论文标题
随机数据包的随机2D信号生成模型被视为随机变量，贝叶斯最佳处理
Stochastic 2D Signal Generative Model with Wavelet Packets Basis Regarded as a Random Variable and Bayes Optimal Processing
论文作者
论文摘要
这项研究涉及使用小波数据包变换的二维（2D）信号处理。当基础未知时，基础候选者相对于信号大小的指数顺序增加。先前的研究并未将基础视为随机虚假。因此，成本函数需要用于选择基础。但是，这种方法通常是一种启发式和贪婪的搜索，因为不可能在所有候选人中搜索大量基地。因此，很难在标准下评估整个信号处理，而且它并不总是使整个信号处理的最优性。在这项研究中，我们提出了一个随机生成模型，其中基础被视为随机变量。这使得在统一标准（即贝叶斯标准）下评估整个信号处理是可能的。此外，我们可以得出达到理论极限的最佳信号处理方案。该派生的方案表明，所有基础都应根据后验组合，而不是选择单个基础。尽管此方案需要指数级计算，但我们已经为该方案得出了一种递归算法，该算法成功地将计算复杂性从指数级阶降低到多项式顺序。
This study deals with two-dimensional (2D) signal processing using the wavelet packet transform. When the basis is unknown the candidate of basis increases in exponential order with respect to the signal size. Previous studies do not consider the basis as a random vaiables. Therefore, the cost function needs to be used to select a basis. However, this method is often a heuristic and a greedy search because it is impossible to search all the candidates for a huge number of bases. Therefore, it is difficult to evaluate the entire signal processing under a criterion and also it does not always gurantee the optimality of the entire signal processing. In this study, we propose a stochastic generative model in which the basis is regarded as a random variable. This makes it possible to evaluate entire signal processing under a unified criterion i.e. Bayes criterion. Moreover we can derive an optimal signal processing scheme that achieves the theoretical limit. This derived scheme shows that all the bases should be combined according to the posterior in stead of selecting a single basis. Although exponential order calculations is required for this scheme, we have derived a recursive algorithm for this scheme, which successfully reduces the computational complexity from the exponential order to the polynomial order.
