Abstract: Based on the statistical properties of coefficients of the Uniform Discrete Curvelet Transform（UDCT）, and the analysis of correlation metric mutual information about the coefficients, this paper chooses the Hidden Markov Tree to model the coefficients finally and trains the sequence with the EM algorithm. With amount of time consuming, an optimization EM algorithm based on HMT of UDCT coefficients is presented; it further optimizes the algorithm by defining the variance and state transition matrix based on the attenuation of coefficients and continuity between the scales. Experimental results show that, in the use of similarity and Peak Signal to Noise Ratio effect as the measurement of image de-noising, under the same conditions, the algorithm proposed has better real-time and de-noising effect than the Wavelet HMT, Contourlet HMT, UDCT HMT algorithm.

Key words: Uniform Discrete Curvelet Transform（UDCT）, mutual information, Hidden Markov Tree model（HMT）, Expectation-Maximization（EM） algorithm, image denoising

摘要： 通过对均匀离散曲波变换（Uniform Discrete Curvelet Transform，UDCT）系数的统计特性研究，同时对系数相关性度量指标互信息量的分析，最终选择隐马尔可夫树模型对其系数建模，且用EM算法训练序列；针对训练时间过长问题，通过分析系数的衰减性和尺度间系数延续性，提出一种新的对算法参数初值的方差和状态转移矩阵的优化方法，实验结果证明，在采用峰值信噪比和相似度作为图像去噪效果的度量时，同等条件下文中提出的算法比Wavelet HMT、Contourlet HMT、UDCT HMT算法有较好的实时性和去噪效果。

关键词: 均匀离散曲波变换, 互信息, 隐马尔可夫树模型（HMT）, 最大期望（EM）算法, 图像去噪