Fast Tomographic Reconstruction From Limited Data Using Artificial Neural Networks

Abstract

Image reconstruction from a small number of projections is a challenging problem in tomography. Advanced algorithms that incorporate prior knowledge can sometimes produce accurate reconstructions, but they typically require long computation times. Furthermore, the required prior knowledge can be very specific, limiting the type of images that can be reconstructed. Here, we present a reconstruction method that automatically learns prior knowledge using an artificial neural network. We show that this method can be viewed as a combination of filtered backprojection steps, and, therefore, has a relatively low computational cost. Results for two different cases show that the new method is able to use the learned information to produce high quality reconstructions in a short time, even when presented with a small number of projections.

Electron tomography based on highly limited data using a neural network reconstruction technique

“…Furthermore, implementing these methods can be difficult and time-consuming as well, since they rely on advanced mathematics. In this paper, we propose an alternative approach called Neural Network Filtered Backprojection (NN-FBP) that was first described in [27], which can effectively exploit sample characteristics to improve reconstruction quality, while still being highly computationally efficient. Here, we apply this new technique for the first time to electron tomography data.…”

“…Streaks can be observed due to the limited number of projections, and the limited angular range leads to elongation and blurring in the Z-direction. In [27], it was found that strong improvements on the reconstruction quality from limited data can be obtained by combining a small number (e.g. 2 or 4) of WBP reconstructions, each obtained using a different filter.…”

“…We will make effective use of a new approach for electron tomographic reconstructions that is based on artificial neural networks. The neural network filtered backprojection method (NN-FBP) is a recently developed reconstruction technique that has been applied successfully to X-ray tomography [27]; however the implementation for electron tomography is completely new. The method that we propose will enable us to reduce the number of necessary projection images for a 3D reconstruction by a factor of 5 or more.…”

Neural network Hilbert transform based filtered backprojection for fast inline x-ray inspection

“…Then, the two datavectors I 1 and I 2 are generated as described by (B.5) and (B.6). For both datavectors, the projection data is shifted so that the central pixel is at the center of the detector as explained in [22] and the data from all projection angles is summed.…”

Filtered backprojection using algebraic filters; application to biomedical micro-CT data

“…Nielsen et al derive filters specifically for a tomosynthesis geometry [7]. Pelt and Batenburg use artificial neural networks to find good filters based on prior knowledge for datasets with a small number of projection angles [8]. They also provide a method to find filters such that the projection error is minimal [9].…”