The use of univariate Bayes regression models for spatial smoothing

Landsat data from satellites are used in monitoring environmental systems, for example, sea surface temperature. One of the practical problems pertaining to images by the Landsat thematic mapper (TM) sensor is to reduce stripe noise due to the sensoring system. We take a smoothing approach to this problem. A spatial smoothing method for TM images is required to be more efficient in computation with less memory storage because each image consists of huge data. In this article, we propose approximated estimates for mean vectors under univariate Bayes linear models. Three procedures depending on smoothness priors are considered. Our method can be rapidly carried out under the small amount of data storage. This univariate smoothing method is applied to the spatial data in such a way that each column is smoothed by this method and each row is similarly re-smoothed. The performance of the spatial smoothing technique is applied to artificial numerical examples in literature, and its performance is favorably examined in terms of mean squared errors. Also, it is used for destriping a Landsat TM image in the water area.