Compressed Sensing (2016)

#1

Post by chaosmachine » Sat, Jul 18, 2020, 7:34 PM UTC

Compressed Sensing (2016)
pyrunner.com

Re: Compressed Sensing (2016)

#2

Post by hatsunearu » Sun, Jul 19, 2020, 3:53 AM UTC

This is incredible, though I'm a little confused as to why the psi matrix is IDCT and not something of a Fourier flavor...

Re: Compressed Sensing (2016)

#3

Post by nine_k » Sun, Jul 19, 2020, 4:13 AM UTC

hatsunearu wrote: post #2

This is incredible, though I'm a little confused as to why the psi matrix is IDCT and not something of a Fourier flavor...

I suppose the Fourier transform can be formulated as a cosine transform?

Re: Compressed Sensing (2016)

#4

Post by nine_k » Sun, Jul 19, 2020, 4:15 AM UTC

Finally, a hands-on guide to implementing the "enhance this image" command from SF movies! Sort of.

Also, an important observation about approximation, outliers, and deviation measures.

Re: Compressed Sensing (2016)

#5

Post by notajoke » Sun, Jul 19, 2020, 4:21 AM UTC

How does the audio example square with nyquist limit? Basically you can get it back, mostly, with some clever tricks, but I’m not crazy thinking that the original was decimated beyond lossless recovery right?

Re: Compressed Sensing (2016)

#6

Post by timeinput » Sun, Jul 19, 2020, 4:43 AM UTC

notajoke wrote: post #5

How does the audio example square with nyquist limit? Basically you can get it back, mostly, with some clever tricks, but I’m not crazy thinking that the original was decimated beyond lossless recovery right?

It was, but the goal isn't lossless recovery it's good enough recovery either in an L1 minimizing sense, or some other criteria

Re: Compressed Sensing (2016)

#7

Post by timeinput » Sun, Jul 19, 2020, 4:45 AM UTC

hatsunearu wrote: post #2

This is incredible, though I'm a little confused as to why the psi matrix is IDCT and not something of a Fourier flavor...

I thing DCT is a special case (only real) version of a Fourier transform.

Re: Compressed Sensing (2016)

#8

Post by hatsunearu » Sun, Jul 19, 2020, 5:48 AM UTC

timeinput wrote: post #7

hatsunearu wrote: post #2

This is incredible, though I'm a little confused as to why the psi matrix is IDCT and not something of a Fourier flavor...

I thing DCT is a special case (only real) version of a Fourier transform.

Well, kind of. The FT on a real signal gives you a symmetric spectrum that is complex.

IDK seems kinda weird, there's a lot of handwavey stuff that I don't fully understand.

And I'm also wondering what the significance of the frequency domain is--can you generalize compressed sensing with other transforms as well?

Re: Compressed Sensing (2016)

#9

Post by occamrazor » Sun, Jul 19, 2020, 8:41 AM UTC

JPEG compression works in a similar way: the image is segmented in blocks, each of them is transformed to frequency domain via DCT and then the frequency coefficients are quantized, or discarded if small. The rules for the last step are optimized to minimize human perception of discrepancy between original and compressed image.

What compressed sensing shows is that even a very rough optimization step, completion unaware of contents and human perception, can give worse but comparable results.

Re: Compressed Sensing (2016)

#10

Post by ilaksh » Sun, Jul 19, 2020, 9:00 AM UTC

Supposedly Helm.ai is using compressed sensing in some way for self-driving car vision. According to an article/interview I saw.

The way it was mentioned made it sound like the compression could be very smart somehow in terms of useful feature extraction. Although I was probably just reading too much into a fluff-piece. Maybe they are just using it to make it easier to get real-time processing (via normal deep learning techniques).