What is Sparsity? 

When I was 10, I got up early on a Saturday for the Smurfs. Now, I get up early for Sparsity. No commercial interruptions. All that's missing is some Lucky Charms.

Life would be so much better when they teach about applications before dry theory as motivation. I am very thankful for these amazing videos.

Thank you so much, Steve! You're connecting the practical implementations with the underlying math incredibly seamlessly, almost a work of art!

Many thanks indeed for providing such great lectures and sharing it with us. :)

Thank you Steve. Your RU-vid videos are a great balance of accessibility of quick bite-sized concepts without the lowering of discussion to menial examples.

Omg, I'm completely in love for signals because of you!! Hope doing something cool soon with all this!

Thank you very much for these amazing and well detailed videos, I'm actually working on my Master's degree thesis about cognitive radio and these videos helped a lot in the compressed sensing chapter!

Thank you Professor Steve. Just what I was looking for! Your tutorials have helped me in my masters in Control engineering, and this new series is a helping hand at the start of my PhD.

Thank you for the video, great as usual

You just made it super interesting. Hats off.

Dear Steve... your lectures are a blessing. Thank you so much 🙏

What a time to be alive!

Holy shit man, I just discovered your channel and it feels like I have found a gold mine! There are soo many useful videos that I don't even know where to begin. Is there any way to support your work so you can continue creating this wonderful content? Patreon, Paypal, Donations?

Dimensionality reduction is simply awesome!

Thanks professor.

Hi Professor Steve, Thanks for the nice idea shear with us.

Man u look like HG Wells from flash series ....luv ur videos ❤

Thank you so much for the lectures!

love those lectures

Useful and concise

Obrigado, Steve! Things make more sense now.

Thank you very much

Just out of curiosity, are you writing backwards, or are you flipping the image with software? Very interesting and effective video making setup.

I just wish this was available 30 years back when I worked on video compression. Great material and well presented indeed. But as far as I recall JPEG relied on DCT, not DFT.

super super interesting

Thank You !

Amazing explanation!! :)

7:30 When the metalhead in you kicks in \\m// :) One question, what is a quantitative measure of sparsity? Like how much percentage of elements should be zero to count a matrix as sparse?

I suspect sparsity and structure might be the same thing. I think that translates to a high degree of linear independence being more informative. Then information is something which is less dependent on circumstance.

Thanks for these amazing videos! I really appreciate if you could talk a little bit about L0 norm also. Thank you!

Is the the sum of the values in the sparse S 'equals to 100%' like they are the whole values that play a role in the equation ?

Thank you for the video! very helpful! is it possible that some basis gives us a more sparse result than others? Like here the DFT may give us 10 non-zero entries of a 1mil entry image, but what happens if we use a different transform that gives us 5 or 20 non-zero entries? Does that make a difference and is it in our interest to look for transforms that keep increasing the sparsity?

steve brunton in 1440p oh my god

In Tailored Basis what is epsilon r and Vr?

for what its worth jpeg uses discrete cosine transform and not discrete fourier transform - awesome vids tho

But how is he writing everything backwards so easily...?