【作者】 肖宿；

【导师】 韩国强；

【作者基本信息】 华南理工大学 ， 计算机应用技术， 2010， 博士

【摘要】 作为图像处理和计算机视觉的基础,图像恢复能够解决图像质量的退化问题。在许多应用领域,如遥感、医学成像和军事监察等,图像退化都是一个普遍存在且亟需解决的问题。因此,图像恢复技术受到广泛研究和应用。本论文研究的重点是贝叶斯框架下的图像恢复问题,包括了参数估计、图像降噪和图像去模糊等。对贝叶斯框架下常见的图像恢复方法进行了深入的研究,针对其中存在的不足之处,如无法找到后验概率闭合形式的解,参数估计缺少良好的准则,最大后验概率属于点估计等,引入了分层最大似然估计方法和变分贝叶斯方法,并通过实验进行了分析验证。本文的研究成果与创新主要包括:1、针对实证分析法通常难以找到闭合形式解的问题,提出了一种分层最大似然估计法。实验结果表明,将该方法应用于图像恢复,可以加快图像恢复问题的求解速度,并且获得了比较理想的恢复结果。2、针对Morozov离差原理、L曲线、广义交叉验证和期望最大化等经典参数估计算法的不足,提出了一种新的贝叶斯参数估计算法,该算法利用分层最大似然估计法,可以在图像恢复的过程中,同步地对多个模型参数进行估计。3、提出了一种基于扩散技术的图像降噪算法,引入梯度算子作为原始图像的先验模型,并采用变分贝叶斯方法估计原始图像。实验结果表明,该算法克服了传统经验贝叶斯方法的不足。4、提出了一种基于空间投影和混合模型的彩色图像降噪算法。在YCbCr空间下,该算法采用混合模型作为原始图像的先验模型,并基于分层最大似然估计方法估计原始图像。实验结果表明,该算法可使降噪后图像的信噪比平均提高1dB~3dB。5、研究了噪声的分布特征,提出用拉普拉斯模分布模型刻画噪声,总变分模型描述原始图像的先验特征,并采用迭代重加权最小二乘法解决该了引入总变分模型和拉普拉斯模型带来的L1-优化问题。实验结果显示,拉普拉斯分布模型可以更真实地反映噪声的分布情况,迭代重加权最小二乘法的引入有效地提高了算法的时间性能。6、将稀疏表示与分层最大似然估法相结合,提出了一种了稀疏图像去模糊算法。该算法引入Donoho等人的稀疏特征模型刻画系数向量的稀疏性,并采用总变分模型描述原始图像的先验特征,最后利用分层最大似然估计法推导原始图像。实验结果显示,该算法为稀疏表示技术用于图像恢复提供一通用的算法框架。7、提出了一种基于调和模型图像去模糊算法,该算法利用调和模型刻画原始图像的分布特征,并通过分层最大似然估计法推导原始图像。实验结果表明,与基于最大后验概率的算法相比,该算法的时间性能和恢复结果更优。8、提出了一种贝叶斯多信道图像盲去模糊算法,算法采用交叉关系模型和平滑模型组成的混合模型来描述点扩散函数的先验特征,同时还引入总变分模型刻画原始图像的先验特征,并基于分层最大似然估计算法推导原始图像和点扩散函数。实验结果表明,相比单信道的图像去模糊算法,多信道图像去模糊算法的恢复结果更优。与同类的多信道算法相比,该算法的速度更快,恢复效果更优。更多还原

【Abstract】 As the foundation of image processing and computer vision, image restoration can solve the problem of image degradation. In many applications, such as remote sensing, medical imaging, and military reconnaissance, image degradation remainds a common and urgent problem to be solved. Thus, image restoration has always been followed with interest and studied earnestly.This thesis focuses on the image restoration in Bayesian framework, which mainly contains research on model parameter estimation, image denoising, and image deblurring. By studying classical algorithm in Bayesian framework, several problems are found, such as the lack of a close-formed solution for posterior probability, the Maximum a Posteriori (MAP) method falling into the point estimation, and the lack of good principles for parameter estimation. This thesis proposes a hierarchical maximum likelihood method and introduces the variational Bayesian method in response to these problems. Both methods are experimentally analyzed and verified.These are the major achievements and innovations:1. Due to the difficulty of using the evidence analysis method in achieving close-formed solutions, we propose a novel hierarchical maximum likelihood method. The experiments demonstrate that the proposed method can obtain better results with satisfactory speeds when used in image restoration.2. A novel Bayesian parameter estimation algorithm is proposed to overcome the drawbacks in Morozov discrepancy principle, L-curve method, generalized cross validation, and expectation maximum method. The proposed algorithm uses the hierarchical maximum likelihood method to estimate multiple model parameters together with image restoration.3. We propose a diffusion-based image denoising algorithm that introduces the gradient operator as the prior model of the original image and utilizes the variational Bayesian method to estimate the original image. Results show that the proposed algorithm overcomes the shortcomings of the classical empirical Bayesian method.4. We propose a novel color image denoising algorithm based on space projection and hybrid model. In the YCbCr space, the proposed algorithm uses the hybrid model to characterize the original image, and the hierarchical maximum likelihood framework is used to estimate the original image. Experiments indicate that the SNR values of denoised images are improved by 1dB to 2dB on average.5. By studying the distribution properties of the noise, we introduce the Laplace distribution model to characterize the noises. We also propose the total variation to model the original image. To solve the problem of L1-optimization difficulty caused by the Laplace model and the total variation, we incorporate the iteratively reweighted norm method into our algorithm. Experiments clearly show that the Laplace model gives a true reflection of the noise natures, and the iteratively reweighted norm truly speeds up the proposed algorithm.6. By combining the sparse representation with the hierarchical maximum likelihood method, a sparse representation-based image deblurring method is proposed. This algorithm introduces Donoho’s sparse model to characterize the sparse coefficient vector, and the total variation model is used to characterize the original image, which is estimated using the hierarchical maximum likelihood method. We theoretically and experimentally prove that the proposed algorithm supplies a unified framework for sparse image restoration.7. We propose a novel harmonic image deblurring algorithm that uses the harmonic model to characterize the original image, and the hierarchical maximum likelihood method to estimate it. Experiments demonstrate that the proposed algorithm achieves better results with faster speed compared to the MAP-based algorithms.8. We propose a novel Bayesian multichannel image deblurring algorithm that utilizes a hybrid model composed of the cross relation model and the smoothing model to characterize point spread function. The proposed algorithm also utilizes total variation to model the original image. Point spread function, together with original image, is estimated alternatively using the hierarchical maximum likelihood method. Results show the competitive performance of the proposed algorithm in vision effects and speed compared to other algorithms.更多还原