What is 'Spatial Coherence' for MNF images?

In ENVI 3.5/3.6, the Spectral Wizard was introduced as a guide through the ENVI "hourglass" processing flow to find and map image spectral endmembers from hyperspectral or multispectral data. Part of this process is to determine the inherent dimensionality of the data so that only the coherent portions are retained for further processing. This is accomplished by thresholding the MNF bands to separate the noise from the data, thus reducing the amount of data to be analyzed and improving spectral processing results. You can allow the Wizard to find this threshold and estimate the data dimensionality by using a Spatial Coherence measure. This Help Article discusses how Spatial Coherence is measured in ENVI.
 
Spatial Coherence is measured using MNF transformed images. MNF is implemented as two cascaded Principal Components (PC) transformations. The first transformation, based on an estimated noise covariance matrix, decorrelates and rescales the noise in the data. This step results in transformed data in which the noise has unit variance and no band-to-band correlations. The second step is a standard PC transformation of the noise-whitened data. The lower MNF bands are expected to have spatial structure and contain most of the "information" while higher MNF bands are expected to have little spatial structure and contain most of the "noise". By retaining only the coherent MNF bands (those with variance above unity), and discarding those that are indistinguishable from the noise (those with variance at or below unity), the dataset is reduced to its inherent dimensionality. This should improve spectral processing results.

The inherent dimensionality of an MNF transformed image can be estimated using the Spatial Coherence calculation. It consists of a correlation coefficient calculation between each spectral band and a 1-line-shifted-down version of itself. Noise, by definition, should have a zero or very low correlation, while an image that has spatial structure bigger than the pixel size will have a much higher correlation.

If higher MNF images are correlated to their line-shifted versions it means there is vertical structure in the "noise" images, such as vertical stripes, which might look like signal in the higher MNF bands. Only true salt and pepper noise will have a zero value.

Vertical stripping noise could be caused by an area array instrument. Most of the HSI methods in ENVI were designed around the concept of a whiskbroom scanner (AVIRIS, HyMap, etc.) that will not have vertical MNF stripes.

Review on 12/31/2013 MM