Denoising of natural images is a basic problem in image processing. The present paper proposes a new algorithm for image denoising based on the maximum a-posteriori (MAP) estimator in undecimated dual-tree complex wavelet transform. The undecimated dual-tree complex wavelet transform (UDT-CWT), along with the directional selectivity of the dual-tree complex wavelet transform (DT-CWT), offers exact translational invariance property through removing the down-sampling of filter outputs together with the up-sampling of the complex filter pairs of DT-CWT. These properties are very important in image denoising. The performance of the MAP estimator depends strongly on the probability of noise-free wavelet coefficients. In our proposed denoising method, multivariate t-distribution is applied as the prior probability of noise-free coefficients. The t-distribution can accurately model the statistics of wavelet coefficients, which have peaky and heavy-tailed characteristics. On the other hand, the multivariate model makes it possible to take into account the dependencies of wavelet coefficients and their neighbors. Also, in our work, the necessary parameters of the multivariate distribution will be estimated in a locally-adaptive way to improve the denoising results via using the correlations among the amplitudes of neighbor coefficients. Simulation results delineate that the proposed algorithm outperforms state-of-the-art denoising algorithms in the literature.

自然图像的去噪是图像处理中的基本问题。本文提出了一种在未抽取双树复小波变换中基于最大后验（MAP）估计量的图像去噪新算法。未抽取的双树复数小波变换（UDT-CWT）以及双树复数小波变换（DT-CWT）的方向选择性，通过消除滤波器输出的下采样和DT-CWT的复数滤波器对的上采样。这些特性在图像去噪中非常重要。MAP估计器的性能在很大程度上取决于无噪声小波系数的概率。在我们提出的去噪方法中，多元t-分布被用作无噪声系数的先验概率。该吨-配送可以精确地模拟的小波系数，其具有尖峰和重尾特性的统计信息。另一方面，多元模型可以考虑小波系数及其邻居的依赖性。同样，在我们的工作中，将通过使用局部系数的方式来估计多元分布的必要参数，以通过使用相邻系数幅度之间的相关性来改善去噪结果。仿真结果表明，该算法优于文献中最新的降噪算法。