CT图像重建滤波反投影算法中指数滤波器的研究

Study on Exponential Filter of Filter Back Projection Algorithm for CT Image Reconstruction

CT技术的核心是图像重建,而图像重建的决定因素是重建算法,其优劣直接影响对重建结果准确性的判断。CT图像重建算法可以分为迭代法和解析法两大类,其中解析法具有比较严密的数学理论基础,且处理速度快,所以在CT技术领域得到广泛应用。在解析重建算法中,滤波反投影算法拥有较高的运算效率,能获得较好的图像重建质量,而且滤波反投影算法的成本低,易于通过并行实现,便于进一步提高其重建速度,所以该算法为解析法中的主流算法。根据滤波反投影算法的实现原理,其中滤波函数的选取对重建结果、重建速度等方面有着举足轻重的作用。针对滤波函数的选择进行研究,首先在分析常用R-L和S-L滤波函数的基础上,引入指数滤波函数的研究,并借助调整指数参数的取值,分析了该函数在无噪声和有噪声情况下对图像重建的影响。通过实验仿真的方法,验证了指数滤波函数在保证较好的空间分辨率的情况下,保持了良好的图像重建特性。

Computed Tomography(CT)image reconstruction playing the core role in CT technique,the performance of reconstruction algorithm is of vital importance to the judgement of accuracy of monitor results.The image of the object is reconstructed from projection data by using algebraic or analytic algorithms.Analytical algorithms are deduced based on rigorous mathematic theories,and have the advantages of fast processing speed.So the analytical algorithms are used widely on CT detection equipment.In the analytic reconstruction algorithms,filter back projection algorithm is the mainstream.The main reason is the filter back projection algorithm has higher operation efficiency,and better reconstructed image quality.It is low cost,easy to realize parallel processing,so it is used in many industrial CT machine.In the process of analytical algorithms,the selection of the filter function playing a decisive role in reconstuction result and efficiency.This paper firstly introduced R-L and S-L filter function,and analyzed their natures.Secondly,it put forward exponential filter function,and analyzed the influence of exponential function in the absence of noise and noise conditions on image reconstruction by adjusting index value of parameter.Lastly,proved by experimental simulation that the exponential filter function can obtain not only better spatial resolution,but also better image properties.