"Compressive Sampling" (Compressive Sensing)...WTF????!
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Old 02-05-2016, 10:28 PM   #1
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Icon4 "Compressive Sampling" (Compressive Sensing)...WTF????!

https://en.wikipedia.org/wiki/Compressed_sensing

Quote:
Compressed sensing
From Wikipedia, the free encyclopedia

Compressed sensing (also known as compressive sensing, compressive sampling, or sparse sampling) is a signal processing technique for efficiently acquiring and reconstructing a signal, by finding solutions to underdetermined linear systems.

This is based on the principle that, through optimization, the sparsity of a signal can be exploited to recover it from far fewer samples than required by the Shannon-Nyquist sampling theorem.

There are two conditions under which recovery is possible.[1] The first one is sparsity which requires the signal to be sparse in some domain. The second one is incoherence which is applied through the isometric property which is sufficient for sparse signals.[2][3]
OK, today my mind got blown.
Time for an upgrade.

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Old 03-05-2016, 08:22 AM   #2
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Re: "Compressive Sampling" (Compressive Sensing)...WTF????!

It really is not that complicated. If we can assume that the signal contains less data than the maximum amount of possible data (In other words: The signal is not pure noise), we can reconstruct the signal from an according number of samples. In other words, because signals are not noise and they contain redundant information, we can reduce them into domains where there are a lot of zero coefficients. Think about your basic piano chord for example. If you just look at the samples themselves, or an oscilloscope shot, it may not seem particularly sparse as a signal. If you look at a spectrograph instead, you will notice that there are a lot of frequencies that are not present in the signal. Essentially the signal is sparse in the frequency domain, but not sparse in the time domain.

Thus we can sample something, say for example an image matrix or a musical excerpt, and we do not need particularly many samples for this. We will essentially get parts of equations from here - or we get values that need to conform to the equations behind them. No unique solution necessarily exists, as we have more unknowns than functions, but if we can assume that the signals are sparse in some domain like the piano chord example before, we can find a satisfactory solution.

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Old 03-05-2016, 08:48 AM   #3
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Re: "Compressive Sampling" (Compressive Sensing)...WTF????!

Sounds a bit like what is done in video compression where the parts that do not change from frame to frame (e.g. a static background) is redundant information while it is not changing.

Getting rid of this redundant informtation enables the kind of compression rates you get in formats such as divx. At least that's how I understood it to be

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Old 04-05-2016, 10:02 PM   #4
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Icon7 Re: "Compressive Sampling" (Compressive Sensing)...WTF????!

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Originally Posted by professurreal View Post
Sounds a bit like what is done in video compression where the parts that do not change from frame to frame (e.g. a static background) is redundant information while it is not changing.

Getting rid of this redundant informtation enables the kind of compression rates you get in formats such as divx. At least that's how I understood it to be
Yeah, I got into this topic after looking up about literally 99 different articles related to digital image enhancement / correction / high-fidelity storage functions (both artistic and technical).

I've been studying a little bit of semi-intelligent/sampled image noise reduction software. I've just got a demo version, but it's so powerful, that I learn a lot from it and then I either edit the results or the source material or both.

The nice thing about understanding a little bit of waveform science is that it translates into several different fields simultaneously. So even if you can't comprehend the Mathematics, it starts to make sense if you see enough incarnations of a applied waveform science.

You guys are both helpful in what you both said, too.

I have the intuition that it's also applicable to things like

Adaptive Differential Pulse Code Modulation

or pretty much any type of modern encoding where the input is compared to the output or the metaoutput and both corrected for errors and/or related to a predicted signal. Often it's more efficient to store the difference instead of the value. Or it's more efficient to store whether or not a condition changes rather than merely the exact values of the conditions.

Calculus is deep as heck in this stuff... In a good way!

I didn't really say this stuff right, but the signal to noise ratio of my comprehension is gradually getting better

Also, of course a signal could be sparse if it's like a wire that's picking up intermittent bursts of noise that are low amplitude and or separated by long silences. The long silences can be compressed and low amplitude might help compensate for the complexity of the noise waveform.

IDK, stuff like that.

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Old 29-06-2016, 06:19 PM   #5
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Re: "Compressive Sampling" (Compressive Sensing)...WTF????!

This is a really interesting article, and it gives a major insight into the future of audio compression. Who knows, we might soon get a FLAC successor that can reach the same compression ratio as OPUS.

I always found the concept of sampling at a variable rate interesting. For example, a recorder that would reduce the sample rate if you're only recording muffled sounds without high frequency content, for example. Then when it detects a bright sound it turns the sample rate up again. I think techniques like this are already being used in the form of variable bitrate, but the sample rate always stays the same even though that might not be necessary.
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Old 30-06-2016, 12:30 AM   #6
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Icon3 Re: "Compressive Sampling" (Compressive Sensing)...WTF????!

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Originally Posted by Kenophos View Post
This is a really interesting article, and it gives a major insight into the future of audio compression. Who knows, we might soon get a FLAC successor that can reach the same compression ratio as OPUS.

I always found the concept of sampling at a variable rate interesting. For example, a recorder that would reduce the sample rate if you're only recording muffled sounds without high frequency content, for example. Then when it detects a bright sound it turns the sample rate up again. I think techniques like this are already being used in the form of variable bitrate, but the sample rate always stays the same even though that might not be necessary.
Interesting concepts. Thanks for comments.

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