One of my recent research topics is the application of wavelets to analyzing synthetic aperture radar, which is used to take a ground image from a satellite or an airplane. Mathematically, the purpose of this analysis is to extract reflection coefficients from a contaminated received signal. In my research work, the received signal is modeled as a continuously mixed (or integral) form and the noise is a non-stationary stochastic processes. This assumption is more natural than conventional modeling, which assumes that the received signal is a sum of reflections from finite point targets on the ground and the noise is independently and identically distributed. With our assumption, reflection coefficients are observed as indirect data with non-stationary noise. The Wavelet-vaguelette decomposition is one of the methods to cope with this difficulty. By using this method, the final goal of this research work is to develop a new system which makes it possible to take a ground image with higher resolution more easily than conventional techniques do.