论文标题
计算机断层扫描图像重建的加速FBP
Accelerated FBP for computed tomography image reconstruction
论文作者
论文摘要
过滤后的投影（FBP）是断层扫描图像重建中常用技术，证明了可接受的质量。该算法的经典直接实现需要执行$θ（n^3）$操作，其中$ n $是2D切片的线性大小。最近的方法包括通过傅立叶切片定理进行重建，需要$θ（n^2 \ log n）$乘法操作。在本文中，我们提出了一种新颖的方法，将算法的计算复杂性降低到$θ（n^2 \ log n）$添加操作，以避免傅立叶空间。为了加快卷积的加速，坡道过滤器是通过一对因果和抗苏氏递质过滤器（也称为无限脉冲响应过滤器）近似的。通过快速离散的Hough变换执行后部投影。模拟数据的实验结果证明了所提出的方法的效率。
Filtered back projection (FBP) is a commonly used technique in tomographic image reconstruction demonstrating acceptable quality. The classical direct implementations of this algorithm require the execution of $Θ(N^3)$ operations, where $N$ is the linear size of the 2D slice. Recent approaches including reconstruction via the Fourier slice theorem require $Θ(N^2\log N)$ multiplication operations. In this paper, we propose a novel approach that reduces the computational complexity of the algorithm to $Θ(N^2\log N)$ addition operations avoiding Fourier space. For speeding up the convolution, ramp filter is approximated by a pair of causal and anticausal recursive filters, also known as Infinite Impulse Response filters. The back projection is performed with the fast discrete Hough transform. Experimental results on simulated data demonstrate the efficiency of the proposed approach.
