To monitor the Earth's surface, the satellite of the NASA Landsat program provides us image sequences of any region on the Earth constantly over time. These image sequences give us a unique resource to study the Earth's surface, changes of the Earth resource over time, and their implications in agriculture, geology, forestry, and more. Besides natural sciences, image sequences are also commonly used in functional magnetic resonance imaging (fMRI) of medical studies for understanding the functioning of brains and other organs. In practice, observed images almost always contain noise and other contaminations. For a reliable subsequent image analysis, it is important to remove such contaminations in advance. This paper focuses on image sequence denoising, which has not been well-discussed in the literature yet. To this end, an edge-preserving image denoising procedure is suggested. The suggested method is based on a jump-preserving local smoothing procedure, in which the bandwidths are chosen such that the possible spatio-temporal correlations in the observed image intensities are accommodated properly. Both theoretical arguments and numerical studies show that this method works well in the various cases considered.
Keywords: bandwidth selection; correlation; edge-preserving image denoising; image sequence; jump regression analysis; local smoothing; nonparametric regression; spatio-temporal data.