Compressed Sensing Electron tomography using adaptive dictionaries: a simulation study

A Alafeef,S Mcvitie,P Cockshott,I Maclaren

doi:10.1088/1742-6596/522/1/012021

A Alafeef, S Mcvitie + Show 2 more

Open Access

https://doi.org/10.1088/1742-6596/522/1/012021

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Abstract

Electron tomography (ET) is an increasingly important technique for examining the three-dimensional morphologies of nanostructures. ET involves the acquisition of a set of 2D projection images to be reconstructed into a volumetric image by solving an inverse problem. However, due to limitations in the acquisition process this inverse problem is considered ill-posed (i.e., no unique solution exists). Furthermore reconstruction usually suffers from missing wedge artifacts (e.g., star, fan, blurring, and elongation artifacts). Compressed sensing (CS) has recently been applied to ET and showed promising results for reducing missing wedge artifacts caused by limited angle sampling. CS uses a nonlinear reconstruction algorithm that employs image sparsity as a priori knowledge to improve the accuracy of density reconstruction from a relatively small number of projections compared to other reconstruction techniques. However, The performance of CS recovery depends heavily on the degree of sparsity of the reconstructed image in the selected transform domain. Prespecified transformations such as spatial gradients provide sparse image representation, while synthesising the sparsifying transform based on the properties of the particular specimen may give even sparser results and can extend the application of CS to specimens that can not be sparsely represented with other transforms such as Total variation (TV). In this work, we show that CS reconstruction in ET can be significantly improved by tailoring the sparsity representation using a sparse dictionary learning principle.

Highlights

In materials science, Electron tomography (ET) is considered an effective technique that provides indispensable information for the study of particles and structures in the Nanoworld
We performed the reconstruction using a weighted back projection (WBP) method (Figure 1-b), a Total variation (TV)-based method (Figure 1-c), and proposed approach (Figure 1-d) using simulated data set consisted of 27 projections
Peak Signal to Noise Ratio (PSNR) in dB is showed for the reconstruction in (Table 1)

Summary

Introduction

Electron tomography (ET) is considered an effective technique that provides indispensable information for the study of particles and structures in the Nanoworld. Where P is the discrete Radon transform that converts the measurements (1D projections) b into object domain (2D imaged object) x. The key prior knowledge employed in CS is that the signal is sparse in a transform domain, meaning that it can be approximated in a more compact form.

Results

Conclusion