【作者】 盛玉霞；

【导师】 柴利；

【作者基本信息】 武汉科技大学 ， 控制理论与控制工程， 2014， 博士

【摘要】 滤波器组广泛应用于图像处理、编码理论、数字通信、鲁棒信息传输等工程领域。在不同的指标下设计最优综合滤波器组是这些应用中重要的研究问题。均方误差(Mean square error, MSE)和结构相似性(Structural similarity index, SSIM)指标是图像质量评价中应用广泛的两个指标。本文研究基于MSE和SSIM指标的综合滤波器组优化设计问题。我们提出了基于MSE指标的格形结构过采样综合滤波器组和重叠变换后置滤波器的优化设计方法，也解决了SSIM指标下最优线性均衡器的设计问题。论文的主要贡献如下：1）提出了格形结构最优综合滤波器组的设计方法。在子带噪声功率谱密度(Power spectral density, PSD)已知时，通过求解李雅普诺夫方程，给出了综合滤波器组的显式表达式；在子带噪声PSD未知时，提出了最小化最大重构误差功率谱范数的凸优化算法。进一步研究了二维可分线性相位滤波器组的设计方法。对于给定的线性相位过采样分析滤波器组，我们给出了线性相位行综合滤波器组和列综合滤波器组的求解算法。仿真实例验证了所提方法的有效性。2）提出了时域过采样重叠变换(Time domain oversampled lapped transform,TDOLT)最优后置滤波器的设计方法。对于TDOLT后置滤波器和部分结构TDOLT后置滤波器，在子带噪声PSD已知时，通过最小化误差信号的功率谱范数，给出了后置滤波器的设计公式。在子带噪声PSD未知时，通过求解线性矩阵不等式，得到了后置滤波器的计算方法。对于多级广义TDOLT，给出了求解方法。将提出的最优后置滤波器设计方法应用在JPEG编解码实例中，实验结果表明，本文方法能减少方块效应和降低量化噪声，有更好的重构效果。3）提出了一种SSIM指标下多通道线性均衡器的优化设计方法。对零均值信源的情形，得到了最优均衡器的计算公式，发现并证明了SSIM指标下的最优均衡器和MSE最优均衡器之间仅相差一个标量因子，并且因子的倒数为最优的SSIM值。对于给定的模糊滤波器，建立了最大SSIM值、最小MSE值和均衡器长度之间的关系。对于更一般的非零均值信源，给出了一种线性均衡器的次优解求解算法。不同的仿真实例证明了本章方法的有效性。4）提出了一种SSIM指标下重叠变换后置滤波器的设计方法。假定信号是广义平稳随机过程，子带噪声是高斯白噪声，针对滤波器的长度和抽取因子相同的特殊情形，给出了基于SSIM指标的后置滤波器的计算公式。将本章方法应用到DCT块变换编码中，实验结果表明，与IDCT和MSE最优后置滤波器相比，SSIM最优后置滤波器组在降低子带噪声的同时，能更好的保留图像的结构信息。更多还原

【Abstract】 Filter banks have been widely applied to many engineering fields as imageprocessing, coding theory, digital communication and robust information transmission.In these applications it is of great importance to design the optimal synthesis filter bankfor different criteria. This dissertation deals with the optimal design of synthesis filterbanks with optimal MSE and SSIM index, which are two typical image qualityassessment indexes. Specifically, we present effective methods to design the optimalsynthesis filter bank with lattice structure constraints and post-filter in lapped transformfor MSE measurement. The problem of designing the equalizer with optimal SSIMindex has also been solved. The main contributions are as follows:1) Methods of designing optimal synthesis filter banks with lattice structure areproposed. For the subband noise with known power spectral density (PSD), the explicitformulae are derived using the Lyapunov equation. For the subband noise withunknown PSD, the convex optimization algorithm is presented to minimize theworst-case reconstruction error. The design method of linear phase separable twodimensional synthesis filter banks is studied. For a given linear phase oversampled filterbank applied to row and column processing, the optimal linear phase synthesis filterbanks are designed for row and column processing respectively. The effectiveness ofthese solutions is demonstrated by numerical examples.2) The optimal post-filter for time domain oversampled lapped transform (TDOLT)is presented. The explicit formulae of post-filters are given for TDOLT and partialTDOLT for noise with known PSD by minimizing the power norm of reconstructionerror. For the subband noise with unknown PSD, a worst-case design algorithm isdeveloped to compute the post-filter by solving linear matrix inequalities. Moreover, amethod is proposed for the multistage TDOLT. The obtained optimal post-filters areapplied to JPEG codec. The performance of improving coding efficiency and reducingblocking are demonstrated by examples. 3) The problem of designing the equalizer with optimal SSIM index is solved forgeneral multichannel systems. The closed form formula is provided for the equalizerwith maximal SSIM index when the mean of the source is zero. One interesting andimportant result is that the equalizer with maximal SSIM index is equal to the one withminimal MSE multiplied by a positive real number, which is shown to be equal to theinverse of the achieved SSIM index. The relation between the maximal SSIM index andthe minimal MSE has been established for fixed blurring filters and the length ofequalizers. An algorithm is presented to compute the suboptimal equalizer for thegeneral sources of which the mean is not zero. Various simulations have been given todemonstrate the effectiveness of the results.4) A method to design the post-filter based on SSIM index for lapped transform isproposed. Under the assumption that the source signal is a wide sense stationary processwith known PSD, that the noise is Gaussian white, and that the filter length is equal tothe decimation number, the closed-form solution is obtained. The method is applied inthe reconstruction of DCT coding systems. Experimental results show that comparedwith IDCT and MSE based method, the proposed method can achieve better structurefeature while maintaining satisfactory ability of noise reduction.更多还原