New scale-space techniques with applications to climate reserach and imaging

Different scale-space methods for independent and dependent data have been developed recently. Such methods are very useful for analysing climate data and medical image data. Peaks in one-dimensional data can be found by the newly developed scale-space me thod entitled posterior smoothing. A two-dimensional version will be developed in the project, which means that we will be able to analyse full images as well as two-dimensional climate data. Project 138460/431 has developed methods to analyse dependent data by use of the frequency domain. Wavelet decomposition is an alternative strategy for a scale-space analysis of dependent data and will be carefully studied in this project. For real data there is typically only one realisation of the data available. Hence we cannot run the analysis several times to see how stable the results are. The essential question is how to resample the data to maintain the datas original features. The project aims to develop tools like variability plots to quantify and visualize the stability of the results.