Obtaining measured Synthetic Aperture Radar (SAR) data for training Automatic Target Recognition (ATR) models can be too expensive (in terms of time and money) and complex of a process in many situations. In response, researchers have developed methods for creating synthetic SAR data for targets using electromagnetic prediction software, which is then used to enrich an existing measured training dataset. However, this approach relies on the availability of some amount of measured data. In this work, we focus on the case of having 100% synthetic training data, while testing on only measured data. We use the SAMPLE dataset public released by AFRL, and find significant challenges to learning generalizable representations from the synthetic data due to distributional differences between the two modalities and extremely limited training sample quantities. Using deep learning-based ATR models, we propose data augmentation, model construction, loss function choices, and ensembling techniques to enhance the representation learned from the synthetic data, and ultimately achieved over 95% accuracy on the SAMPLE dataset. We then analyze the functionality of our ATR models using saliency and feature-space investigations and find them to learn a more cohesive representation of the measured and synthetic data. Finally, we evaluate the out-oflibrary detection performance of our synthetic-only models and find that they are nearly 10% more effective than baseline methods at identifying measured test samples that do not belong to the training class set. Overall, our techniques and their compositions significantly enhance the feasibility of using ATR models trained exclusively on synthetic data.

Motivated by the minimax concave penalty based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions and their Moreau envelopes. Properties of these functions are developed by leveraging their structure. In particular, we provide sparsity guarantees for the general family of functions. We further study the behavior of the proximity operators of several special functions including indicator functions of closed convex sets, piecewise quadratic functions, and the linear combinations of them. To demonstrate these properties, several concrete examples are presented and existing instances are featured as special cases.

Tensors, which provide a powerful and flexible model for representing multi-attribute data and multiway interactions, play an indispensable role in modern data science across various fields in science and engineering. A fundamental task is to faithfully recover the tensor from highly incomplete measurements in a statistically and computationally efficient manner. Harnessing the low-rank structure of tensors in the Tucker decomposition, this paper develops a scaled gradient descent (ScaledGD) algorithm to directly recover the tensor factors with tailored spectral initializations, and shows that it provably converges at a linear rate independent of the condition number of the ground truth tensor for two canonical problemstensor completion and tensor regression -as soon as the sample size is above the order of n 3/2 ignoring other parameter dependencies, where n is the dimension of the tensor. This leads to an extremely scalable approach to low-rank tensor estimation compared with prior art, which suffers from at least one of the following drawbacks: extreme sensitivity to ill-conditioning, high per-iteration costs in terms of memory and computation, or poor sample complexity guarantees. To the best of our knowledge, ScaledGD is the first algorithm that achieves near-optimal statistical and computational complexities simultaneously for low-rank tensor completion with the Tucker decomposition. Our algorithm highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the underlying symmetry in low-rank tensor factorization.

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