The PCLT, MNFLT, and LINTRN programs are used to compute the parameters of bandwise linear data transformations and their inverses and to apply these. This is part of a process for random noise removal. These programs are designed such that, the generation of parameters of these linear transformations (and their inverses) is decoupled from their application to an image. PCLT and MNFLT generate the parameters for principal components (PC) and maximum noise fraction (MNF) linear transformations, respectively, and their inverses. In both cases, the transformation parameters are written to a MATLAB save/load format file. The contents of a transformation parameters file may be printed using PRINTLT.
LINTRN transforms an image using the parameters read from a transformation parameters file. LINTRN may be used to apply either the forward or inverse transformation. Typically, an image is transformed, a small number of bands in the transformed image are subjected to noise-removal processing, and the result is inverse-transformed to replace the original image. This is a method of removing noise from the original image.
The motivation behind using a PC or MNF transformation in this process is that the image noise that is distributed across many bands of the original image will often be concentrated into a few bands of the transformed image. A noise band in the transformed image may be subjected to very aggressive smoothing, or may even be replaced by a band whose pixels are all set to the mean pixel value of the noise band (reasonable when the non-noise content of the band appears to be negligible). This may be done with little risk of information loss in the inverse-transformed result.
The PC transformation parameters are computed from the band-vector covariance matrix, whereas the MNF transformation parameters additionally requires a noise-value covariance matrix. MNFLT accepts either an explicit noise image that models the type of noise that is to be be removed from the original image, or it can derive an approximation for certain kinds of noise, including "salt and pepper" and image striping. This noise image approximation consist of a band of between-neighbor differences for each input band.
The MNF transformation is more versatile than the PC transformation. The PC transformation result will have bands that are ordered in terms of decreasing image quality only when the noise in the original bands is uncorrelated and has equal variance over all those bands. The MNF tranformation result will have bands that are ordered in terms of increasing signal-to-noise ratio (i.e., decreasing "noise fraction") with respect to the modelled noise.
MNFNR is a convenient single-step implementation of a special case of the application of the MNF transformation to noise removal. MNFNR is appropriately applied in a case where one member of a set of image bands is considered to have significantly more noise than the other bands, and it is desirable to transform that band such that its noise content is close to that of the other bands. In this case, it is not necessary to know the noise variance in any band in order to define the MNF transform. MNFNR may be applied multiple times to the same image in order to reduce the noise in multiple bands.
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