! :-O

@kristinacollins

3 жыл бұрын

If I'm not mistaken, it's mirror-flipped and he's actually writing with his left hand.