Accelerated FBP for computed tomography image reconstruction

TL;DR

This paper introduces a faster filtered back projection method for computed tomography that reduces computational complexity by using recursive filters and the fast discrete Hough transform, demonstrated on simulated data.

Contribution

It presents a novel approach that lowers the computational complexity of FBP from $ heta(N^3)$ to $ heta(N^2 ext{log} N)$ operations without Fourier transforms.

Findings

Reduced computational complexity to $ heta(N^2 ext{log} N)$

Efficient convolution via recursive ramp filter approximation

Validated on simulated data showing improved speed

Abstract

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 $\Theta(N^3)$ operations, where $N$ is the linear size of the 2D slice. Recent approaches including reconstruction via the Fourier slice theorem require $\Theta(N^2\log N)$ multiplication operations. In this paper, we propose a novel approach that reduces the computational complexity of the algorithm to $\Theta(N^2\log N)$ 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.