¹Department of Mathematical Modelling, Technical University of
Denmark, Building 321,
DK-2800 Lyngby, Denmark, email@example.com
²Danish National Survey and Cadastre,
DK-2400 Copenhagen NV, Norway
The GEOSONAR project is devoted to developing methods for integrating multi-sensor and multi-channel satellite data for improved recovery of the sea level height and analysis of the gravity field. The project addresses interdisciplinary investigations and involves most agencies and research institutes in Denmark interested in ocean dynamic. Difficult problems are encountered as the remotely sensed multi-variate images often are corrupted by cloud coverage. The influence of these undesired spectra must be minimised to enhance the underlying information in the signal related to the ocean colour. We suggest a novel method to address the problem by i) identifying the undesired spectra by means of an unsupervised classifier followed by ii) partial unmixing done by determining a transformation that projects the data onto a subspace orthogonal to the undesired spectra.
The suggested approach is to apply a multi-scale fuzzy clustering algorithm extended to include both spectral and spatial features. For each pixel in the image the classifier assigns a membership to each class. The memberships are then used to obtain estimates of the weighted mean spectra. We assume that the realised spectral observations can be expressed as linear combinations of desired and undesired spectra with an added noise term. Minimising the influence of the cloud signal leads to a projection of the data onto a subspace orthogonal to the undesired spectra. This transformation is known as the orthogonal subspace projection.
Two consecutive SeaWiFS scenes acquired with a 48-hour interval are analysed and the results are presented. To validate that the resulting components are indeed related to the enhanced ocean-signal a canonical correlation analysis is performed that produces new orthogonal components with maximum correlation. Despite the difference in cloud cover new components with high correlation over time are obtained. In addition to suppressing undesired spectra, means of reducing noise in the multivariate images are also briefly described. In particular the maximum autocorrelation transform has proven a valuable data driven tool for reducing noise in spatial data.