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A Guide to the Minimum Noise Fraction (MNF) Statistics Files
The Minimum Noise Fraction (MNF) transform is a linear transformation that consists of two separate PCA rotations and a noise whitening step. Unlike the PCA routine, the MNF transform produces two separate statistics files, which ENVI refers to as the MNF Noise Stats and the MNF Stats. While these appear to be ordinary ENVI statistics files, these files actually contain information unique to the MNF, and omit data typically found in ENVI statistics files.
In order to perform a forward MNF rotation the following statistics must be computed:
- The mean for each band of the input image (in order to mean correct the data)
- The covariance statistics of the noise (for the noise rotation and normalization)
- The covariance statistics of the noise whitened and rescaled input image data
The two statistics files that are produced by the MNF routine do indeed contain these statistics, although not necessarily in the location you would expect to find them! In addition, the MNF Stats file contains an extra transformation matrix -- unique to the MNF -- that alone can completely describe the MNF rotation.
The first rotation uses the principal components of the noise covariance matrix, and its complete set of covariance statistics are stored in the MNF Noise Statistics file. However, the Noise Stats file contains only the noise covariance statistics, all other data ordinarily found in an ENVI stats file are omitted. The second rotation uses the principal components derived from the original image data after it has been noise whitened by the first rotation and rescaled by the noise standard deviation. This second rotation's eigenvector matrix and eigenvalues are stored in the MNF Statistics file in the normal locations. However, the rest of the covariance statistics for the second rotation are not saved because the covariance 'slot' in the MNF Stats file is used to store a special 'composite' MNF transformation matrix. The composite transformation matrix describes the net result of both PC rotations as well as the band-independent scaling introduced by the noise normalization. This non-orthogonal, non-unit length matrix allows an inverse MNF rotation to be applied in a single step.
Contents of Stats Files Generated by the MNF
| Statistics Category |
MNF Noise Stats File |
MNF Stats File |
| Mean |
empty |
of the original input bands |
| Maximum |
empty |
empty |
| Minimum |
empty |
empty |
| Standard Deviation |
empty |
empty |
| EigenValues |
of noise covariance matrix |
of 2nd PC rotation |
| Covariance Matrix |
of the noise |
composite transformation matrix |
| Correlation Matrix |
of the noise |
spurious data -- do not use! |
| EigenVector Matrix |
of noise covariance matrix |
of 2nd PC rotation |