The least statistically-dependent basis and its applications

Statistical independence is one of the most desirable properties of a coordinate system for representing and modeling images. In this paper we propose an algorithm to rapidly construct a coordinate system "closest" to the statistically independent one from a dictionary of bases such as the wavelet packets and local Fourier bases. The criterion is to minimize the sum of the coordinate-wise differential entropy and is quite different from the joint best basis (JBB) of Wickerhauser (1994). We demonstrate the use of the LSDB for image approximation and modeling, and compare its performance with Karhunen-Loeve basis (KLB) and JBB.