Image approximation and modeling via least statistically dependent bases

摘要

Statistical independence is one of the most desirable properties of a coordinate system for representing and modeling images. In reality, however, truly independent coordinates may not exist for a given set of images, or it may be too difficult to compute them in practice. Therefore, we propose a new method to rapidly compute the least statistically dependent basis (LSDB) from a basis dictionary (e.g., the local cosine or wavelet packet dictionaries) containing a huge number of orthonormal (or biorthogonal) bases. Our new basis selection criterion is minimization of the mutual information of the distributions of the basis coefficients as a measure of statistical dependence, which in turn is equivalent to minimization of the sum of the differential entropy of each coordinate in the basis dictionary. In this sense, we can view this LSDB algorithm as the best-basis version of the Independent Component Analysis (ICA), which is increasingly gaining popularity. This criterion is different from that of the Joint Best Basis (JBB) proposed by Wickerhauser, which can be viewed as the best-basis version of the Karhunen–Loève basis (KLB). We demonstrate the usefulness of the LSDB for image approximation and modeling and compare its performance with that of KLB and JBB using a collection of real geophysical acoustic waveforms and an image database of human faces.