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From: bhaskara@fc.hp.com (Vasudev Bhaskara)
Subject: Re: Whatever happened to SVD?
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Date: Tue, 4 Apr 1995 22:07:43 GMT
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Mitchell R Grunes (grunes@news.nrl.navy.mil) wrote:
: In article <stusch-0104952247030001@stusch.tiac.net> stusch@tiac.net (Stu Schaffner) writes:
: >Just curious... I remember reading a book several years back about the
: >use of Singular Value Decompositions for image compression (and other
: >things). It sounded good at the time, but the technique doesn't seem
: >to be in wide use now. Could anybody briefly comment on why?

: Someone or other claimed that SVD and DCT were typically very close in 
: the spatial domain, and DCT is faster.  And it obviously involves
: more overhead.  But some people still use it, I think.

: On the other hand, at a recent DCC session oriented towards Navy
: applications (but open to the public), someone mentioned that SVD seemed 
: to work much better in the spectral domain (e.g., across the three
: bands of RGB in a simple color image, to take a simpler example.)

: Quite reasonable--different electromagnetic frequencies may represent 
: different physics, including abrupt transitions at the frequencies where 
: substances absorb or emit light.  And it might work well in the 
: polarization domain, or in multi-sensor domains, as well.

SVD has a very interesting property in noisy channels. In the case of DCT
coded data, channel noise manifests as (in many cases) a black block in the
spatial domain. In the case of SVD, you tend to affect one eigenvector and
it shows up as a line artifact (if SVD is also done on same blocksize as DCT,
the line artifact is the same length as the block-size, e.g. a NxN block
will give a N pixel line artifact for SVD and a NxN block artifact for DCT).
So, SVD can claim to have better SNR in noisy channels. Also, noise reduction
is easy in this case since a simple median filter will fix this. 
I did some work on comparing SVD with DCT with DHT long before DCTs were
fashionable (around the early 80's). Another feature with SVD is that
reconstruction is a sum of inner products and so, one can get a progressive
transmission scheme at very little cost (DCT proponents will take issue with
me on this since a cleverly organized DCT output can facilitate this as well -
it just requires less work in the SVD case). Of course, as Steve Eddins
pointed out, SVD encoding is very(very) expensive. Last year's
Picture Coding Symposium (held at UC Davis - for proceedings, you might
try and contact Prof. Ralph Algazi) had a paper on SVD coding for images.

- Vasudev

    Bhaskaran Vasudev                  
    Visual Computing Department        Email: bhaskara@hplvab.hpl.hp.com
    Hewlett Packard Labs               Tel: (415) 857-7153
    1501 Page Mill Road                Fax: (415) 852-3791
    Palo Alto, CA 94304, USA
