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Karhunen Loeve interpolation?

Started by Unknown September 6, 2007
I had the idea to try interpolation based on KLT.
I tried searching for this with 4 search engines and only found one
paper that mentions this concept in passing, but without a citation.
Any ideas where I might find out more about such interpolation?

u235bomb@ml1.net wrote:
> I had the idea to try interpolation based on KLT. > I tried searching for this with 4 search engines and only found one > paper that mentions this concept in passing, but without a citation. > Any ideas where I might find out more about such interpolation? >
There is a somewhat obscure search engine called Google. If you search on "Karhunen Loeve" at Google you get 223,000 hits, on the transform, and the expansion. You get hits on applications in image and multi-channel audio processing, recognition techniques, and masses of other interesting stuff. In fact, I found so much interesting stuff in the first few screenfuls, I had to tear myself away before I ended up spending the whole day reading interesting it. Steve
On Sep 9, 6:35 pm, Steve Underwood <ste...@dis.org> wrote:
> u235b...@ml1.net wrote: > There is a somewhat obscure search engine called Google. If you search > on "Karhunen Loeve" at Google you get 223,000 hits, on the transform, > and the expansion. You get hits on applications in image and > multi-channel audio processing, recognition techniques, and masses of > other interesting stuff. In fact, I found so much interesting stuff in > the first few screenfuls, I had to tear myself away before I ended up > spending the whole day reading interesting it. > > Steve
actually I tried the over-rated Google, and didn't find what I wanted. i.e. nothing with all keywords, and zillions if you try one keyword less. After my original post, I tried a has-been search engine called Alta Vista, and it spewed forth half a dozen results that were almost useful.
u235bomb@ml1.net writes:

> On Sep 9, 6:35 pm, Steve Underwood <ste...@dis.org> wrote: >> u235b...@ml1.net wrote: >> There is a somewhat obscure search engine called Google. If you search >> on "Karhunen Loeve" at Google you get 223,000 hits, on the transform, >> and the expansion. You get hits on applications in image and >> multi-channel audio processing, recognition techniques, and masses of >> other interesting stuff. In fact, I found so much interesting stuff in >> the first few screenfuls, I had to tear myself away before I ended up >> spending the whole day reading interesting it. >> >> Steve > > actually I tried the over-rated Google, and didn't find what I wanted. > i.e. nothing with all keywords, and zillions if you try one > keyword less. > After my original post, I tried a has-been search engine called > Alta Vista, and it spewed forth half a dozen results that were > almost useful.
I'd say this is a problem with "the web" and not with any particular search engine. It is too easy for anyone to post any drivel they please, thus authoritative, accurate material is difficult to discern from the chaff. -- % Randy Yates % "...the answer lies within your soul %% Fuquay-Varina, NC % 'cause no one knows which side %%% 919-577-9882 % the coin will fall." %%%% <yates@ieee.org> % 'Big Wheels', *Out of the Blue*, ELO http://home.earthlink.net/~yatescr
On Sep 9, 7:29 pm, u235b...@ml1.net wrote:

> Well, in geophysics there are various algorithms to reduce > random noise. Sometimes somebody else adapts the > algorithm to interpolate data, either to predict missing > traces, or a regular 2:1 interpolation. > Now the KLT can be used for random noise attenuation. > Most random noise attenuation algorithms require the > signal to have linear alignment to be separated from the > noise. But I understand the KLT will recognise curves > as signal, therefore would be better at preserving > coherent signal in the presence of noise. > So I was curious if anybody had mutated the KLT > noise attenuation into an interpolation method.
I think you are confusing a bunch of things here. Some denoising algorithms can be used for interpolation, fine, but not all of them can be used that way. Do you know what a "KLT" is? It basically finds the subspace (and a basis that corresponds to it) that contains most of a signal's energy. Usually this done via the second-order, covariance structure of the signal. This can be used for denoising, if you assume that the noise is uncorrelated with the signal, and that the signal is oversampled or overrepresented in some sense. Note that the above has nothing to do with interpolation. I suppose that you can interpolate the basis. I would be surprised if this is totally new. Plus, I think you can do better than this, at least computationally. Using a KLT to get to this just seems like a roundabout way of doing it. Julius