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Recent years have seen the rapid growth of new approaches to optical imaging, with an emphasis on extracting three-dimensional (3D) information from what is normally a two-dimensional (2D) image capture. Perhaps most importantly, the rise of computational imaging enables both new physical layouts of optical components and new algorithms to be implemented. This paper concerns the convergence of two advances: the development of a transparent focal stack imaging system using graphene photodetector arrays, and the rapid expansion of the capabilities of machine learning including the development of powerful neural networks. This paper demonstrates 3D tracking of point-like objects with multilayer feedforward neural networks and the extension to tracking positions of multi-point objects. Computer simulations further demonstrate how this optical system can track extended objects in 3D, highlighting the promise of combining nanophotonic devices, new optical system designs, and machine learning for new frontiers in 3D imaging.

 

Image security is becoming an increasingly important issue due to advances in deep learning based image manipulations, such as deep image inpainting and deepfakes. There has been considerable work to date on detecting such image manipulations using improved algorithms, with little attention paid to the possible role that hardware advances may have for improving security. We propose to use a focal stack camera as a novel secure imaging device, to the best of our knowledge, that facilitates localizing modified regions in manipulated images. We show that applying convolutional neural network detection methods to focal stack images achieves significantly better detection accuracy compared to single image based forgery detection. This work demonstrates that focal stack images could be used as a novel secure image file format and opens up a new direction for secure imaging.

 

While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. 

Recent research in the theory of overparametrized learning has sought to establish generalization guarantees in the interpolating regime. Such results have been established for a few common classes of methods, but so far not for ensemble methods. We devise an ensemble classification method that simultaneously interpolates the training data, and is consistent for a broad class of data distributions. To this end, we define the manifold-Hilbert kernel for data distributed on a Riemannian manifold. We prove that kernel smoothing regression and classification using the manifold-Hilbert kernel are weakly consistent in the setting of Devroye et al. [19]. For the sphere, we show that the manifold-Hilbert kernel can be realized as a weighted random partition kernel, which arises as an infinite ensemble of partition-basedclassifiers.