### Enhancement of Ocean Related Signal by Suppression of
Undesired Spectra in Remotely Sensed Multi-variate SeaWiFS Images in the
GEOSONAR Project

#### K.B. Hilger¹, A.A. Nielsen¹, P. Knudsen² and O.B. Andersen²

¹Department of Mathematical Modelling, Technical University of
Denmark, Building 321,

DK-2800 Lyngby, Denmark, kbh@imm.dtu.dk

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.