Robust Hyperspectral Image Fusion with Simultaneous Guide Image Denoising via Constrained Convex Optimization

The paper proposes a new high spatial resolution hyperspectral (HR-HS) image estimation method based on convex optimization. The method assumes a low spatial resolution HS (LR-HS) image and a guide image as observations, where both observations are contaminated by noise. Our method simultaneously estimates an HR-HS image and a noiseless guide image, so the method can utilize spatial information in a guide image even if it is contaminated by heavy noise. The proposed estimation problem adopts hybrid spatio-spectral total variation as regularization and evaluates the edge similarity between HR-HS and guide images to effectively use apriori knowledge on an HR-HS image and spatial detail information in a guide image. To efficiently solve the problem, we apply a primal-dual splitting method. Experiments demonstrate the performance of our method and the advantage over several existing methods.Comment: Accepted to IEEE Transactions on Geoscience and Remote Sensin

Sparse Index Tracking: Simultaneous Asset Selection and Capital Allocation via ℓ0\ell_0-Constrained Portfolio

Sparse index tracking is one of the prominent passive portfolio management strategies that construct a sparse portfolio to track a financial index. A sparse portfolio is desirable over a full portfolio in terms of transaction cost reduction and avoiding illiquid assets. To enforce the sparsity of the portfolio, conventional studies have proposed formulations based on $\ell_p$-norm regularizations as a continuous surrogate of the $\ell_0$-norm regularization. Although such formulations can be used to construct sparse portfolios, they are not easy to use in actual investments because parameter tuning to specify the exact upper bound on the number of assets in the portfolio is delicate and time-consuming. In this paper, we propose a new problem formulation of sparse index tracking using an $\ell_0$-norm constraint that enables easy control of the upper bound on the number of assets in the portfolio. In addition, our formulation allows the choice between portfolio sparsity and turnover sparsity constraints, which also reduces transaction costs by limiting the number of assets that are updated at each rebalancing. Furthermore, we develop an efficient algorithm for solving this problem based on a primal-dual splitting method. Finally, we illustrate the effectiveness of the proposed method through experiments on the S\&P500 and NASDAQ100 index datasets.Comment: Submitted to IEEE Open Journal of Signal Processin

A General Destriping Framework for Remote Sensing Images Using Flatness Constraint

This paper proposes a general destriping framework using flatness constraints, where we can handle various regularization functions in a unified manner. Removing stripe noise, i.e., destriping, from remote sensing images is an essential task in terms of visual quality and subsequent processing. Most of the existing methods are designed by combining a particular image regularization with a stripe noise characterization that cooperates with the regularization, which precludes us to examine different regularizations to adapt to various target images. To resolve this, we formulate the destriping problem as a convex optimization problem involving a general form of image regularization and the flatness constraints, a newly introduced stripe noise characterization. This strong characterization enables us to consistently capture the nature of stripe noise, regardless of the choice of image regularization. For solving the optimization problem, we also develop an efficient algorithm based on a diagonally preconditioned primal-dual splitting algorithm (DP-PDS), which can automatically adjust the stepsizes. The effectiveness of our framework is demonstrated through destriping experiments, where we comprehensively compare combinations of image regularizations and stripe noise characterizations using hyperspectral images (HSI) and infrared (IR) videos.Comment: submitted to IEEE Transactions on Geoscience and Remote Sensin

Variable-Wise Diagonal Preconditioning for Primal-Dual Splitting: Design and Applications

This paper proposes a method of designing appropriate diagonal preconditioners for a preconditioned primal-dual splitting method (P-PDS). P-PDS can efficiently solve various types of convex optimization problems arising in signal processing and image processing. Since the appropriate diagonal preconditioners that accelerate the convergence of P-PDS vary greatly depending on the structure of the target optimization problem, a design method of diagonal preconditioners for PPDS has been proposed to determine them automatically from the problem structure. However, the existing method has two limitations: it requires direct access to all elements of the matrices representing the linear operators involved in the target optimization problem, and it is element-wise preconditioning, which makes certain types of proximity operators impossible to compute analytically. To overcome these limitations, we establish an Operator-norm-based design method of Variable-wise Diagonal Preconditioning (OVDP). First, the diagonal preconditioners constructed by OVDP are defined using only the operator norm or its upper bound of the linear operator thus eliminating the need for their explicit matrix representations. Furthermore, since our method is variable-wise preconditioning, it keeps all proximity operators efficiently computable. We also prove that our preconditioners satisfy the convergence conditions of PPDS. Finally, we demonstrate the effectiveness and utility of our method through applications to hyperspectral image mixed noise removal, hyperspectral unmixing, and graph signal recovery.Comment: Submitted to IEEE Transactions on Signal Processin

Graph Spatio-Spectral Total Variation Model for Hyperspectral Image Denoising

The spatio-spectral total variation (SSTV) model has been widely used as an effective regularization of hyperspectral images (HSI) for various applications such as mixed noise removal. However, since SSTV computes local spatial differences uniformly, it is difficult to remove noise while preserving complex spatial structures with fine edges and textures, especially in situations of high noise intensity. To solve this problem, we propose a new TV-type regularization called Graph-SSTV (GSSTV), which generates a graph explicitly reflecting the spatial structure of the target HSI from noisy HSIs and incorporates a weighted spatial difference operator designed based on this graph. Furthermore, we formulate the mixed noise removal problem as a convex optimization problem involving GSSTV and develop an efficient algorithm based on the primal-dual splitting method to solve this problem. Finally, we demonstrate the effectiveness of GSSTV compared with existing HSI regularization models through experiments on mixed noise removal. The source code will be available at https://www.mdi.c.titech.ac.jp/publications/gsstv.Comment: Accepted to IEEE Geoscience and Remote Sensing Letters. The code is available at https://www.mdi.c.titech.ac.jp/publications/gsst