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New Sampling Techniques Make Up For Lost Data
An unnamed reader writes: "Professors at Vanderbilt and the University of Connneticut have published a non-uniform sampling theory that could yield better quality digital signals than the standard Uniform sampling techniques pioneered by Shannon at Bell Labs.
The Vanderbilt press release and link to the published paper can be found here."
No.
As the abstract says
"The new theory, however, handles situations where the sampling is non-uniform and the signal is not band-limited."
So it isn't applicable to digital music (as this is band-limited by our hearing, and we can pick the sampling interval) but other signals that cannot be sampled well by regular sampling (either in time or in space). Examples given are seismic surveys and MRI scans. But you knew this as you'd have taken the time to read the linked article first, wouldn't you?
What's the practicality of this? Well, spiral MRIs, for example, where for mechanical reasons you don't want to have to stop-and-start the very heavy "scanner", wasting time and jarring sensitive equipment. As I said, niche applications.
As for compressing audio, there are already plenty of other psychoacoustic compression schemes -- whether non-uniform sampling is better or worse will likely depend on the application.
It was at Bell Labs ... but the guy who developed the Uniform Sampling Theorem was Nyquist, not Shannon.
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About 7 years ago, I was involved in a research project, trying to use video teleconferencing and doctors for remote diagnosis of patients.
We found that jpeg compression of images made medical diagnosis unreliable. Hairline fractures in x-rays are exactly the kind of small details that tend to get washed away in 'lossy' compression, and the banding caused can lead to false assumptions as well.
The article suggests that this is still a lossy compression with small amounts of data loss. I know Doctors that would take that admission as a condemnation of the technique.
Doctor to patient, after looking at the reconstructed images: "Ah there is the problem. The cause of your headaches is that you have a bunch of inch-long bony spikes sticking out of your neck, plus a bunch of holes in your skull."
example. It was not provided to show a compression mechanism in which the original image could be compressed. It was intended to show that if you sample randomly, then their algorithm can come up with a highly accurate representation of the original. The implication here is that given current capability to sample, if you apply the new technique, you can get a better image/audio recording using their technique, than you can using the current fixed sampling interval technique, making the image more vivid, or the musical recording more lifelike than current sampling provides.
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Along your point, there's actually a technique that uses the self similarity of images to help you compress themselves. For example, you might have seen the "Sierpinsky Triangle." You can generate this image with a few very simple recursive move/resize/draw operations.
Fractal compression uses this technique on abstract images. It aims to find a set of operations (sometimes very large) to generate any given input picture. It's very cool, and you can get more information (including example pictures) at this page.
The "state of the art" of fractal compression beats JPEG compression at some compression ratios, but looses at others. It's also interesting that a fractally-compressed image has no implicit size (ie: 640x460), so it enlarges MUCH better than simple image enlargement.
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This is not quite accurate. The original signal is not "required" to be band-limited. Rather, it is accepted that frequencies outside of your design bandwidth will not be captured. The signal can stray outside of the "defined limits", but should it do so that information will be lost. Furthermore, Fourier's math tells us that a signal that is limited in time is unlimited in frequency, and a signal that is limited in frequency is unlimited in time. This has important ramifications. The biggest - and most obvious - is that all man-made signals are limited in time and therefore unlimited in frequency. Ergo there will ALWAYS be information lost no matter what bandwidth you design for.
Now to read the rest of the article - it sounds intriguing...
Any medical imaging technique can only be so accurate, due to either machine or physical limitations. This defines a maximal meaningful sampling rate or resolution for that imaging modality. For example, positron emission tomography (PET) has a physical resolution limit of 10mm because positrons can propagate up to 10mm from where they are generated before they decay into gamma radiation that can be detected by the machine. With this technique, a doctor can get an image with better than 10mm resolution, something that the machine by itself could never do.
BTW, sampling doesn't mean that you're guessing. The sampled data points are the actual measured values of the signal at specified points in time or space. You have to sample because there is no way that you could collect all values for the signal for all points in time or space, and there is usually a sampling rate at which point you're collecting more data than you need to accurately represent the signal.
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I have a question/theory about nonuniform sampling rates. Okay, sticking with a 44kHz sample rate, will you hear the differeces between 8, 16, and 24 bit samples? Yes, of course. It's common in digital audio to use 16 bit samples to save space, not because it's the ultimate sample size. (While it's arguable the 44kHz rate side of the equation is pretty darn good.) It's subjective and some ears don't need any "more" audio information to be happy, but I see the choice of sample size as more of a variable than the "provable" sufficient rate for 20kHz audio cutoff behing 44kHz. All I'm saying is that there is potentially audible information below 20kHz that isn't getting encoded and recreated not because of sample rate, but because of sample size. For example, if my source material didn't "need" 44kHz througout a song, could the sample rate be trimmed back in places while the sample size was increased? In the end, it's all just a stream of x samples per second, y bits deep. So if a new sampling technique allows us to reproportion (optimize) those two dimensionons in the same amount of overall space, it's possible that better audio will result. Thoughts?