The development of fast and accurate image reconstruction algorithms is a central aspect of computed tomography. In this paper, we investigate this issue for the sparse data problem in photoacoustic tomography (PAT). We develop a direct and highly efficient reconstruction algorithm based on deep learning. In our approach, image reconstruction is performed with a deep convolutional neural network (CNN), whose weights are adjusted prior to the actual image reconstruction based on a set of training data. The proposed reconstruction approach can be interpreted as a network that uses the PAT filtered backprojection algorithm for the first layer, followed by the U-net architecture for the remaining layers. Actual image reconstruction with deep learning consists in one evaluation of the trained CNN, which does not require time-consuming solution of the forward and adjoint problems. At the same time, our numerical results demonstrate that the proposed deep learning approach reconstructs images with a quality comparable to state of the art iterative approaches for PAT from sparse data.

How to deal with continuously flexing molecules is one of the biggest outstanding challenges in single-particle analysis of proteins from cryogenic-electron microscopy (cryo-EM) images. Here, we present DynaMight, a software tool that estimates a continuous space of conformations in a cryo-EM dataset by learning three-dimensional deformations of a Gaussian pseudo-atomic model of a consensus structure for every particle image. Inversion of the learned deformations is then used to obtain an improved reconstruction of the consensus structure. We illustrate the performance of DynaMight for several experimental cryo-EM datasets. We also show how error estimates on the deformations may be obtained by independently training two variational autoencoders on half sets of the cryo-EM data, and how regularization of the three-dimensional deformations through the use of atomic models may lead to important artifacts due to model bias. DynaMight is distributed as free, open-source software, as part of RELION-5.

The point centromere of budding yeast specifies assembly of the large kinetochore complex to mediate chromatid segregation. Kinetochores comprise the centromere-associated inner kinetochore (CCAN) complex and the microtubule-binding outer kinetochore KNL1-MIS12-NDC80 (KMN) network. The budding yeast inner kinetochore also contains the DNA binding centromere-binding factor 1 (CBF1) and CBF3 complexes. We determined the cryo–electron microscopy structure of the yeast inner kinetochore assembled onto the centromere-specific centromere protein A nucleosomes (CENP-A ^Nuc ). This revealed a central CENP-A ^Nuc with extensively unwrapped DNA ends. These free DNA duplexes bind two CCAN protomers, one of which entraps DNA topologically, positioned on the centromere DNA element I (CDEI) motif by CBF1. The two CCAN protomers are linked through CBF3 forming an arch-like configuration. With a structural mechanism for how CENP-A ^Nuc can also be linked to KMN involving only CENP-QU, we present a model for inner kinetochore assembly onto a point centromere and how it organizes the outer kinetochore for chromosome attachment to the mitotic spindle.

Recently, a large number of efficient deep learning methods for solving inverse problems have been developed and show outstanding numerical performance. For these deep learning methods, however, a solid theoretical foundation in the form of reconstruction guarantees is missing. In contrast, for classical reconstruction methods, such as convex variational and frame-based regularization, theoretical convergence and convergence rate results are well established. In this paper, we introduce deep synthesis networks for regularizing inverse problems (DESYRE) using neural networks as nonlinear synthesis operator bridging the gap between these two worlds. The proposed method allows to exploit the deep learning benefits of being well adjustable to available training data and on the other hand comes with a solid mathematical foundation. We present a complete convergence analysis with convergence rates for the proposed deep synthesis regularization. We present a strategy for constructing a synthesis network as part of an analysis–synthesis sequence together with an appropriate training strategy. Numerical results show the plausibility of our approach.