Multi-Resolution-Analysis-in-R
Application of Discrete Wavelet Transform in the Spatial Analysis of Sea Ice
Wavelet transform is a new a promising tool in the study of spatial analysis for analyzing stationary process and multi-scale structures. Spectral analysis using wavelets is a new and fast becoming a popular tool in statistics that involve time series data with localized variations. Important application of estimating smooth and roughs (trends and residuals) lies in the field of texture analysis, which concerned with segmentation of images at different resolutions. In this study, we performed a one-dimensional multi-resolution analysis of sea-ice data as a demonstration of the discrete wavelet transform. Of the two classes of discrete wavelet transform algorithm, we demonstrate the power of maximal-overlap algorithm in correctly estimating the variance and covariance of the albedo and brightness temperature at different scales.
This study is based on Lindsay, R. W., Percival, D. B., & Rothrock, D. (1996). The discrete wavelet transform and the scale analysis of the surface properties of sea ice. IEEE Transactions on Geoscience and Remote Sensing, 34(3), 771-787.