A Transformation for Ordering Multispectral Data in Terms of Image Quality with Implications for Noise Removal

Although principal components transformations on remotely sensed multispectral data often produce components that show decreasing image quality with increasing component number, there are numerous examples, especially among aircraft scanner data, where this is not the case. This has led us to define a new trans€ormation, known as the maximum noise fraction (MNF) transformation, which always produces new components ordered by image quality. It can be shown that this transforniation is equivalent to principal components when the noise variance is the same in all bands and that it reduces to a multiple linear regression when noise is in one band only. Noise can be effectively removed from multispettral data by transforming to the MNF space, smoothing or rejecting the most noisy components, and then retransforming to the original space. In this way much more intense smoothing can be applied to the MNF components with high noise and low signal content than could be applied to each band of the original data. The MNF transformation requires knowledge of both the signal and noise covariance mhtrices. Except whbn the noise is in one band only, the noise covariance matrix needs to be estimated. One procedure for doing this is discussed and examples of cleaned images are presented.