【作者】 陈建军；

【导师】 田逢春；

【作者基本信息】 重庆大学 ， 电路与系统， 2009， 博士

【摘要】 偏微分方法在图像处理、信号处理以及图像压缩等领域中得到了广泛的应用,然而其庞大的计算量制约了偏微分方法应用的进一步推广。将偏微分方法与多尺度分析方法结合起来,利用这两种方法各自的优点,形成新的图像处理方法,可以极大地减少偏微分方法所花的计算时间,这是很有理论和实用价值的。目前,偏微分方法已经被应用于边缘提取、特征提取、模式识别、图像分割、机器视觉等领域,显示出很好的应用前景。但是,现有的偏微分方法对噪声比较敏感,这一定程度上限制了它在图像降噪和图像修复领域中的应用。为此,本文全面系统地阐述了偏微分方法的发展动态和基本理论,详细分析了非下采样Contourlet多尺度变换特性,深入研究了在像素域和变换域进行偏微分扩散的图像降噪和图像修复方法。提出了自适应的P-Laplace的扩散方法。其中关键参数p能根据图像局部几何信息的曲率和梯度自适应地改变,并控制扩散方向和扩散强度。首先,利用变分原理,推导出P-Laplace的扩散方法所对应的欧拉方程,利用图像的局部正交坐标系,分析其扩散能力。扩散过程中,在图像的边缘区域,沿边缘方向扩散应具有较大的扩散系数,沿垂直边缘方向扩散应具有很小的扩散系数;在图像的平坦区域,向周围等强度扩散,而且扩散强度值较大。其次,根据对自适应的P-Laplace扩散方法的分析,利用半点差分格式,设计出图像修复的数值方法。理论分析和实验结果都表明,基于自适应的P-Laplace扩散的图像修复模型比基于TV修复的模型更有效;同时通过实验表明基于自适应的P-Laplace扩散的图像修复模型比基于常数p的P-Laplace扩散的图像修复模型在提高图像修复质量方面更有效。提出了一种基于非下采样Contourlet变换的自适应降噪方法,先对图像进行非下采样Contourlet变换得到不同尺度和不同方向上的变换系数,然后用分解尺度的系数和区域能量来表示图像的纹理信息。在相同分解尺度下,分解能量越大,表示该方向具有更多的纹理信息,阈值设置应该设置就越低,反之阈值设置就越大。再根据变换系数特征,引入非下采样Contourlet变换的方向因子,自适应地确定降噪阈值。最后对变换系数进行反变换,实现图像降噪。实验结果表明,与小波变换和Contourlet变换相比,非下采样Contourlet变换降噪方法保留了更多的图像轮廓细节,提高了图像的PSNR值。提出了基于非下采样Contourlet变换和自适应P-Laplace扩散的图像降噪方法。这种方法的主要目的是在图像降噪时,能减少吉普斯震荡现象。同时论文提出了用扩散因子在不同区域控制不同的扩散强度。首先,通过非下采样Contourlet变换阈值得到初步的降噪图像;然后,把阈值变换后本来需要置零的高频系数保留,再利用P-Laplace算法进行扩散,得到高频扩散图像;最后,把这部分高频扩散图像融合到阈值方法得到的降噪图像中,得到最终降噪图像。数值结果表明,论文方法在提高图像质量的同时,能有效保持图像的纹理细节。提出了在非下采样Contourlet变换域进行自适应P-Laplace扩散的图像修复方法。许多传统的方法是在像素域进行扩散,但是论文中提出的修复方式是在非下采样Contourlet变换域直接进行。由于在图像压缩保存和传输过程中可能丢失部分系数,论文提出的方法可以在变换域直接进行系数修复。理论分析和实验结果都表明,基于变换域的修复方法是有效的,即使在丢失大量系数的情况下,也可以较好地实现修复,明显地提高图像的质量。针对图像复原问题,提出了一种基于各向异性和非线性规整化的自适应P-Laplace扩散的图像盲复原新算法。该算法主要结合图像梯度和曲率的性质采用基于各向异性的空间自适应规整化处理,建立了具有非线性和空间各向异性的规整化函数,使其在恢复目标图像时能自适应地进行梯度平滑和边缘保留。通过交替最小化方案来极小化代价函数和通过定点迭代策略将非线性方程进行线性化处理,快速地恢复图像。更多还原

【Abstract】 PDE method has been extensively applied to many fields, such as image processing and signal processing. However, its application is restricted by its computational complexity. Therefore, the PDE and multi-scale image analysis are combined to form a new image processing method. The new method can be applied in image denoising and image inpainting, and can greatly reduce the computation time spent on PDE. The new method has theoretical and practical value. At present, PDE has been applied to many fields, such as edge and feature extracton, pattern recognition, image segmentation as well as computer vision, and showed good prospects. But many PDE methods suffer from the staircase effect easily, which restricts its application in some fields such as image denoising and image inpainting. So, the fundamental theory and developments of PDE were systematically described in this dissertation. The characteristics of PDE and multi-scale image analysis were analyzed for image denoising and image inpainting in pixel domain and transform domain in detail. The principle and implementation of these methods were deeply studied in this paper.The adaptive P-Laplace diffusion method for images denoising is proposed in this dissertation. An adaptive factor p is proposed based on the local geometry characteristic of curvature and gradient feature of images. The adaptive factor p can control the diffusion direction and diffusion intensity. The Euler-Lagrange equations of the P-Laplace diffusion method are deduced. The diffusion performance of the adaptive P-Laplace diffusion equation is analyzed. The adaptive P-Laplace diffusion has strong diffusion coefficient in the edge direction and has small diffusion coefficient in the gradient direction when diffusion was performed at edge region. But the adaptive P-Laplace diffusion has the same diffusion coefficient at smooth region. The image inpainting algorithm of finite difference is proposed with the half point differential scheme based on the analysis of the adaptive P-Laplace diffusion. Theoretic analysis and experimental results show that the new method has better performances both in vision effect and image quality than the TV method and the constant P-Laplace method.An adaptive de-noising algorithm was proposed based on the nonsubsampled Contourlet transform. Firstly the coefficients in different scales and different directions are obtained by image decomposition using the nonsubsampled Contourlet transform. The texture of the image information is introduced by using the mean of decomposition scale and the variance of region. The threshold should be set lowly when the image has many textures at each decomposition scale. On the contrary, the threshold should be set large. Threshold functions are set with these coefficients adaptively. After the de-noising and reconstruction of these coefficients, image de-noising is implemented. Comparing to the wavelet transform threshold and Contourlet transform threshold, the nonsubsampled Contourlet transform picks up the image detail better and improves signal-to-noise ratio of the peak.We proposed a nonsubsampled Contourlet transform (NSCT) formulation combined with the adaptive P-Laplace variation method for images denoising. Our method aims at reducing Gibbs-type artifacts. The diffusion factor has different diffusional intensity at different region. Firstly, the denoised image which by threshold method of nonsubsampled Contourlet transform is obtained. Secondly, the NSCT coefficients which have been set to zero by the threshold procedure are retained, and the P-Laplace diffusion directly to the reconstruction image from the retained coefficients. Finally, the diffusion image is fused with the denoised image with the thresholds method, and the final denoising image is obtained. The experimental results indicate that our method can improve image quality and maintain much more detail information.We proposed a novel image inpainting method. The new method is anisotropic diffusion. It can control and restore the missing or damaged regions in the nonsubsampled Contourlet transform (NSCT) domain, instead of the pixel domain in which traditional inpainting problems are defined. In the wireless communication of these images, it could happen that certain wavelet packets are randomly lost or damaged during the transmission process. Our method can remedy the lost coefficients in the transform domain. Experimental results show that the proposed algorithm can remedy images effectively and improve image quality significantly, even with relatively large number of lost coefficients.A blind restoration algorithm of P-Laplace diffusion based on anisotropic and nonlinear regularizations is proposed for restoring degraded images, in which the anisotropic and adaptive regularizations are adopted according to the character of image curvature and gradient. The nonlinear and spatial anisotropic regularization functions are suggested to smooth adaptively in the process of recovering the object image. Finally, the cost functions are minimized by alternate minimization scheme. The nonlinear equations are linear by fixed-point iteration scheme. The images can be recovered quickly.更多还原