Hierarchical fast decoding of fractal image representation using quadtree partitioning

Fractal image coding using either fixed-size blocks or variable-size blocks in a quadtree structure is by now common. However, a fast decoding algorithm based on a hierarchical representation, which requires only a finite number of iterations to exactly reach the fixed point of the fractal transformation, has been shown only for fixed-size blocks. In this work, a generalization of the fast decoding algorithm is made, enabling its use with a quadtree image partitioning. A theorem extending the hierarchical representation of the fractal transformation fixed point to include quadtree partitioning is given and proved.