Generate a maximum noise fraction linear transformation

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MNFLT generates and saves a linear transformation matrix (and its inverse) which can then be used by LINTRN to transform selected channels of an input image into channels that show steadily decreasing image quality with increasing channel numbers.
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Name Type Caption Length Value range
FILI* String Input file name 1 - 192  
FILLT* String Input linear transformation parameters file name 1 - 192  
DBIC Integer Input raster channel(s) 0 -    
WLENINT Float Wavelength interval 0 - 2  
VALONLY String Valid bands only 0 - 3 YES | NO
Default: NO
SAMPINT Integer Sampling interval 0 - 2 1 -
Default: 1,1
NOISSRC String Noise estimate source 0 - 3 MAF | NIM
Default: MAF
MAFDEL Integer Delta X, Y to use in MAF calculation 0 - 2 Default: 1,1
FILNIM String Noise image file name 0 - 192  
DBIW Integer Input window 0 - 4 Xoffset, Yoffset, Xsize, Ysize
REPORT String Report mode 0 - 192 Quick links
MONITOR String Monitor mode 0 - 3 ON, OFF
Default: ON

* Required parameter
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Parameter descriptions


Specifies the name of the image file containing the channels for which the transformation is to be computed.


Specifies the name of the MATLAB save/load format file that will be created and to which the parameters of the linear transformation will be written.


Specifies a subset of the input channels to which the channel selection is to be restricted.

Ranges of channels or segments can be specified with negative values. For example, {1,-4,10} is internally expanded to {1,2,3,4,10}. When you are not specifying a range in this way, only 48 numbers can be specified explicitly.


Specifies that the selected bands are to be restricted to those whose center wavelength is either inside or outside a closed interval, specified in nanometers. By default, no restriction is applied.

The wavelength interval may be specified as follows:

This parameter has no effect if the input file contains no band center wavelength metadata.


Specifies whether the selected bands are to be restricted to those with "plot" or "bmask" (begin mask) quality values. The default is NO.

This parameter has no effect if the input file contains no band-validity metadata.


Specifies the X and Y sampling interval within the specified input window.


Specifies the source of the input image noise estimate.

Supported values are:


Specifies the X and Y pixel coordinate differences to be used in the MAF calculation.

This parameter is used only if the Input Image Noise Estimate Source (NOISSRC) parameter is set to MAF.

The default value is 1 for both differences (1, 1). At least one of the differences must be greater than zero.


Specifies the file that contains an image of noise channels. This image must have the same number of channels as the input image (FILI).

This parameter is used only if the Input Image Noise Estimate Source (NOISSRC) parameter is set to NIM.


Specifies a rectangular window of the noise image channels from which the noise statistics will be extracted.

Xoffset, Yoffset define the upper-left starting pixel coordinates of the window. Xsize is the number of pixels that define the window width. Ysize is the number of lines that define the window height.


Specifies where to direct the generated report.

Available options are:


The program progress can be monitored by printing the percentage of processing completed. A system parameter, MONITOR, controls this activity.

Available options are:

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MNFLT considers an image to be a raster of image-value vectors, with one vector per pixel location. The components of these vectors are drawn from pixel values in selected channels at the same pixel location.

The forward transformation of each image-value vector consists of subtracting the mean vector from the image-value vector, then pre-multiplying the vector by the forward transformation matrix.

The mean vector subtraction and application of the linear transformation is meant to be performed using LINTRN. The application of the inverse of the linear transformation to a modified (for example, for noise removal) forward transformation result, followed by the addition of the mean vector can also be performed using LINTRN.

Typically, the input image data for the inverse transformation is a modified version of forward-transformed channels. The modification typically consists of filtering the component images in which noise is concentrated. The output of the inverse transformation is typically used to replace the original input image channels with their modified (noise removed) counterparts.

The maximum noise fraction (MNF) transformation is a method for producing component images ordered in terms of image quality. This method seeks to concentrate image noise present in the input channels (DBIC) into as few output components as possible. In contrast, the principal components (PC) transformation seeks to concentrate image variance into as few output components as possible. Only when the noise in the set of input channels is uncorrelated and has equal variance across all the bands will the PC transformation produce component images that are ordered in terms of image quality.

Whereas the PC transformation is computed from the image-value vector covariance matrix alone, the MNF transformation also requires a noise-value vector covariance matrix (or, simply, noise covariance matrix). MNFLT accepts either an explicit noise image from which the noise covariance matrix is computed, or it can derive an approximation of the noise image for some types of noise, including additive 'salt and pepper' noise and image striping. This noise image approximation consists of a band of between-neighbor differences for each input band. When this approximation is used, the transformation is referred to as the maximum/minimum autocorrelation factors (MAF) transformation. The NOISSRC (Input Image Noise Estimate Source) parameter specifies the source of the noise information. The MAFDEL (Delta X,Y for MAF Calculation) parameter specifies the between-neighbor offsets.

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EASI>fili	=	"cuprad.pix"
EASI>fillt	=	"cuprad_mnflt.mat"
EASI>dbic	=	108, -112
EASI>wlenint	=		! default, no wavelength interval restriction
EASI>valonly	=		! default, no band validity restriction
EASI>sampint	=		! default, no subsampling
EASI>noissrc	=	"MAF"	! max/min autocorrelation factors
EASI>mafdel	=
EASI>filnim	=
EASI>dbiw	=

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In the MNF transformation, the rows of the linear transformation matrix are the left-hand eigenvectors of the product of the noise covariance and image band vector covariance matrix. For further details of the computation, see the References section.

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PCI Geomatics received financial support from the Canadian Space Agency/L'Agence Spatiale Canadienne through the Earth Observation Application Development Program (EOADP) for the development of this software, under contract 9F028-0-4902/12.

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Green, A. A., M. Berman, P. Switzer, and M. D. Craig, "A Transformation for Ordering Multispectral Data in Terms of Image Quality with Implications for Noise Removal," IEEE Transactions on Geoscience and Remote Sensing, Vol. 26, No. 1 (1988), pp.65-74.

G. Ravichandran and D. Casasent, "Minimum noise and correlation energy optical correlation filter," Appl. Opt. 31, 1823-1833 (1992).

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