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This study deals with two-dimensional (2D) signal processing using thewavelet packet transform. When the basis is unknown the candidate of basisincreases in exponential order with respect to the signal size. Previousstudies do not consider the basis as a random vaiables. Therefore, the costfunction needs to be used to select a basis. However, this method is often aheuristic and a greedy search because it is impossible to search all thecandidates for a huge number of bases. Therefore, it is difficult to evaluatethe entire signal processing under a criterion and also it does not alwaysgurantee the optimality of the entire signal processing. In this study, wepropose a stochastic generative model in which the basis is regarded as arandom variable. This makes it possible to evaluate entire signal processingunder a unified criterion i.e. Bayes criterion. Moreover we can derive anoptimal signal processing scheme that achieves the theoretical limit. Thisderived scheme shows that all the bases should be combined according to theposterior in stead of selecting a single basis. Although exponential ordercalculations is required for this scheme, we have derived a recursive algorithmfor this scheme, which successfully reduces the computational complexity fromthe exponential order to the polynomial order.

Stochastic 2D Signal Generative Model with Wavelet Packets Basis Regarded as a Random Variable and Bayes Optimal Processing