A Compressed Overview of Sparsity

This talk presents a high level overview of compressed sensing, especially as it relates to engineering applied mathematics. We provide context for sparsity and compression, followed by good rules of thumb and key ingredients to apply compressed sensing.
This video was produced at the University of Washington

[@anantchopra1663]

The thought experiment which concluded that most natural signals will be sparse in some appropriate basis simply blew my mind! I had never thought of it that way! I guess that explanation will stay with me for life! :D You're an amazing teacher, Prof Brunton!

[@guruprasadsomasundaram9273]

Dr. Steve Brunton - fabulous job explaining compressed sensing and sparsity! You earned a subscriber.

[@arnavdas3139]

Free education is a blessing god decided to give in recent times.... you're the 3blue1brown of engineering sir 🙏🙏...

[@bhaveshamarsingh1656]

Hello Steve Sir, Thank you for this overview lecture. And thank you for all other recent videos of yours too. Amazing to the point content with great set of examples. :-)

[@Eigensteve]

Glad you like them!

[@HilberSpaceess1]

Sir, I'm really happy to find your KZbin channel. Thank you for uploading good video!

[@pavanms6924]

Thank you so much for explaining the intuition behind the math...

[@mohammadrezanargesi2439]

Thanks to you Steve, much helped

[@elijahkuska14]

Fantastic video. Thank you Dr. Brunton. Is the 128 compressive sampling frequency universal or is it specific to the example? If specific, how is that frequency determined?

[@ricardopalanco-zamora4454]

Thank you for creating this these extremely pedagogical and very thought-over series of lectures. I bought the last edition of the book to pay back for these wonderful material but also for the hope of finding the access code to some of the videos on compressed sensing that have gone on Private Mode, in concrete videos 74-77, 86-88 and 93-100. I recently discovered your channel and had only time to watch 74 and 76 on compressed sensing. Why have then gone Private now ?. Are they under revision ?. The book is really well written and accessible but your online delivery helps connecting many dots of areas I learnt more than 20 years ago and opening my eyes to recently new mathematical developments. Thank you for preparing this inspiring material.

[@jbiful]

very nice course, thank you very much

[@MarkSimithraaratchy]

Fantastic grounding on compressive sensing. I used this to augment some other lectures from school (which I found were rather sparse).

[@CTT36544]

Hi, Steve, could you pls tell me how you made this video (by which app)? It is amazing that you are standing behind the formulation screen. Did you make the video only with yourself, and then make the presentation slides/video, and then merge these two? I would really appreciate if you can let me know the method. Thanks!

[@scienteer3562]

Dear Prof, really interesting lectures. I thinking of loads of applications for this type of processing. I was just wondering if this is how the Horizon VLBI scientists reconstructed the image of the black hole using what was actually a very sparse array of radio telescopes spaced around the planet?

[@georgepalafox5967]

Sir, great video. Heard u mention that CS won’t work well for wideband signals. How about signals that are heavy noise environments?

[@suningok]

Hi, thanks very much for the video. Do you have an introduction video on "sparse regression"? I heard it several times in multiple videos?

[@Eigensteve]

Yes, that is my next lecture series and should be coming out in about 1-2 months.

[@xchen3132]

Hi Sir, in the end of this video, you said there is another video concerning application of compressed sensing in dynamic mode decomposition. Could you please tell where can I get that video?

[@Eigensteve]

kzbin.info/www/bejne/aqWvhKSVhap5o9U

[@Grlypyt]

I'm understanding in a broad sense but struggling to recreate it practically, do you have the matlab code available for the signal reconstruction of the sinusoidal wave?

[@Eigensteve]

Yes, this code is all in Chapter 3 of our new book (databookuw.com), and the code is in a CODE.zip link on the main webpage.

[@user-wf6sw3xg5e]

Dear Steve Please after compress the image, how you can get the compression ratio because the size of the output image after reconstructed by IDWT same as input image size. I work on the programming one by myself and other by MATLAB commands but same result. Best regards Nada

[@iwtwb8]

I think in regression the errors are considered just in y, so you are minimizing distance in only the vertical direction.

[@Z.Snowdrop]

thank you that was perfect. is there any slides for this viedo or anything else?

[@giuseppepapari8870]

25:25 Are you that the L1 Norm is equal to zero on points on a 'plus sign' centered on the origin? I would say the L1 norm is zero iff all components are equal to zero. Or maybe I am missing something? Thank you in advance.

[@benzaterhadj7880]

thanks for the course, please can u give me the used code that recovers sinosoids spectrum to zeros?

[@sundarkrishnan8428]

very good explanation sir, i would like to try CS on images , sir could you please send me some basic matlab code

[@Eigensteve]

It is actually pretty hard to do this on images, because they are pretty large and aren't quite as sparse as we would like often. There are some software packages out there that do this. I think "L1magic" and also the split Bregman algorithm. If you find a good modern code, please let me know.

[@sundarkrishnan8428]

@@Eigensteve thank you so much sir for ur valuable reply

[@xiucai-finance]

Hi Sir, the Matlab code link seems to be invalid now. Could you please send it again? Thanks.

[@user-yj2kv9uq4y]

I have a quesiton. What is the ambient dimension?

[@BruinChang]

Meaningful images are something like interpretable positions on the chess board.

[@user-lp1ir3rj8t]

pretty good vedio

[@InquilineKea]

How is convex optimization relevant here?

[@vincentchung6316]

This acturally proves that god exists!

[@stevenhutt815]

The explanation that images lie in some small structured subspace of pixel space is not convincing. Simply because sampling is unlikely to result in an image of a stream just means that natural images are rare in pixel space. It doesn't mean that natural images lie in a useful subspace that is amenable to compression techniques.