RETRACTED CHAPTER: Affine Frames

Affine frames, generated by affine transform of one or several frame generator elements, can provide redundant but sparse representations of complex data. Such redundant feature guarantees the realization of robust data transmission through sparse reconstruction and noise suppression achieved at the same time. Frame tree is a tree-like connection among affine frame generators, each of which can provide a refined partition of some spatial-scale region linked with different branches in frame trees. The depth of frame trees, which determines how fine of spatial-scale cells in frame representation, may be finite or infinite. A suitable frame can be picked up fast from frame tree to mine complex data with abrupt changes only on small spatial-scale regions.