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Register a new userIs There Any Recovery Guarantee with Coupled Structured Matrix Factorization for Hyperspectral Super-Resolution?
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Wing-Kin Ma
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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Coupled structured matrix factorization (CoSMF) for hyperspectral super-resolution (HSR) has recently drawn significant interest in hyperspectral imaging for remote sensing. Presently there is very few work that studies the theoretical recovery guarantees of CoSMF. This paper makes one such endeavor by considering the CoSMF formulation by Wei et al., which, simply speaking, is similar to coupled non-negative matrix factorization. Assuming no noise, we show sufficient conditions under which the globably optimal solution to the CoSMF problem is guaranteed to deliver certain recovery accuracies. Our analysis suggests that sparsity and the pure-pixel (or separability) condition play a hidden role in enabling CoSMF to achieve some good recovery characteristics.
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This paper develops a first-order optimization method for coupled structured matrix factorization (CoSMF) problems that arise in the context of hyperspectral super-resolution (HSR) in remote sensing. To best leverage the problem structures for computational efficiency, we introduce a hybrid inexact block coordinate descent (HiBCD) scheme wherein one coordinate is updated via the fast proximal gradient (FPG) method, while another via the Frank-Wolfe (FW) method. The FPG-type methods are known to take less number of iterations to converge, by numerical experience, while the FW-type methods can offer lower per-iteration complexity in certain cases; and we wish to take the best of both. We show that the limit points of this HiBCD scheme are stationary. Our proof treats HiBCD as an optimization framework for a class of multi-block structured optimization problems, and our stationarity claim is applicable not only to CoSMF but also to many other problems. Previous optimization research showed the same stationarity result for inexact block coordinate descent with either FPG or FW updates only. Numerical results indicate that the proposed HiBCD scheme is computationally much more efficient than the state-of-the-art CoSMF schemes in HSR.
Hyperspectral super-resolution (HSR) fuses a low-resolution hyperspectral image (HSI) and a high-resolution multispectral image (MSI) to obtain a high-resolution HSI (HR-HSI). In this paper, we propose a new model, named coupled tensor ring factorization (CTRF), for HSR. The proposed CTRF approach simultaneously learns high spectral resolution core tensor from the HSI and high spatial resolution core tensors from the MSI, and reconstructs the HR-HSI via tensor ring (TR) representation (Figure~ref{fig:framework}). The CTRF model can separately exploit the low-rank property of each class (Section ref{sec:analysis}), which has been never explored in the previous coupled tensor model. Meanwhile, it inherits the simple representation of coupled matrix/CP factorization and flexible low-rank exploration of coupled Tucker factorization. Guided by Theorem~ref{th:1}, we further propose a spectral nuclear norm regularization to explore the global spectral low-rank property. The experiments have demonstrated the advantage of the proposed nuclear norm regularized CTRF (NCTRF) as compared to previous matrix/tensor and deep learning methods.
Channel estimation is crucial for modern WiFi system and becomes more and more challenging with the growth of user throughput in multiple input multiple output configuration. Plenty of literature spends great efforts in improving the estimation accuracy, while the interpolation schemes are overlooked. To deal with this challenge, we exploit the super-resolution image recovery scheme to model the non-linear interpolation mechanisms without pre-assumed channel characteristics in this paper. To make it more practical, we offline generate numerical channel coefficients according to the statistical channel models to train the neural networks, and directly apply them in some practical WiFi prototype systems. As shown in this paper, the proposed super-resolution based channel estimation scheme can outperform the conventional approaches in both LOS and NLOS scenarios, which we believe can significantly change the current channel estimation method in the near future.
Magnetic monopoles have been a subject of study for more than a century since the first ideas by A. Vaschy and P. Curie, circa 1890. In 1974, Y. Nambu proposed a model for magnetic monopoles exploring a parallelism between the broken symmetry Higgs and the superconductivity Ginzburg-Landau theories in order to describe the pions quark-antiquark confinement states. There, Nambu describes an energetic string where its end points behave like two magnetic monopoles with opposite magnetic charges -- quark and antiquark. Consequently, not only the interaction among monopole and antimonopole, mediated by a massive vector boson (Yukawa potential), but also the energetic string (linear potential) contributes to the effective interaction potential. We propose here a monopole-antimonopole non confining attractive interaction of the Nambu-type, and then investigate the formation of bound states, the monopolium. Some necessary conditions for the existence of bound states to be fulfilled by the proposed Nambu-type potential, Kato weakness, Set^o and Bargmann conditions, are verified. In the following, ground state energies are estimated for a variety of monopolium reduced mass, from $10^2$MeV to $10^2$TeV, and Compton interaction lengths, from $10^{-2}$am to $10^{-1}$pm, where discussion about non relativistic and relativistic limits validation is carried out.
An eternally inflating universe produces an infinite amount of spatial volume, so every possible event happens an infinite number of times, and it is impossible to define probabilities in terms of frequencies. This problem is usually addressed by means of a measure, which regulates the infinities and produces meaningful predictions. I argue that any measure should obey certain general axioms, but then give a simple toy model in which one can prove that no measure obeying the axioms exists. In certain cases of eternal inflation there are measures that obey the axioms, but all such measures appear to be unacceptable for other reasons. Thus the problem of defining sensible probabilities in eternal inflation seems not be solved.
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