基于先验信息的图像重建迭代算法

The iteration methods are the available algorithms for image reconstruction, the reasonable and available utilization of image prior data can gain the better reconstructed images from less projection data. Guided Image Filtering is an image processing method which is a simple, easy to implement and can be applied availably to image restoration, blurring/sharpening, feature extraction, edge detection. One of the most attentions to the reconstructed image is the edges of the image. The edges of the images reconstructed by analytic and iterative methods become smoothing especially for less projection data. This project studied the optimal and accelerated convergence methods of relaxation coefficients, to solve the semi-convergence problems of algebraic iterative methods with noise projection data. Combing with Guided Image Filtering and utilizing the prior image data reasonably and availably, we propose the Guided Image Filtering-based algebraic iterative method to maintain the original edge feature of the image. Using the directional wavelet sparse presentation of image, we study the Guided Image Filtering-based iterative algorithm and compressed sensing reconstruction algorithm, and incorporating the propagation law of the Radon transform singularity and using wavelet to detect the signal singularity, study the Guided Image Filtering-based iterative algorithm. The project will provide the available iteration methods of reconstructing the images and their edges from less projection data, utilizing the prior image data reasonably and availably。

迭代方法是有效的图像重建算法，图像先验信息的合理有效地使用可以在适当少的投影数据的情况用迭代方法获得好的重建图像。引导滤波方法是简单，易于实现，能够有效地用于图像恢复、去模糊、特征提取，边缘探测和处理图像处理方法。重建的图像被关注的重要性之一是它的边缘，无论是解析方法或迭代方法，特别对于少的投影数据，在重建图像的边缘会变得适当的平滑。本项目研究有噪声投影数据代数迭代算法的最优松弛方法，解决有噪声投影数据时迭代的半收敛问题；结合图像处理的引导滤波方法，合理利用图像的先验信息，为了保持图像的本质边缘信息，提出基于引导滤波的图像重建代数迭代算法；用图像方向小波的稀疏表示，研究基于引导滤波的迭代算法和压缩感知重建算法；结合Radon变换的奇性传播规律，小波检测信号奇性方法研究引导滤波的图像重建迭代算法。本项目提供合理利用图像先验信息在少投影数据下有效重建工业和医学图像以及边缘信息的迭代重建算法。

迭代方法是有效的图像重建算法，图像先验信息的合理有效地使用可以在适当少的投影数据的情况用迭代方法获得好的重建图像。本项目结合迭代方法和引导滤波方法，开展基于先验信息的图像重建迭代算法研究，具体做了如下的研究和重要进展: 有噪声投影数据Landweber迭代算法的最优和加速收敛松弛方法；基于导引图滤波的同时代数迭代重建算法；基于导引滤波和TV-L1模型的类同轴相位CT环状伪影校正方法；基于Laplace范数的稀疏信号阈值重建算法；Richardson 迭代法松弛策略；基于Hessian Schatten 范数的自适应字典的图像恢复算法；带限信号外推和有限角图像重建的加权Landweber 迭代算法；同步辐射 CT 图像对比度增强算法；加权正交匹配追踪的盲多带信号重建方法；稀疏信号重建加权重建算法；极大似然期望算法的加速收敛松弛策略。