Denoising an image, while retaining the important features of the image, has been a fundamental problem in image processing. Dual-tree complex wavelet transform is a recently created transform that offers both near shift invariance and improved directional selectivity properties. This transform has been used in many techniques, including denoising. However, these techniques have used the real and imaginary components of the complex-valued sub-band coefficients separately. This paper proposes the use of coefficient magnitudes to provide an improvement in image denoising. Our proposed algorithm is based on the maximum a posteriori estimator, wherein the heavy-tailed scale mixtures of bivariate Rayleigh distribution are considered as the noise-free wavelet coefficient magnitudes’ prior distribution. Also, in our work, the necessary parameters of the bivariate distributions are estimated in a locally adaptive way to improve the denoising results via using the correlation between the amplitudes of neighbor coefficients. Simulation results delineate the performance of the proposed algorithm in both MSSIM and PSNR metrics.

中文翻译：

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使用瑞利分布的尺度混合进行图像去噪的双树复小波系数幅度建模

对图像去噪，同时保留图像的重要特征，一直是图像处理中的一个基本问题。双树复小波变换是最近创建的变换，它提供近移不变性和改进的方向选择性特性。这种变换已用于许多技术，包括去噪。然而，这些技术分别使用了复值子带系数的实部和虚部。本文提出使用系数幅度来改进图像去噪。我们提出的算法基于最大后验估计量，其中双变量瑞利分布的重尾尺度混合被认为是无噪声小波系数幅度的先验分布。另外，在我们的工作中，双变量分布的必要参数以局部自适应的方式估计，以通过使用相邻系数幅度之间的相关性来改善去噪结果。仿真结果描述了所提出算法在 MSSIM 和 PSNR 指标中的性能。