In wavelet shrinkage and thresholding, most of the standard techniques do not consider information that wavelet coefficients might be bounded, although information about bounded energy in signals can be readily available. To address this, we present a Bayesian approach for shrinkage of bounded wavelet coefficients in the context of non-parametric regression. We propose the use of a zero-contaminated beta distribution with a support symmetric around zero as the prior distribution for the location parameter in the wavelet domain in models with additive gaussian errors. The hyperparameters of the proposed model are closely related to the shrinkage level, which facilitates their elicitation and interpretation. For signals with a low signal-to-noise ratio, the associated Bayesian shrinkage rules provide significant improvement in performance in simulation studies when compared with standard techniques. Statistical properties such as bias, variance, classical and Bayesian risks of the associated shrinkage rules are presented and their performance is assessed in simulations studies involving standard test functions. Application to real neurological data set on spike sorting is also presented.

在小波收缩和阈值化中，尽管有关信号中有界能量的信息很容易获得，但是大多数标准技术都没有考虑小波系数可能有界的信息。为了解决这个问题，我们提出了一种在非参数回归的情况下缩小有界小波系数的贝叶斯方法。我们建议在具有加性高斯误差的模型中，使用零污染的β分布和零附近的对称性作为小波域中位置参数的先验分布。所提出模型的超参数与收缩水平密切相关，这有助于它们的推导和解释。对于低信噪比的信号，与标准技术相比，相关的贝叶斯收缩规则在仿真研究中显着改善了性能。给出了相关收缩规则的统计属性，如偏差，方差，经典和贝叶斯风险，并在涉及标准测试功能的模拟研究中评估了它们的性能。还介绍了对尖峰排序的真实神经学数据集的应用。