Image Representation and Compression Using Multisplines and Adaptive Scale-space Atom Selection

We define a new stochastic process for representing images. We call this process the Ordered-Tree process (OTP). We show the existence of such a process and derive the optimal compression algorithm for such a process. Experimental results have indicated that the algorithm outperforms many existing image compression algorithms. In order to define the stochastic process, we first define a Tree-Structured analysis (TSA). This is a generalization of a multiresolution analysis (MRA) that extracts only those properties of an MRA that serve well in image compression. In particular, we place no requirement on self-similarity or orthogonality of basis functions. We give a detailed example of the TSA and the OTP. Several theorems are proved that explore the properties of the TSA and the OTP.