Shunsuke Ono

Saori Takeyama, Shunsuke Ono

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.

Eisuke Yamagata, Shunsuke Ono

Sparse index tracking is a prominent passive portfolio management strategy that constructs a sparse portfolio to track a financial index. A sparse portfolio is preferable to a full portfolio in terms of reducing transaction costs and avoiding illiquid assets. To achieve portfolio sparsity, conventional studies have utilized $\ell_p$-norm regularizations as a continuous surrogate of the $\ell_0$-norm regularization. Although these formulations can construct sparse portfolios, their practical application is challenging due to the intricate and time-consuming process of tuning parameters to define the precise upper limit of assets in the portfolio. 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. Moreover, our approach offers a choice between constraints on portfolio and turnover sparsity, further reducing transaction costs by limiting asset updates at each rebalancing interval. 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 Russell3000 index datasets.

Yuki Nakamura, Shingo Takemoto, Shunsuke Ono

We propose Comprehensive Robust Dynamic Mode Decomposition (CR-DMD), a novel framework that robustifies the entire DMD process - from mode extraction to dimensional reduction - against mixed noise. Although standard DMD widely used for uncovering spatio-temporal patterns and constructing low-dimensional models of dynamical systems, it suffers from significant performance degradation under noise due to its reliance on least-squares estimation for computing the linear time evolution operator. Existing robust variants typically modify the least-squares formulation, but they remain unstable and fail to ensure faithful low-dimensional representations. First, we introduce a convex optimization-based preprocessing method designed to effectively remove mixed noise, achieving accurate and stable mode extraction. Second, we propose a new convex formulation for dimensional reduction that explicitly links the robustly extracted modes to the original noisy observations, constructing a faithful representation of the original data via a sparse weighted sum of the modes. Both stages are efficiently solved by a preconditioned primal-dual splitting method. Experiments on fluid dynamics datasets demonstrate that CR-DMD consistently outperforms state-of-the-art robust DMD methods in terms of mode accuracy and fidelity of low-dimensional representations under noisy conditions.

Masako Kishida, Shunsuke Ono

This extended abstract introduces a class of graph learning applicable to cases where the underlying graph has polytopic uncertainty, i.e., the graph is not exactly known, but its parameters or properties vary within a known range. By incorporating this assumption that the graph lies in a polytopic set into two established graph learning frameworks, we find that our approach yields better results with less computation.

Keitaro Yamashita, Kazuki Naganuma, Shunsuke Ono

This paper proposes a method for vertex-wise flexible sampling of a broad class of graph signals, designed to attain the best possible recovery based on the generalized sampling theory. This is achieved by designing a sampling operator by an optimization problem, which is inherently non-convex, as the best possible recovery imposes a rank constraint. An existing method for vertex-wise flexible sampling is able to control the number of active vertices but cannot incorporate prior knowledge of mandatory or forbidden vertices. To address these challenges, we formulate the operator design as a problem that handles a constraint of the number of active vertices and prior knowledge on specific vertices for sampling, mandatory inclusion or exclusion. We transformed this constrained problem into a difference-of-convex (DC) optimization problem by using the nuclear norm and a DC penalty for vertex selection. To solve this, we develop a convergent solver based on the general double-proximal gradient DC algorithm. The effectiveness of our method is demonstrated through experiments on various graph signal models, including real-world data, showing superior performance in the recovery accuracy by comparing to existing methods.

Ryosuke Isono, Shunsuke Ono

This paper proposes a novel spatiotemporal (ST) fusion framework for satellite images, named Temporally-Similar Structure-Aware ST fusion (TSSTF). ST fusion is a promising approach to address the trade-off between the spatial and temporal resolution of satellite images. In real-world scenarios, observed satellite images are severely degraded by noise due to measurement equipment and environmental conditions. Consequently, some recent studies have focused on enhancing the robustness of ST fusion methods against noise. However, existing noise-robust ST fusion approaches often fail to capture fine spatial structure, leading to oversmoothing and artifacts. To address this issue, TSSTF introduces two key mechanisms: Temporally-Guided Total Variation (TGTV) and Temporally-Guided Edge Constraint (TGEC). TGTV is a novel regularization function that promotes spatial piecewise smoothness while preserving structural details, guided by a reference high spatial resolution image acquired on a nearby date. TGEC enforces consistency in edge locations between two temporally adjacent images, while allowing for spectral variations. We formulate the ST fusion task as a constrained optimization problem incorporating TGTV and TGEC, and develop an efficient algorithm based on a preconditioned primal-dual splitting method. Experimental results demonstrate that TSSTF performs comparably to state-of-the-art methods under noise-free conditions and outperforms them under noisy conditions. Additionally, we provide a comprehensive set of recommended parameter values that consistently yield high performance across diverse target regions and noise conditions, aiming to enhance reproducibility and practical utility.

Kazuki Naganuma, Shunsuke Ono

This paper proposes a foreground-background separation (FBS) method with a novel foreground model based on convolutional sparse representation (CSR). In order to analyze the dynamic and static components of videos acquired under undesirable conditions, such as hardware, environmental, and power limitations, it is essential to establish an FBS method that can handle videos with low frame rates and various types of noise. Existing FBS methods have two limitations that prevent us from accurately separating foreground and background components from such degraded videos. First, they only capture either data-specific or general features of the components. Second, they do not include explicit models for various types of noise to remove them in the FBS process. To this end, we propose a robust FBS method with a CSR-based foreground model. This model can adaptively capture specific spatial structures scattered in imaging data. Then, we formulate FBS as a constrained multiconvex optimization problem that incorporates CSR, functions that capture general features, and explicit noise characterization functions for multiple types of noise. Thanks to these functions, our method captures both data-specific and general features to accurately separate the components from various types of noise even under low frame rates. To obtain a solution of the optimization problem, we develop an algorithm that alternately solves its two convex subproblems by newly established algorithms. Experiments demonstrate the superiority of our method over existing methods using two types of degraded videos: infrared and microscope videos.

Shingo Takemoto, Kazuki Naganuma, Shunsuke Ono

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.

Keiichiro Shirai, Tatsuya Baba, Shunsuke Ono et al.

This paper proposes an automatic image correction method for portrait photographs, which promotes consistency of facial skin color by suppressing skin color changes due to background colors. In portrait photographs, skin color is often distorted due to the lighting environment (e.g., light reflected from a colored background wall and over-exposure by a camera strobe), and if the photo is artificially combined with another background color, this color change is emphasized, resulting in an unnatural synthesized result. In our framework, after roughly extracting the face region and rectifying the skin color distribution in a color space, we perform color and brightness correction around the face in the original image to achieve a proper color balance of the facial image, which is not affected by luminance and background colors. Unlike conventional algorithms for color correction, our final result is attained by a color correction process with a guide image. In particular, our guided image filtering for the color correction does not require a perfectly-aligned guide image required in the original guide image filtering method proposed by He et al. Experimental results show that our method generates more natural results than conventional methods on not only headshot photographs but also natural scene photographs. We also show automatic yearbook style photo generation as an another application.

Marie Katsurai, Shunsuke Ono

Mapping the knowledge structure from word co-occurrences in a collection of academic papers has been widely used to provide insight into the topic evolution in an arbitrary research field. In a traditional approach, the paper collection is first divided into temporal subsets, and then a co-word network is independently depicted in a 2D map to characterize each period's trend. To effectively map emerging research trends from such a time-series of co-word networks, this paper presents TrendNets, a novel visualization methodology that highlights the rapid changes in edge weights over time. Specifically, we formulated a new convex optimization framework that decomposes the matrix constructed from dynamic co-word networks into a smooth part and a sparse part: the former represents stationary research topics, while the latter corresponds to bursty research topics. Simulation results on synthetic data demonstrated that our matrix decomposition approach achieved the best burst detection performance over four baseline methods. In experiments conducted using papers published in the past 16 years at three conferences in different fields, we showed the effectiveness of TrendNets compared to the traditional co-word representation. We have made our codes available on the Web to encourage scientific mapping in all research fields.

Masaki Onuki, Shunsuke Ono, Keiichiro Shirai et al.

We propose an approximation method for thresholding of singular values using Chebyshev polynomial approximation (CPA). Many signal processing problems require iterative application of singular value decomposition (SVD) for minimizing the rank of a given data matrix with other cost functions and/or constraints, which is called matrix rank minimization. In matrix rank minimization, singular values of a matrix are shrunk by hard-thresholding, soft-thresholding, or weighted soft-thresholding. However, the computational cost of SVD is generally too expensive to handle high dimensional signals such as images; hence, in this case, matrix rank minimization requires enormous computation time. In this paper, we leverage CPA to (approximately) manipulate singular values without computing singular values and vectors. The thresholding of singular values is expressed by a multiplication of certain matrices, which is derived from a characteristic of CPA. The multiplication is also efficiently computed using the sparsity of signals. As a result, the computational cost is significantly reduced. Experimental results suggest the effectiveness of our method through several image processing applications based on matrix rank minimization with nuclear norm relaxation in terms of computation time and approximation precision.

Takuya Ikeda, Masaaki Nagahara, Shunsuke Ono

In this paper, we propose a new design method of discrete-valued control for continuous-time linear time-invariant systems based on sum-of-absolute-values (SOAV) optimization. We first formulate the discrete-valued control design as a finite-horizon SOAV optimal control, which is an extended version of L1 optimal control. We then give simple conditions that guarantee the existence, discreteness, and uniqueness of the SOAV optimal control. Also, we give the continuity property of the value function, by which we prove the stability of infinite-horizon model predictive SOAV control systems. We provide a fast algorithm for the SOAV optimization based on the alternating direction method of multipliers (ADMM), which has an important advantage in real-time control computation. A simulation result shows the effectiveness of the proposed method.