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jpeg2000 Allows 200:1 Wavelet Compression
Polo writes "Here is an
EE times article about the ISO JPEG2000 standard that has been
finalized and allows a new wavelet compression scheme that gives
good results at as much as 200:1 compression ratios. It looks
pretty promising. It is royalty-free, but there is also discussion
about a second standard that allows third-party, royalty-based extensions. I wonder if motion-jpeg with wavelets could fit a movie
on a CD or something."
That was pretty much about time someone took the wavelets into image compression.
:)
I worked with wavelet transforms (Daubechies wavelets) a year and a half ago, and back then it was pretty clear that it would be possible to compress images and sound much harder using the wavelet domain rather than the Fourier domain.
For those who don't know, the trick is:
JPEG/MPEG/MP3 uses Fourier transform to transform the image/sound data into their spectral components. But this spectral representation of the data does not say anything about the _locality_ of the frequency components. Therefore representing spikes/discontinuties will require a very large number of frequency components when using Fourier domain, which in turn leads to poor compression. You can see this problem by drawing a few sharp lines in an image and compressing it hard with JPEG.
Wavelets on the other hand, represent both an equivalent of the frequency component, along with locality information. Spikes/discontinuities can be approximated well using only a few wavelets. This in turn leads to good compression.
Another nice thing about wavelet compression is, that wavelets tend to represent discontinuities well, even with hard compression (eg. a lot of missing or roughly approximated wavelet components). Therefore a very hard compressed image will still have fairly sharp edges, completely contrary to JPEG compression. This is pretty important if you compress a picture holding text.
Anyways, someone is now working on JPEG with wavelets... What about sound and video ?? There is no reason as to why wavelets should not provide equal improvements in both audio and video.
My personal conspiracy theory is, that there exists a *LOT* of expensive hardware that can do Fouries forwards and back to allow real-time encoding and decoding of MPEG movies in good quality. The companies producing these devices will lobby any standards-organisation to *NOT* consider wavelets and stick to good old Fourier. If this holds, it will take a few years until we see Wavelet compressed video
White noise, by definition, has no redundancy.
:-)
Many things that look like white noise are not, but white noise itself?
Incidentally static is what white noise sounds like, and any efficiently compressed signal looks like white noise, which is why a modem sounds like static.
Another interesting fact - a compressed file is a pretty good source of random data, and a compressed encrypted file is substantially more secure than a file just encrypted with the same algorithm. OTOH an encrypted compressed file is a PoS. The encryption messes up the attempted compression.
Cheers,
Ben
My usual seat in the cluetrain is at A HREF="http://pub4.ezboard.com/biwethey.ht
The JPEG committee page has links to more information regarding this image format. http://www.jpeg.org/public/jpeglinks.htm
Did wavelets a few years ago in uni, so I hope I've not screwed up my information in the few years lag, but another few points to add to this excellent summary:
1) It has been proved that a wavelets can represent the theoretical minimum information for an image. Proof uses the information's counterpart of the Heisenberg's Uncertainty Principle. That's right folks - you cannot get any more compressed than that - it simply isn't possible.
2) Unfortunately, finding the coefficients for the minimum possible representation is a bit hard on the computation side - so normally certain constraints are made like fixing the angles of the wavelet. However, decompression is pretty much standard in any case - easier. But nothing quite as close as FFT.
3) JPEG chops the picture into managable bits - you may get discontinuities at boundaries. Wavelets sweep across the picture, from big to small, gradually improving the quality at smaller areas. So you can get a nice smooth degradation of details if you decrease the size of the file - or in other words, if you are downloading incrementally, your picture kinda shimmers in nicely.
4) Wavelets have a normal like-curve. Normal like curves occur frequently in nature -- for example the human face can actually be represented by very few wavelets - the eyes, nose, mouth, face all fit quite nicely. Probably good for photos.
Barthel said this patented variable-sized window-scanning technique has been incorporated into the JPEG2000 committee draft. Besides LuraTech, Ricoh and several other committee members found bits and pieces of their patented technology in the spec. Barthel said all involved companies have signed agreements that give developers royalty-free rights to part one of JPEG2000.
The open source community should be very conserned about this issues. We don't want the LZW patent screw-up with the GIF format to happen again. There are two sollutions: either drop the patent (I don't know if this can be done, any lawyers?), or make sure that the software using it can be GPLed forever. The word "forever" is very important, so that we won't have any problems.
I believe that we should put enough pressure on this standart and make it really free. If the screenshots are real, it is definitely worth it.
By the way, I am not completely sure that this is real. Something like this usually pops up every second year, and usually it's fake. I remember reading about fractal compression, which was supposed to blow JPG away. It was in the early 90s, and obviously it didn't have much effect on the industry.
Such advances are really great for the IT industry and the commmunity. I can't wait for downloadable high qualit movies to become available. The next big thing after MP3 will be movies. Either pirated or commercial, movies will be available on the Internet. I can see all the big movie companies making movies available for download for a small charge (even if it's $3 or $5 I will gladly pay it, instead of spending hours looking for the same movie on some pirate site. The Internet will drop the marketing and distribution costs for most of the movies, and it will make it profitable to make the files available, even if the piracy level stays high.