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

Abstract

Gold nanoparticles are studied extensively due to their unique optical and catalytical properties. Their exact shape determines the properties and thereby the possible applications. Electron tomography is therefore often used to examine the three‐dimensional shape of nanoparticles. However, since the acquisition of the experimental tilt series and the 3D reconstructions are very time consuming, it is difficult to obtain statistical results concerning the 3D shape of nanoparticles. We propose a new approach for electron tomography that is based on artificial neural networks, which enables us to reduce the number of projection images with a factor of 5 or more 1 . The application of neural network filtered backprojection method (NN‐FBP) 2 to electron tomography consists of two phases: (i) a learning phase , in which full tilt series and their corresponding reconstructions are used to calibrate the reconstruction algorithm and (ii) a reconstruction phase , in which large batches of limited tilt series (i.e. using fewer projection images) are rapidly reconstructed. The parameters of the NN‐FBP are trained by high quality 3D reconstructions, based on 151 projection images, in the learning phase. In the reconstruction phase, a tilt series of only 10 projection images of a gold nanoparticle is used as input. As opposed to previous advanced reconstruction methods, specific prior knowledge is not explicitly used in the NN‐FBP method. Also, since NN‐FBP is based on the efficient Weighted Backprojection algorithm, it is computationally efficient as well, enabling high throughput of 3D reconstructions. We show that the NN‐FBP reconstruction algorithm is able to yield electron tomography reconstructions based on highly limited data with a comparable quality to a reconstruction based on a full data series with a tilt increment of 1° (Figure 1). The decrease in acquisition time and the use of an efficient reconstruction method enables us to examine a broad range of nanostructures in a statistical manner. Using the NN‐FBP approach, the average radius of a batch of 70 nanospheres was obtained. These results confirm the reliability of the NN‐FBP algorithm and demonstrate the possibility of combining electron tomography and statistical measurements (Figure 2).