We have mapped flooded areas in data collected by the NASA/JPL Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR) using two convolutional neural network (CNN) image classifier architectures: U-Net and SegNet. Our study area was a region around Houston, TX, USA affected by widespread flooding in 2017 due to Hurricane Harvey. To train and test the classifiers, we manually labelled over 10000 image segments in two flight lines. Both U-Net and SegNet yielded higher accuracy than a previous non-machine learning classifier we used as a baseline. U-Net had slightly higher accuracy than SegNet. The classifiers performed better in areas with more homogeneous land cover. To independently validate the classifier accuracy we used NOAA aerial imagery, with overall accuracy around 80%. Future work includes assessing the classifier robustness in other study areas, assessing the classifier dependence on UAVSAR incidence angle, particularly for open water and bare ground, and collecting more training data, particularly in urban areas. This study demonstrates the potential of CNN image classifiers for mapping flooded areas in airborne polarimetric SAR imagery, and for land cover classification of polarimetric SAR imagery more generally.

Given n discrete random variables, its entropy vector is the 2n- 1-dimensional vector obtained from the joint entropies of all non-empty subsets of the random variables. It is well known that there is a close relation between such an entropy vector and a certain group-characterizable vector obtained from a finite group and n of its subgroups; indeed, roughly speaking, knowing the region of all such group-characterizable vectors is equivalent to knowing the region of all entropy vectors. This correspondence may be useful for characterizing the space of entropic vectors and for designing network codes. If one restricts attention to abelian groups then not all entropy vectors can be obtained. This is an explanation for the fact shown by Dougherty et al. that linear network codes cannot achieve capacity in general network coding problems (since linear network codes come from abelian groups). All abelian groupcharacterizable vectors, and by fiat all entropy vectors generated by linear network codes, satisfy a linear inequality called the Ingleton inequality. General entropy vectors, however, do not necessarily have this property. It is, therefore, of interest to identify groups that violate the Ingleton inequality. In this paper, we study the problem of finding nonabelian finite groups that yield characterizable vectors, which violate the Ingleton inequality. Using a refined computer search, we find the symmetric group S5 to be the smallest group that violates the Ingleton inequality. Careful study of the structure of this group, and its subgroups, reveals that it belongs to the Ingleton-violating family PGL(2, q) with a prime power q ≥ 5, i.e., the projective group of 2 × 2 nonsingular matrices with entries in Fq. We further interpret this family of groups, and their subgroups, using the theory of group actions and identify the subgroups as certain stabilizers. We also extend the construction to more general groups such as PGL(n, q) and GL(n, q). The families of groups identified here are therefore good candidates for constructing network codes more powerful than linear network codes, and we discuss some considerations for constructing such group network codes.

Many problems in areas such as compressive sensing and coding theory seek to design a set of equal-norm vectors with large angular separation. This idea is essentially equivalent to constructing a frame with low coherence. The elements of such frames can in turn be used to build high-performance spherical codes, quantum measurement operators, and compressive sensing measurement matrices, to name a few applications. In this paper, we allude to the group-frame construction first described by Slepian and further explored in the works of Vale and Waldron. We present a method for selecting representations of a finite group to construct a group frame that achieves low coherence. Our technique produces a tight frame with a small number of distinct inner product values between the frame elements, in a sense approximating a Grassmannian frame. We identify special cases in which our construction yields some previously known frames with optimal coherence meeting the Welch lower bound, and other cases in which the entries of our frame vectors come from small alphabets. In particular, we apply our technique to the problem choosing a subset of rows of an Hadamard matrix so that the resulting columns form a low-coherence frame. Finally, we give an explicit calculation of the average coherence of our frames, and find regimes in which they satisfy the strong coherence property described by Mixon, Bajwa, and Calderbank.

We examine an error-correcting coding framework in which each coded symbol is constrained to be a function of a fixed subset of the message symbols. With an eye toward distributed storage applications, we seek to design systematic codes with good minimum distance that can be decoded efficiently. On this note, we provide theoretical bounds on the minimum distance of such a code based on the coded symbol constraints. We refine these bounds in the case where we demand a systematic linear code. Finally, we provide conditions under which each of these bounds can be achieved by choosing our code to be a subcode of a Reed-Solomon code, allowing for efficient decoding. This problem has been considered in multisource multicast network error correction. The problem setup is also reminiscent of locally repairable codes.

We explore the problem of deterministically constructing frames and matrices with low coherence, which arises in areas such as compressive sensing, spherical codes, and MIMO communications. In particular, we present a generalization of the familiar harmonic frame by selecting a subset of rows of the generalized discrete Fourier transform matrix over finite groups. We apply our methods to the group SL2(Fq) and show how to produce frames with remarkably low coherence, for which we provide upper bounds.

The problem of designing low coherence matrices and low-correlation frames arises in a variety of fields, including compressed sensing, MIMO communications and quantum measurements. The challenge is that one must control the (n over 2) pairwise inner products of the columns of the matrix. In this paper, we follow the group code approach of David Slepian [1], which constructs frames using unitary group representations and which in general reduces the number of distinct inner products to n-1. We examine representations of cyclic groups as well as generalized dihedral groups, and we expand upon previous results which bound the coherence of the resulting frames.

Designing low coherence matrices and low-correlation frames is a point of interest in many fields including compressed sensing, MIMO communications and quantum measurements. The challenge is that one must control the (n2) pairwise inner products between the frame elements. In this paper, we exploit the group code approach of David Slepian [1], which constructs frames using unitary group representations and which in general reduces the number of distinct inner products to n - 1. We demonstrate how to efficiently find optimal representations of cyclic groups, and we show how basic abelian groups can be used to construct tight frames that have the same dimensions and inner products as those arising from certain more complex nonabelian groups. We support our work with theoretical bounds and simulations.

We propose a new algorithm to recover a sparse signal from a system of linear measurements. By projecting the measured signal onto a properly chosen subspace, we can use the projection to zero in on a low-sparsity portion of our original signal, which we can recover using ℓ1-minimization. We can then recover the remaining portion of our signal from an overdetermined system of linear equations. We prove that our scheme improves the threshold of ℓ1-minimization, and we derive an upper bound for this new threshold. We support our theoretical results with numerical simulations which demonstrate that certain classes of signals come close to achieving this upper bound.

In principle, network codes derived from non-Abelian groups can be used to attain every point in the capacity region of wired acyclic networks. However, group codes derived from a particular group, and its subgroups, is useful only if it can model independent sources, as well as violate the Ingleton bound which restricts the capacity region obtainable by linear network codes. We study both the independent source and the Ingleton-violating requirement for subgroups of the groups PGL(2, ρ) and GL(2, ρ) with primes ρ ≥ 5. For both these groups we demonstrate that the requirements can be met, which suggests that PGL(2, ρ) and GL(2, ρ) are rich enough groups to construct network codes superior to linear ones. We also construct a model for independent sources using the direct product of the aforementioned groups.