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Second-order Total Variation for Compressed Sensing Cryo-ET and Subtomogram Averaging

Cryo-electron tomography (cryo-ET) is a key tool for imaging macromolecules in cellular environments. Together with subtomogram averaging (STA), cryo-ET can be used for structure determination. Weak visibility of many structures in cryo-ET as well as the volume of data required for STA, however, motivate the exploration of advanced image processing for cryo-ET. Compressed sensing is a mathematically rigorous signal processing approach to sampling with far fewer measurements than traditionally required, with significant applications in limited angle, undersampled electron tomography in the physical sciences [1,2]. Compressed sensing electron tomography (CS-ET) holds that for sample features that can be described as sparse, i.e., those requiring only a few coefficients to represent the object in a particular mathematical transform domain, a set of measurements can be devised to directly identify the tomographic reconstruction that also adheres to that sparsity, in contrast to post-processing approaches. This idea is related to image compression, where an image can be represented by only a small number of coefficients to reduce the storage requirements of the fully sampled image. CS-ET enables reducing data quantities while recovering high-fidelity reconstructions, or provides improved visibility and precision of image features for a given number of samples (measurements) [1–3].