random thought fragments on multiresolution analysis

someday i'd like to write a textbook on multiresolution techniques in surrogate modeling. in the intro i would present a unified approach to orthogonal decompositions like eigensystems, svd, and ffts with wavelets, linear model sensitivity analysis, and mdl. i would go on to answer questions like, 'how much information is gained in terms of the modes and singular values if i update an svd representation of a surrogate model?' and how do i do an svd surrogate model in the first place? will it capture features on different scales, or can i force it to? how do i use that predicted information gain to guide adaptive sampling?