Multi-dimensional, paraunitary principal component filter banks

Abstract

This paper presents a generalization of the one-dimensional principal component filter bank (PCFB) derived by Tsatsanis (see Univ. of Virginia, Ph.D. Thesis, Sept. 1992.) to higher dimensions. Previously, the results of Tsatsanis were extended to two-dimensional signals, but this was limited to 2D signals and separable resampling operators. The filter bank discussed results in minimizing the mean squared error when only Q out of P subbands are retained. Furthermore, it is shown that the filter bank maximizes the theoretical coding gain (TCG). Simulations are presented, showing the results for reconstructing an image from only the first subband signal, demonstrating the potential of the PCFB.