Supervised deep-learning (SDL) techniques with paired training datasets have been widely studied for X-ray computed tomography (CT) image reconstruction. However, due to the difficulties of obtaining paired training datasets in clinical routine, the SDL methods are still away from common uses in clinical practices. In recent years, self-supervised deep-learning (SSDL) techniques have shown great potential for the studies of CT image reconstruction. In this work, we propose a self-supervised cross-task mutual learning (SS-CTML) framework for CT image reconstruction. Specifically, a sparse-view scanned and a limited-view scanned sinogram data are first extracted from a full-view scanned sinogram data, which results in three individual reconstruction tasks, i.e., the full-view CT (FVCT) reconstruction, the sparse-view CT (SVCT) reconstruction, and limited-view CT (LVCT) reconstruction. Then, three neural networks are constructed for the three reconstruction tasks. Considering that the ultimate goals of the three tasks are all to reconstruct high-quality CT images, we therefore construct a set of cross-task mutual learning objectives for the three tasks, in which way, the three neural networks can be self-supervised optimized by learning from each other. Clinical datasets are adopted to evaluate the effectiveness of the proposed framework. Experimental results demonstrate that the SS-CTML framework can obtain promising CT image reconstruction performance in terms of both quantitative and qualitative measurements.

In this paper, we propose a new super-expressive activation function called the Parametric Elementary Universal Activation Function (PEUAF). We demonstrate the effectiveness of PEUAF through systematic and comprehensive experiments on various industrial and image datasets, including CIFAR10, Tiny-ImageNet, and ImageNet. Moreover, we significantly generalize the family of super-expressive activation functions, whose existence has been demonstrated in several recent works by showing that any continuous function can be approximated to any desired accuracy by a fixed-size network with a specific super-expressive activation function. Specifically, our work addresses two major bottlenecks in impeding the development of super-expressive activation functions: the limited identification of super-expressive functions, which raises doubts about their broad applicability, and their often peculiar forms, which lead to skepticism regarding their scalability and practicality in real-world applications.