Compressed Sensing Electron Tomography for Determining Biological Structure

There has been growing interest in applying compressed sensing (CS) theory and practice to reconstruct 3D volumes at the nanoscale from electron tomography datasets of inorganic materials, based on known sparsity in the structure of interest. Here we explore the application of CS for visualizing the 3D structure of biological specimens from tomographic tilt series acquired in the scanning transmission electron microscope (STEM). CS-ET reconstructions match or outperform commonly used alternative methods in full and undersampled tomogram recovery, but with less significant performance gains than observed for the imaging of inorganic materials. We propose that this disparity stems from the increased structural complexity of biological systems, as supported by theoretical CS sampling considerations and numerical results in simulated phantom datasets. A detailed analysis of the efficacy of CS-ET for undersampled recovery is therefore complicated by the structure of the object being imaged. The numerical nonlinear decoding process of CS shares strong connections with popular regularized least-squares methods, and the use of such numerical recovery techniques for mitigating artifacts and denoising in reconstructions of fully sampled datasets remains advantageous. This article provides a link to the software that has been developed for CS-ET reconstruction of electron tomographic data sets.