arXiv subjects

Yuichi Tanaka

Publications and source records attributed to Yuichi Tanaka.

At least 37 records · Page 2Linked to original sources

arXiv2025

PHISWID: Physics-Inspired Underwater Image Dataset Synthesized from RGB-D Images

This paper introduces the physics-inspired synthesized underwater image dataset (PHISWID), a dataset tailored for enhancing underwater image processing through physics-inspired image synthesis. For underwater image enhancement, data-driven approaches (e.g., deep neural networks) typically demand extensive datasets, yet acquiring paired clean atmospheric images and degraded underwater images poses significant challenges. Existing datasets have limited contributions to image enhancement due to lack of physics models, publicity, and ground-truth atmospheric images. PHISWID addresses these issues by offering a set of paired atmospheric and underwater images. Specifically, underwater images are synthetically degraded by color degradation and marine snow artifacts from atmospheric RGB-D images. It is enabled based on a physics-based underwater image observation model. Our synthetic approach generates a large quantity of the pairs, enabling effective training of deep neural networks and objective image quality assessment. Through benchmark experiments with some datasets and image enhancement methods, we validate that our dataset can improve the image enhancement performance. Our dataset, which is publicly available, contributes to the development in underwater image processing.

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arXiv2025

Joint Graph Estimation and Signal Restoration for Robust Federated Learning

We propose a robust aggregation method for model parameters in federated learning (FL) under noisy communications. FL is a distributed machine learning paradigm in which a central server aggregates local model parameters from multiple clients. These parameters are often noisy and/or have missing values during data collection, training, and communication between the clients and server. This may cause a considerable drop in model accuracy. To address this issue, we learn a graph that represents pairwise relationships between model parameters of the clients during aggregation. We realize it with a joint problem of graph learning and signal (i.e., model parameters) restoration. The problem is formulated as a difference-of-convex (DC) optimization, which is efficiently solved via a proximal DC algorithm. Experimental results on MNIST and CIFAR-10 datasets show that the proposed method outperforms existing approaches by up to $2$--$5\%$ in classification accuracy under biased data distributions and noisy conditions.

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arXiv2024

Multiscale Graph Construction Using Non-local Cluster Features

This paper presents a multiscale graph construction method using both graph and signal features. Multiscale graph is a hierarchical representation of the graph, where a node at each level indicates a cluster in a finer resolution. To obtain the hierarchical clusters, existing methods often use graph clustering; however, they may ignore signal variations. As a result, these methods could fail to detect the clusters having similar features on nodes. In this paper, we consider graph and node-wise features simultaneously for multiscale clustering of a graph. With given clusters of the graph, the clusters are merged hierarchically in three steps: 1) Feature vectors in the clusters are extracted. 2) Similarities among cluster features are calculated using optimal transport. 3) A variable $k$-nearest neighbor graph (V$k$NNG) is constructed and graph spectral clustering is applied to the V$k$NNG to obtain clusters at a coarser scale. Additionally, the multiscale graph in this paper has \textit{non-local} characteristics: Nodes with similar features are merged even if they are spatially separated. In experiments on multiscale image and point cloud segmentation, we demonstrate the effectiveness of the proposed method.

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arXiv2024

Dynamic Sensor Placement Based on Sampling Theory for Graph Signals

In this paper, we consider a sensor placement problem where sensors can move within a network over time. Sensor placement problem aims to select K sensor positions from N candidates where K < N. Most existing methods assume that sensor positions are static, i.e., they do not move, however, many mobile sensors like drones, robots, and vehicles can change their positions over time. Moreover, underlying measurement conditions could also be changed, which are difficult to cover with statically placed sensors. We tackle the problem by allowing the sensors to change their positions in their neighbors on the network. We dynamically determine the sensor positions based on graph signal sampling theory such that the non-observed signals on the network can be best recovered from the observations. For signal recovery, the dictionary is learned from a pool of observed signals. It is also used for the sensor position selection. In experiments, we validate the effectiveness of the proposed method via the mean squared error of the reconstructed signals. The proposed dynamic sensor placement outperforms the existing static ones for both synthetic and real data.

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arXiv2024

Time-Varying Graph Signal Estimation among Multiple Sub-Networks

This paper presents an estimation method for time-varying graph signals among multiple sub-networks. In many sensor networks, signals observed are associated with nodes (i.e., sensors), and edges of the network represent the inter-node connectivity. For a large sensor network, measuring signal values at all nodes over time requires huge resources, particularly in terms of energy consumption. To alleviate the issue, we consider a scenario that a sub-network, i.e., cluster, from the whole network is extracted and an intra-cluster analysis is performed based on the statistics in the cluster. The statistics are then utilized to estimate signal values in another cluster. This leads to the requirement for transferring a set of parameters of the sub-network to the others, while the numbers of nodes in the clusters are typically different. In this paper, we propose a cooperative Kalman filter between two sub-networks. The proposed method alternately estimates signals in time between two sub-networks. We formulate a state-space model in the source cluster and transfer it to the target cluster on the basis of optimal transport. In the signal estimation experiments of synthetic and real-world signals, we validate the effectiveness of the proposed method.

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arXiv2024

Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map simply to ones in a similarity-transformed positive graph Laplacian, thus enabling reuse of well-studied spectral filters designed for positive graphs. We propose a fast method to learn a balanced signed graph Laplacian directly from data. Specifically, for each node $i$, to determine its polarity $β_i \in \{-1,1\}$ and edge weights $\{w_{i,j}\}_{j=1}^N$, we extend a sparse inverse covariance formulation based on linear programming (LP) called CLIME, by adding linear constraints to enforce ``consistent" signs of edge weights $\{w_{i,j}\}_{j=1}^N$ with the polarities of connected nodes -- i.e., positive/negative edges connect nodes of same/opposing polarities. For each LP, we adapt projections on convex set (POCS) to determine a suitable CLIME parameter $ρ> 0$ that guarantees LP feasibility. We solve the resulting LP via an off-the-shelf LP solver in $\mathcal{O}(N^{2.055})$. Experiments on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables the use of spectral filters and graph convolutional networks (GCNs) designed for positive graphs on signed graphs.

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arXiv2024

Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer

An image denoiser can be used for a wide range of restoration problems via the Plug-and-Play (PnP) architecture. In this paper, we propose a general framework to build an interpretable graph-based deep denoiser (GDD) by unrolling a solution to a maximum a posteriori (MAP) problem equipped with a graph Laplacian regularizer (GLR) as signal prior. Leveraging a recent theorem showing that any (pseudo-)linear denoiser $\boldsymbol Ψ$, under mild conditions, can be mapped to a solution of a MAP denoising problem regularized using GLR, we first initialize a graph Laplacian matrix $\mathbf L$ via truncated Taylor Series Expansion (TSE) of $\boldsymbol Ψ^{-1}$. Then, we compute the MAP linear system solution by unrolling iterations of the conjugate gradient (CG) algorithm into a sequence of neural layers as a feed-forward network -- one that is amenable to parameter tuning. The resulting GDD network is "graph-interpretable", low in parameter count, and easy to initialize thanks to $\mathbf L$ derived from a known well-performing denoiser $\boldsymbol Ψ$. Experimental results show that GDD achieves competitive image denoising performance compared to competitors, but employing far fewer parameters, and is more robust to covariate shift.

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arXiv2024

Edge Sampling of Graphs: Graph Signal Processing Approach With Edge Smoothness

Finding important edges in a graph is a crucial problem for various research fields, such as network epidemics, signal processing, machine learning, and sensor networks. In this paper, we tackle the problem based on sampling theory on graphs. We convert the original graph to a line graph where its nodes and edges, respectively, represent the original edges and the connections between the edges. We then perform node sampling of the line graph based on the edge smoothness assumption: This process selects the most critical edges in the original graph. We present a general framework of edge sampling based on graph sampling theory and reveal a theoretical relationship between the degree of the original graph and the line graph. We also propose an acceleration method for edge sampling in the proposed framework by using the relationship between two types of Laplacian of the node and edge domains. Experimental results in synthetic and real-world graphs validate the effectiveness of our approach against some alternative edge selection methods.

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arXiv2024

Lossy Compression of Adjacency Matrices by Graph Filter Banks

This paper proposes a compression framework for adjacency matrices of weighted graphs based on graph filter banks. Adjacency matrices are widely used mathematical representations of graphs and are used in various applications in signal processing, machine learning, and data mining. In many problems of interest, these adjacency matrices can be large, so efficient compression methods are crucial. In this paper, we propose a lossy compression of weighted adjacency matrices, where the binary adjacency information is encoded losslessly (so the topological information of the graph is preserved) while the edge weights are compressed lossily. For the edge weight compression, the target graph is converted into a line graph, whose nodes correspond to the edges of the original graph, and where the original edge weights are regarded as a graph signal on the line graph. We then transform the edge weights on the line graph with a graph filter bank for sparse representation. Experiments on synthetic data validate the effectiveness of the proposed method by comparing it with existing lossy matrix compression methods.

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arXiv2024

Optimizing $k$ in $k$NN Graphs with Graph Learning Perspective

In this paper, we propose a method, based on graph signal processing, to optimize the choice of $k$ in $k$-nearest neighbor graphs ($k$NNGs). $k$NN is one of the most popular approaches and is widely used in machine learning and signal processing. The parameter $k$ represents the number of neighbors that are connected to the target node; however, its appropriate selection is still a challenging problem. Therefore, most $k$NNGs use ad hoc selection methods for $k$. In the proposed method, we assume that a different $k$ can be chosen for each node. We formulate a discrete optimization problem to seek the best $k$ with a constraint on the sum of distances of the connected nodes. The optimal $k$ values are efficiently obtained without solving a complex optimization. Furthermore, we reveal that the proposed method is closely related to existing graph learning methods. In experiments on real datasets, we demonstrate that the $k$NNGs obtained with our method are sparse and can determine an appropriate variable number of edges per node. We validate the effectiveness of the proposed method for point cloud denoising, comparing our denoising performance with achievable graph construction methods that can be scaled to typical point cloud sizes (e.g., thousands of nodes).

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arXiv2024

Marine Snow Removal Benchmarking Dataset

This paper introduces a new benchmarking dataset for marine snow removal of underwater images. Marine snow is one of the main degradation sources of underwater images that are caused by small particles, e.g., organic matter and sand, between the underwater scene and photosensors. We mathematically model two typical types of marine snow from the observations of real underwater images. The modeled artifacts are synthesized with underwater images to construct large-scale pairs of ground truth and degraded images to calculate objective qualities for marine snow removal and to train a deep neural network. We propose two marine snow removal tasks using the dataset and show the first benchmarking results of marine snow removal. The Marine Snow Removal Benchmarking Dataset is publicly available online.

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arXiv2023

Regularity-Constrained Fast Sine Transforms

This letter proposes a fast implementation of the regularity-constrained discrete sine transform (R-DST). The original DST \textit{leaks} the lowest frequency (DC: direct current) components of signals into high frequency (AC: alternating current) subbands. This property is not desired in many applications, particularly image processing, since most of the frequency components in natural images concentrate in DC subband. The characteristic of filter banks whereby they do not leak DC components into the AC subbands is called \textit{regularity}. While an R-DST has been proposed, it has no fast implementation because of the singular value decomposition (SVD) in its internal algorithm. In contrast, the proposed regularity-constrained fast sine transform (R-FST) is obtained by just appending a regularity constraint matrix as a postprocessing of the original DST. When the DST size is $M\times M$ ($M=2^\ell$, $\ell\in\mathbb{N}_{\geq 1}$), the regularity constraint matrix is constructed from only $M/2-1$ rotation matrices with the angles derived from the output of the DST for the constant-valued signal (i.e., the DC signal). Since it does not require SVD, the computation is simpler and faster than the R-DST while keeping all of its beneficial properties. An image processing example shows that the R-FST has fine frequency selectivity with no DC leakage and higher coding gain than the original DST. Also, in the case of $M=8$, the R-FST saved approximately $0.126$ seconds in a 2-D transformation of $512\times 512$ signals compared with the R-DST because of fewer extra operations.

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arXiv2023

Clustering of Time-Varying Graphs Based on Temporal Label Smoothness

We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal processing, machine learning, and data mining. Although most existing studies focus on the clustering of nodes in static graphs, we often encounter time-varying graphs for time-series data, e.g., social networks, brain functional connectivity, and point clouds. In this paper, we formulate a node clustering of time-varying graphs as an optimization problem based on spectral clustering, with a smoothness constraint of the node labels. We solve the problem with a primal-dual splitting algorithm. Experiments on synthetic and real-world time-varying graphs are performed to validate the effectiveness of the proposed approach.

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arXiv2023

Attention-based Graph Convolution Fusing Latent Structures and Multiple Features for Graph Neural Networks

We present an attention-based spatial graph convolution (AGC) for graph neural networks (GNNs). Existing AGCs focus on only using node-wise features and utilizing one type of attention function when calculating attention weights. Instead, we propose two methods to improve the representational power of AGCs by utilizing 1) structural information in a high-dimensional space and 2) multiple attention functions when calculating their weights. The first method computes a local structure representation of a graph in a high-dimensional space. The second method utilizes multiple attention functions simultaneously in one AGC. Both approaches can be combined. We also propose a GNN for the classification of point clouds and that for the prediction of point labels in a point cloud based on the proposed AGC. According to experiments, the proposed GNNs perform better than existing methods. Our codes open at https://github.com/liyang-tuat/SFAGC.

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arXiv2023

Multi-channel Sampling on Graphs and Its Relationship to Graph Filter Banks

In this paper, we consider multi-channel sampling (MCS) for graph signals. We generally encounter full-band graph signals beyond the bandlimited one in many applications, such as piecewise constant/smooth and union of bandlimited graph signals. Full-band graph signals can be represented by a mixture of multiple signals conforming to different generation models. This requires the analysis of graph signals via multiple sampling systems, i.e., MCS, while existing approaches only consider single-channel sampling. We develop a MCS framework based on generalized sampling. We also present a sampling set selection (SSS) method for the proposed MCS so that the graph signal is best recovered. Furthermore, we reveal that existing graph filter banks can be viewed as a special case of the proposed MCS. In signal recovery experiments, the proposed method exhibits the effectiveness of recovery for full-band graph signals.

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arXiv2022

Graph Signal Sampling Under Stochastic Priors

We propose a generalized sampling framework for stochastic graph signals. Stochastic graph signals are characterized by graph wide sense stationarity (GWSS) which is an extension of wide sense stationarity (WSS) for standard time-domain signals. In this paper, graph signals are assumed to satisfy the GWSS conditions and we study their sampling as well as recovery procedures. In generalized sampling, a correction filter is inserted between sampling and reconstruction operators to compensate for non-ideal measurements. We propose a design method for the correction filters to reduce the mean-squared error (MSE) between original and reconstructed graph signals. We derive the correction filters for two cases: The reconstruction filter is arbitrarily chosen or predefined. The proposed framework allows for arbitrary sampling methods, i.e., sampling in the vertex or graph frequency domain. We also show that the graph spectral response of the resulting correction filter parallels that for generalized sampling for WSS signals if sampling is performed in the graph frequency domain. Furthermore, we reveal the theoretical connection between the proposed and existing correction filters. The effectiveness of our approach is validated via experiments by comparing its MSE with existing approaches.

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arXiv2022

Graph Signal Restoration Using Nested Deep Algorithm Unrolling

Graph signal processing is a ubiquitous task in many applications such as sensor, social, transportation and brain networks, point cloud processing, and graph neural networks. Often, graph signals are corrupted in the sensing process, thus requiring restoration. In this paper, we propose two graph signal restoration methods based on deep algorithm unrolling (DAU). First, we present a graph signal denoiser by unrolling iterations of the alternating direction method of multiplier (ADMM). We then suggest a general restoration method for linear degradation by unrolling iterations of Plug-and-Play ADMM (PnP-ADMM). In the second approach, the unrolled ADMM-based denoiser is incorporated as a submodule, leading to a nested DAU structure. The parameters in the proposed denoising/restoration methods are trainable in an end-to-end manner. Our approach is interpretable and keeps the number of parameters small since we only tune graph-independent regularization parameters. We overcome two main challenges in existing graph signal restoration methods: 1) limited performance of convex optimization algorithms due to fixed parameters which are often determined manually. 2) large number of parameters of graph neural networks that result in difficulty of training. Several experiments for graph signal denoising and interpolation are performed on synthetic and real-world data. The proposed methods show performance improvements over several existing techniques in terms of root mean squared error in both tasks.

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arXiv2021

Directional Analytic Discrete Cosine Frames

Block frames called directional analytic discrete cosine frames (DADCFs) are proposed for sparse image representation. In contrast to conventional overlapped frames, the proposed DADCFs require a reduced amount of 1) computational complexity, 2) memory usage, and 3) global memory access. These characteristics are strongly required for current high-resolution image processing. Specifically, we propose two DADCFs based on discrete cosine transform (DCT) and discrete sine transform (DST). The first DADCF is constructed from parallel separable transforms of DCT and DST, where the DST is permuted by row. The second DADCF is also designed based on DCT and DST, while the DST is customized to have no DC leakage property which is a desirable property for image processing. Both DADCFs have rich directional selectivity with slightly different characteristics each other and they can be implemented as non-overlapping block-based transforms, especially they form Parseval block frames with low transform redundancy. We perform experiments to evaluate our DADCFs and compare them with conventional directional block transforms in image recovery.

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