Nikos: > > Which resolution is to be enhanced? The geometric? Is it meant > > to keep PC1 and mix it with the rest, or keep the Pan and throw > > away PC1?
> > Principal Component 1 will contain the highest variance of > > your input data -- which, in fact, is a composition of different > > amount of information originated from all input bands. If you > > throw that away you are left with a dataset which is likely to > > be useless! Hamish: > (not talking about pan-sharpening, but in general,) > how about the situation where you have a map data ( we are talking about multi-dimensional data, right? ) > which is loudly dominated by a signal, and you want to try and remove that > loud signal so that you can look at the subtle variations caused by a > different source that the loud signal had been masking? Yes, this _can_ be a perfect use-case. Especially if the presence of the feature in question, is in at least one or in some of the input dimensions near/close to zero. This last statement is based on Pielou's (flawless explanation of how PCA works) [1] and own experiences [2]. A separation/isolation attempt of the feature in question from dominant variances will be "supported". The "loud" signal would be channeled among the first few PCs and the "subtle variations" _could_ then be more evident in some of the higher order components. All in all, one has to look at the numbers -- drawing conclusions from the PC images is not safe! > is removing PC1 then back-inverting a suitable method for that sort of task? Short answer: yes, it can be, but back-inverting might not be necessary! Longer story: if the "subtle variations" (featueres of low(er) variance, rather homogenous stuff) are, as expected, more evident (read: enhanced as compared to the original data set) in some of the higher order components, why bother to back-invert? Supervised classification techniques can directly operate on selected PCs and attempt to extract whatever is of your interest. More on the subject of back-inverting -- quotting from Dr. Koutsias paper: "A critical issue in the back-transformation process is the amount of information taken from each PC axis. The original spectral pattern of the satellite image is modified to a degree that depends on the amount of the information taken from each PC axis." In this work (mapping burned areas), "back-transformation coefficients", in the range of 0 to 1, were worked-out in order to 'grep' specific percentages (0 to 100%) from each of the produced PCs and channel them back (via inverse-PCA) to a data set _similar_ to the original one, though different to the extent of the removed information (excluded PC). > or is there another more suitable method? Dunno more... :-( Kindest regards, Nikos --- [1] Book: Pielou, E. C. The interpretation of ecological data: a primer on classification and ordination Wiley, New York, 1984 [2] <Dissertation: Burned area mapping via non-centered PCA using Public Domain Data and Free Open Source Software Institut für Forstökonomie, Fakultät für Forst- und Umweltwissenschaften, Albert-Ludwigs-Universität Freiburg, 2011> [3] <Koutsias, N.; Mallinis, G. & Karteris, M. A forward/backward principal component analysis of Landsat-7 ETM+ data to enhance the spectral signal of burnt surfaces ISPRS Journal of Photogrammetry and Remote Sensing, 2009, 64, 37> _______________________________________________ grass-dev mailing list grass-dev@lists.osgeo.org http://lists.osgeo.org/mailman/listinfo/grass-dev