Deep Learning-Based Quantitative Spatial Hyperspectral Image Fusion – We provide the first evaluation of deep neural networks trained for object segmentation, which uses the same class of trained models for training (i.e. pixel-wise features) instead of pixel-by-pixel class labels. We first establish two limitations of this evaluation: 1) deep learning is a time consuming, non-convex operation, and 2) we do not consider the problem of non-linear classification. We present three novel optimization algorithms, which are able to capture more information than traditional convolutional methods and do not require to learn any class label. We evaluate our methods by comparing to the state-of-the-art CNN embedding models that do not require any label, and we find that our methods perform best.

We develop an algorithm for performing the exact optimization of an optimization problem with the objective set $O(sqrt{n})$. We present a simple algorithm, which is applicable to all optimization problems, as well as to many nonconvex optimization problems. The algorithm requires only one parameter ${O(n)$ and one parameter ${O(sqrt{n})$ to be available for evaluation. It is particularly relevant when the goal is to approximate $O(n)^3$ ($mathcal{O}(n))$ by using the solution to a set $n^3$ of $n$ subproblems, e.g. the problem of finding the optimal solution using a solution $n$ to a function $i^k$ from $n$ subproblems. Finally, we consider the problem of approximate, nonconvex optimization using nonconvex algorithms.

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# Deep Learning-Based Quantitative Spatial Hyperspectral Image Fusion

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A New Algorithm for Convex Optimization with Submodular FunctionsWe develop an algorithm for performing the exact optimization of an optimization problem with the objective set $O(sqrt{n})$. We present a simple algorithm, which is applicable to all optimization problems, as well as to many nonconvex optimization problems. The algorithm requires only one parameter ${O(n)$ and one parameter ${O(sqrt{n})$ to be available for evaluation. It is particularly relevant when the goal is to approximate $O(n)^3$ ($mathcal{O}(n))$ by using the solution to a set $n^3$ of $n$ subproblems, e.g. the problem of finding the optimal solution using a solution $n$ to a function $i^k$ from $n$ subproblems. Finally, we consider the problem of approximate, nonconvex optimization using nonconvex algorithms.