基于小波域隐马尔可夫模型的信号超分辨率重建

摘要

A signal super-resolution reconstruction algorithm based on wavelet-domain hidden Markov model (WHMM) is proposed. According to the Bayesian principle and the maximum a posteriori probability estimation theory, a signal super-resolution reconstruction model is obtained using WHMM as the prior knowledge. The Euler-Lagrange equation of the reconstruction problem and the differential of log-likelihood function are deduced in detail, and a concise linear equation is concluded to solve the signal super-resolution problem. Finally, the expectation maximization (EM) algorithm and the conjugate gradient algorithm are adopted to compute WHMM parameters and high resolution signal, alternately. Experimental results with one and two dimensional signals demonstrate that the presented method can preserve more high-frequency details while denoising. Under the same degradation, for one dimensional test signals, the peak signal-to-noise-ratio (PSNR) values of the proposed algorithm are averagely increased by about 2.399 4 dB and 4.474 2 dB compared with cubic interpolation and Tikhonov regularization, respectively; for two dimensional test signals, the PSNR improvements are 1.174 1 dB and 0.648 7 dB compared with bicubic interpolation and Tikhonov regularization,respectively.%提出一种基于小波城隐马尔可夫模型(WHMM)的信号超分辨率重建算法.根据贝叶斯原理和最大后验概率估计理论,将WHMM作为先验知识给出一般信号的超分辨率重建模型;详细推导了重建问题的Euler-Lagrange方程及对数似然函数的导数计算,将信号的超分辨率重建归结为一个简单线性方程组的求解;最后采用期望最大化(EM)算法和共轭梯度算法交替迭代计算WHMM的模型参数和高分辨率重建信号.一维和二维测试信号的实验结果表明该方法在有效抑制噪声的同时,能够很好地重建出信号的高频细节.在相同的信号降质条件下,针对一维情形,本文重建方法的峰值信噪比(PSNR)较三次插值和Tikhonov正则化方法平均提高2.399 4 dB和4.474 2 dB;针对二维情形,本文重建方法的PSNR较双三次插值和Tikhonov正则化方法平均提高1.174 1 dB和0.648 7 dB.