【作者】 韩玉兵； 殷玮玮； 吴乐南；

【Author】 HAN Yu-Bing +, YIN Wei-Wei, WU Le-Nan (Department of Radio Engineering, Southeast University, Nanjing 210096, China)

【机构】 东南大学无线电工程系；

【摘要】 提出一种基于小波域隐马尔可夫模型的图像超分辨率重建算法。首先介绍图像信号的小波域隐马尔可夫模型;然后将其作为先验知识给出了超分辨率重建算法;详细推导了对数似然的导数计算;试验表明该方法的有效性。更多还原

【Abstract】 The wavelet transform has emerged as an exciting new tool for statistical signal and image processing, which has several attractive properties such as time-frequency (or space-frequency) locality, the sparsity of wavelet coefficient, and multi-resolution etc. On the other hand, the hidden Markov model (HMM) is an elegant mathematic method for modeling a random processes with a hidden markovian state chain, which has proved tremendously useful in a variety of applications, including speech recognition and image processing. In this paper, a super-resolution reconstruction algorithm is proposed based on wavelet-domain hidden Markov model (WHMM). In the first, after introduced the discrete wavelet transform briefly, we use the two-state Gaussian mixture model (GMM) to describe the non-Gaussian feature of an individual wavelet coefficient, one state is “high”, corresponding to a wavelet component containing significant contributions of signal energy, the other is “low”, representing coefficients with little signal energy. To capture the key statistical dependency and persistence property of the joint probability density of the whole wavelet coefficients of real-world signals, the hidden Markov tree (HMT) structure is adopted. The model training and the likelihood determination associated with the WHMM have been thoroughly studied. Then, from the Bayesian viewpoint and under the maximum a posteriori (MAP) probability estimation framework, we conclude a minimum functional for the image super-resolution reconstruction using WHMM as the prior knowledge or penalized regularization term. Thirdly, the gradient descent method is performed to solve the minimum problem, and the differential of log-likelihood function has been deduced in detail by means of orthogonal wavelet transform and differential list principle. Finally, a concise linear equation is obtained and the expectation maximization (EM) algorithm and conjugate gradient (CG) algorithm are adopted to compute the HMT parameters and reconstruction image alternately. Experimental results indicate that the proposed algorithms outperform conventional Tikhonov regularization in terms of both objective measurements and visual evaluation.更多还原