arXiv subjects

Kazuki Naganuma

Publications and source records attributed to Kazuki Naganuma.

10 recordsLinked to original sources

arXiv2026

Generalized Graph Signal Sampling by Difference-of-Convex Optimization

We propose a comprehensive framework for the generalized sampling and recovery of generalized graph signals by leveraging difference-of-convex (DC) optimization. A fundamental challenge in graph signal processing is sampling, especially for graph signals that are not bandlimited. To accurately capture complex real-world phenomena, it is essential to handle beyond bandlimited graph signals, moving past traditional bandlimited assumptions. Consequently, extending the generalized sampling theory to graph signals has been studied, enabling the best possible recovery for a wide range of signals by assuming signal priors. However, achieving the best possible recovery requires handling inherently non-convex and computationally intractable constraints such as full rank constraint. As a result, existing methods have relied on either aggressive convex relaxations that sacrifice accuracy or greedy algorithms that risk falling into poor suboptimal solutions, facing a fundamental dilemma between modeling accuracy and optimization tractability. To overcome this dilemma, we propose a DC optimization-based method for designing an aggregation sampling operator for beyond bandlimited graph signals that comprehensively handles arbitrary signal priors assumed in the generalized sampling theory. Specifically, the intractable full rank constraint is tightly relaxed using the nuclear norm, reformulating the design problem into a DC optimization problem. We developed a solver based on the general double-proximal gradient DC algorithm, which theoretically guarantees convergence to a critical point. Experimental results on synthetic and real-world data demonstrate the superiority of our method in sampling and recovering beyond bandlimited graph signals compared to existing approaches.

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arXiv2025

Sampling Method for Generalized Graph Signals with Pre-selected Vertices via DC Optimization

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.

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arXiv2025

Spatio-Spectral Structure Tensor Total Variation for Hyperspectral Image Denoising and Destriping

This paper proposes a novel regularization method, named Spatio-Spectral Structure Tensor Total Variation (S3TTV), for denoising and destriping of hyperspectral (HS) images. HS images are inevitably contaminated by various types of noise, during acquisition process, due to the measurement equipment and the environment. For HS image denoising and destriping tasks, Spatio-Spectral Total Variation (SSTV) is widely known as a powerful regularization approach that models the spatio-spectral piecewise smoothness. However, since SSTV refers only to the local differences of pixels/bands, edges and textures that extend beyond adjacent pixels are not preserved during denoising process. To address this problem, we newly introduce S3TTV, which is designed to preserve two essential physical characteristics of HS images: semi-local spatial structures and spectral correlation across all bands. Specifically, we define S3TTV as the sum of the nuclear norms of spatio-spectral structure tensors, which are matrices formed by arranging second-order spatio-spectral difference vectors within semi-local areas. Furthermore, we formulate the HS image denoising and destriping problem as a constrained convex optimization problem involving S3TTV and develop an algorithm based on a preconditioned primal-dual splitting method to solve this problem efficiently. Finally, we demonstrate the effectiveness of S3TTV by comparing it with existing methods, including state-of-the-art ones through denoising and destriping experiments.

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arXiv2025

Robust Foreground-Background Separation for Severely-Degraded Videos Using Convolutional Sparse Representation Modeling

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.

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arXiv2024

Robust Time-Varying Graph Signal Recovery for Dynamic Physical Sensor Network Data

We propose a time-varying graph signal recovery method for estimating the true time-varying graph signal from corrupted observations by leveraging dynamic graphs. Most of the conventional methods for time-varying graph signal recovery have been proposed under the assumption that the underlying graph that houses the signals is static. However, in light of rapid advances in sensor technology, the assumption that sensor networks are time-varying like the signals is becoming a very practical problem setting. In this paper, we focus on such cases and formulate dynamic graph signal recovery as a constrained convex optimization problem that simultaneously estimates both time-varying graph signals and sparsely modeled outliers. In our formulation, we use two types of regularizations, time-varying graph Laplacian-based and temporal differencebased, and also separately modeled missing values with known positions and unknown outliers to achieve robust estimations from highly degraded data. In addition, an algorithm is developed to efficiently solve the optimization problem based on a primaldual splitting method. Extensive experiments on simulated drone remote sensing data and real-world sea surface temperature data demonstrate the advantages of the proposed method over existing methods.

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arXiv2024

Towards Robust Hyperspectral Unmixing: Mixed Noise Modeling and Image-Domain Regularization

Hyperspectral (HS) unmixing is the process of decomposing an HS image into material-specific spectra (endmembers) and their spatial distributions (abundance maps). Existing unmixing methods have two limitations with respect to noise robustness. First, if the input HS image is highly noisy, even if the balance between sparse and piecewise-smooth regularizations for abundance maps is carefully adjusted, noise may remain in the estimated abundance maps or undesirable artifacts may appear. Second, existing methods do not explicitly account for the effects of stripe noise, which is common in HS measurements, in their formulations, resulting in significant degradation of unmixing performance when such noise is present in the input HS image. To overcome these limitations, we propose a new robust hyperspectral unmixing method based on constrained convex optimization. Our method employs, in addition to the two regularizations for the abundance maps, regularizations for the HS image reconstructed by mixing the estimated abundance maps and endmembers. This strategy makes the unmixing process much more robust in highly-noisy scenarios, under the assumption that the abundance maps used to reconstruct the HS image with desirable spatio-spectral structure are also expected to have desirable properties. Furthermore, our method is designed to accommodate a wider variety of noise including stripe noise. To solve the formulated optimization problem, we develop an efficient algorithm based on a preconditioned primal-dual splitting method, which can automatically determine appropriate stepsizes based on the problem structure. Experiments on synthetic and real HS images demonstrate the advantages of our method over existing methods.

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arXiv2024

Robust Spatiotemporal Fusion of Satellite Images: A Constrained Convex Optimization Approach

This paper proposes a novel spatiotemporal (ST) fusion framework for satellite images, named Robust Optimization-based Spatiotemporal Fusion (ROSTF). ST fusion is a promising approach to resolve a trade-off between the temporal and spatial resolution of satellite images. Although many ST fusion methods have been proposed, most of them are not designed to explicitly account for noise in observed images, despite the inevitable influence of noise caused by the measurement equipment and environment. Our ROSTF addresses this challenge by formulating noise removal and ST fusion as a unified optimization problem. Specifically, first, we define observation models for satellite images possibly contaminated with random noise, outliers, and/or missing values, and then introduce certain assumptions that would naturally hold between the observed images and the target high-resolution image. Then, based on these models and assumptions, we formulate the fusion problem as a constrained optimization problem and develop an efficient algorithm based on a preconditioned primal-dual splitting method for solving the problem. The performance of ROSTF was verified using simulated and real data. The results show that ROSTF performs comparably to several state-of-the-art ST fusion methods in noiseless cases and outperforms them in noisy cases.

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arXiv2023

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

This paper proposes a method for designing diagonal preconditioners for a preconditioned primal-dual splitting method (P-PDS), an efficient algorithm that solves nonsmooth convex optimization problems. To speed up the convergence of P-PDS, a design method has been proposed to automatically determine appropriate preconditioners from the problem structure. However, the existing method has two limitations. One is that it directly accesses all elements of matrices representing linear operators involved in a given problem, which is inconvenient for handling linear operators implemented as procedures rather than matrices. The other is that it takes an element-wise preconditioning approach, which turns certain types of proximity operators into analytically intractable forms. To overcome these limitations, we establish an Operator norm-based design method of Variable-wise Diagonal Preconditioning (OVDP). First, OVDP constructs diagonal preconditioners using only (upper bounds) of the operator norms of linear operators, thus eliminating the need for their explicit matrix representations. Furthermore, since OVDP takes a variable-wise preconditioning approach, it keeps any proximity operator analytically computable. We also prove that our preconditioners satisfy the convergence condition of P-PDS. Finally, we demonstrate the effectiveness and usefulness of OVDP through applications to mixed noise removal of hyperspectral images, hyperspectral unmixing, and graph signal recovery.

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arXiv2022

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.

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arXiv2022

A General Destriping Framework for Remote Sensing Images Using Flatness Constraint

Removing stripe noise, i.e., destriping, from remote sensing images is an essential task in terms of visual quality and subsequent processing. Most existing destriping methods are designed by combining a particular image regularization with a stripe noise characterization that cooperates with the regularization, which precludes us to examine and activate different regularizations to adapt to various target images. To resolve this, two requirements need to be considered: a general framework that can handle a variety of image regularizations in destriping, and a strong stripe noise characterization that can consistently capture the nature of stripe noise, regardless of the choice of image regularization. To this end, this paper proposes a general destriping framework using a newly-introduced stripe noise characterization, named flatness constraint, where we can handle various regularization functions in a unified manner. Specifically, we formulate the destriping problem as a nonsmooth convex optimization problem involving a general form of image regularization and the flatness constraint. The constraint mathematically models that the intensity of each stripe is constant along one direction, resulting in a strong characterization of stripe noise. 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 a variety of image regularizations and stripe noise characterizations using hyperspectral images (HSI) and infrared (IR) videos.

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