The Takagi problem on the disk and bidisk

We give a new proof on the disk that a Pick problem can be solved by a rational function that is unimodular on the unit circle and for which the number of poles inside the disk is no more than the number of non-positive eigenvalues of the Pick matrix. We use this method to find rational solutions to Pick problems on the bidisk

State-of-the-art and gaps for deep learning on limited training data in remote sensing

Deep learning usually requires big data, with respect to both volume and variety. However, most remote sensing applications only have limited training data, of which a small subset is labeled. Herein, we review three state-of-the-art approaches in deep learning to combat this challenge. The first topic is transfer learning, in which some aspects of one domain, e.g., features, are transferred to another domain. The next is unsupervised learning, e.g., autoencoders, which operate on unlabeled data. The last is generative adversarial networks, which can generate realistic looking data that can fool the likes of both a deep learning network and human. The aim of this article is to raise awareness of this dilemma, to direct the reader to existing work and to highlight current gaps that need solving.Comment: arXiv admin note: text overlap with arXiv:1709.0030

A Comprehensive Survey of Deep Learning in Remote Sensing: Theories, Tools and Challenges for the Community

In recent years, deep learning (DL), a re-branding of neural networks (NNs), has risen to the top in numerous areas, namely computer vision (CV), speech recognition, natural language processing, etc. Whereas remote sensing (RS) possesses a number of unique challenges, primarily related to sensors and applications, inevitably RS draws from many of the same theories as CV; e.g., statistics, fusion, and machine learning, to name a few. This means that the RS community should be aware of, if not at the leading edge of, of advancements like DL. Herein, we provide the most comprehensive survey of state-of-the-art RS DL research. We also review recent new developments in the DL field that can be used in DL for RS. Namely, we focus on theories, tools and challenges for the RS community. Specifically, we focus on unsolved challenges and opportunities as it relates to (i) inadequate data sets, (ii) human-understandable solutions for modelling physical phenomena, (iii) Big Data, (iv) non-traditional heterogeneous data sources, (v) DL architectures and learning algorithms for spectral, spatial and temporal data, (vi) transfer learning, (vii) an improved theoretical understanding of DL systems, (viii) high barriers to entry, and (ix) training and optimizing the DL.Comment: 64 pages, 411 references. To appear in Journal of Applied Remote Sensin

Fusion of an Ensemble of Augmented Image Detectors for Robust Object Detection

A significant challenge in object detection is accurate identification of an object's position in image space, whereas one algorithm with one set of parameters is usually not enough, and the fusion of multiple algorithms and/or parameters can lead to more robust results. Herein, a new computational intelligence fusion approach based on the dynamic analysis of agreement among object detection outputs is proposed. Furthermore, we propose an online versus just in training image augmentation strategy. Experiments comparing the results both with and without fusion are presented. We demonstrate that the augmented and fused combination results are the best, with respect to higher accuracy rates and reduction of outlier influences. The approach is demonstrated in the context of cone, pedestrian and box detection for Advanced Driver Assistance Systems (ADAS) applications.Comment: 21 pages, 12 figures, journal paper, MDPI Sensors, 201

Belief Maintenance Systems: Initial Prototype Specification

A fundamental need in future information systems is an effective method of accurately representing and monitoring dynamic, real-world situations inside a computer. Information is represented using an Extended Open World Assumption (EOWA), in which the data are explicitly true or false. Reasoning within the EOWA is done through the use of a dynamic dependency net which only represents those beliefs and justifications that are both currently valid and in current use. In this paper, we present definitions and uses of the EOWA and dynamic dependency net in our current research of developing a database with which we can use deductive reasoning with limited resources. A prototype has been implemented for determining the existing problems of creating such a belief management system for operation in real-world applications

Estimates for measures of sections of convex bodies

A $\sqrt{n}$ estimate in the hyperplane problem with arbitrary measures has recently been proved in \cite{K3}. In this note we present analogs of this result for sections of lower dimensions and in the complex case. We deduce these inequalities from stability in comparison problems for different generalizations of intersection bodies