Multi-dimensional, Paraunitary Principal Component Filter Banks

z In this paper, the one-dimensional principal component filter banks (PCFB's) derived in [17] are generalized to higher dimensions. As presented in [17], PCFB's minimize the mean-squared error (MSE) when only Q out of P subbands are retained. Previously, 2D PCFB's were proposed in [16]. The work in [16] was limited to 2D signals and separable resampling operators. The formulation presented here is general in that it can easily accommodate signals of arbitrary (yet finite) dimension and non-separable sampling. A major result presented in this paper is that in addition to minimizing MSE when reconstructing from Q out of P subbands, the PCFB's result in maximizing theoretical coding gain (TCG) y This work was supported in part by the National Science Foundation under grants NCR-9303868, MIP9116683, USE-9250721, and CDA-9121675. Dr. Bamberger is the contact author. z EDICS Category: SP 2.4.2. Permission to publish this abstract separately is granted. Actually, the PCFB's maximize..