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Register a new userHybrid Inexact BCD for Coupled Structured Matrix Factorization in Hyperspectral Super-Resolution
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Added by
Ruiyuan Wu
Publication date
2019
fields
Electronic Engineering
and research's language is
English
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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.
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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.
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.
Hyperspectral image (HSI) with narrow spectral bands can capture rich spectral information, but it sacrifices its spatial resolution in the process. Many machine-learning-based HSI super-resolution (SR) algorithms have been proposed recently. However, one of the fundamental limitations of these approaches is that they are highly dependent on image and camera settings and can only learn to map an input HSI with one specific setting to an output HSI with another. However, different cameras capture images with different spectral response functions and bands numbers due to the diversity of HSI cameras. Consequently, the existing machine-learning-based approaches fail to learn to super-resolve HSIs for a wide variety of input-output band settings. We propose a single Meta-Learning-Based Super-Resolution (MLSR) model, which can take in HSI images at an arbitrary number of input bands peak wavelengths and generate SR HSIs with an arbitrary number of output bands peak wavelengths. We leverage NTIRE2020 and ICVL datasets to train and validate the performance of the MLSR model. The results show that the single proposed model can successfully generate super-resolved HSI bands at arbitrary input-output band settings. The results are better or at least comparable to baselines that are separately trained on a specific input-output band setting.
This paper investigates the hybrid precoding design for millimeter wave (mmWave) multiple-input multiple-output (MIMO) systems with finite-alphabet inputs. The precoding problem is a joint optimization of analog and digital precoders, and we treat it as a matrix factorization problem with power and constant modulus constraints. Our work presents three main contributions: First, we present a sufficient condition and a necessary condition for hybrid precoding schemes to realize unconstrained optimal precoders exactly when the number of data streams Ns satisfies Ns = minfrank(H);Nrfg, where H represents the channel matrix and Nrf is the number of radio frequency (RF) chains. Second, we show that the coupled power constraint in our matrix factorization problem can be removed without loss of optimality. Third, we propose a Broyden-Fletcher-Goldfarb-Shanno (BFGS)-based algorithm to solve our matrix factorization problem using gradient and Hessian information. Several numerical results are provided to show that our proposed algorithm outperforms existing hybrid precoding algorithms.
Hyperspectral super-resolution (HSR) is a problem that aims to estimate an image of high spectral and spatial resolutions from a pair of co-registered multispectral (MS) and hyperspectral (HS) images, which have coarser spectral and spatial resolutions, respectively. In this paper we pursue a low-rank matrix estimation approach for HSR. We assume that the spectral-spatial matrices associated with the whole image and the local areas of the image have low-rank structures. The local low-rank assumption, in particular, has the aim of providing a more flexible model for accounting for local variation effects due to endmember variability. We formulate the HSR problem as a global-local rank-regularized least-squares problem. By leveraging on the recent advances in non-convex large-scale optimization, namely, the smooth Schatten-p approximation and the accelerated majorization-minimization method, we develop an efficient algorithm for the global-local low-rank problem. Numerical experiments on synthetic, semi-real and real data show that the proposed algorithm outperforms a number of benchmark algorithms in terms of recovery performance.
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