arXiv subjects

Shunsuke Ono

Publications and source records attributed to Shunsuke Ono.

34 records · Page 2Linked to original sources

arXiv2022

Data-Driven Sensor Selection Method Based on Proximal Optimization for High-Dimensional Data With Correlated Measurement Noise

The present paper proposes a data-driven sensor selection method for a high-dimensional nondynamical system with strongly correlated measurement noise. The proposed method is based on proximal optimization and determines sensor locations by minimizing the trace of the inverse of the Fisher information matrix under a block-sparsity hard constraint. The proposed method can avoid the difficulty of sensor selection with strongly correlated measurement noise, in which the possible sensor locations must be known in advance for calculating the precision matrix for selecting sensor locations. The problem can be efficiently solved by the alternating direction method of multipliers, and the computational complexity of the proposed method is proportional to the number of potential sensor locations when it is used in combination with a low-rank expression of the measurement noise model. The advantage of the proposed method over existing sensor selection methods is demonstrated through experiments using artificial and real datasets.

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arXiv2022

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.

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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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arXiv2021

Epigraphical Relaxation for Minimizing Layered Mixed Norms

This paper proposes an epigraphical relaxation (ERx) technique for non-proximable mixed norm minimization. Mixed norm regularization methods play a central role in signal reconstruction and processing, where their optimization relies on the fact that the proximity operators of the mixed norms can be computed efficiently. To bring out the power of regularization, sophisticated layered modeling of mixed norms that can capture inherent signal structure is a key ingredient, but the proximity operator of such a mixed norm is often unavailable (non-proximable). Our ERx decouples a layered non-proximable mixed norm into a norm and multiple epigraphical constraints. This enables us to handle a wide range of non-proximable mixed norms in optimization, as long as both the proximal operator of the outermost norm and the projection onto each epigraphical constraint are efficiently computable. Moreover, under mild conditions, we prove that ERx does not change the minimizer of the original problem despite relaxing equality constraints into inequality ones. We also develop new regularizers based on ERx: one is decorrelated structure-tensor total variation for color image restoration, and the other is amplitude-spectrum nuclear norm for low-rank amplitude recovery. We examine the power of these regularizers through experiments, which illustrates the utility of ERx.

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arXiv2021

Guided Facial Skin Color Correction

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.

cs.GR↗

arXiv2021

Randomized Subspace Newton Convex Method Applied to Data-Driven Sensor Selection Problem

The randomized subspace Newton convex methods for the sensor selection problem are proposed. The randomized subspace Newton algorithm is straightforwardly applied to the convex formulation, and the customized method in which the part of the update variables are selected to be the present best sensor candidates is also considered. In the converged solution, almost the same results are obtained by original and randomized-subspace-Newton convex methods. As expected, the randomized-subspace-Newton methods require more computational steps while they reduce the total amount of the computational time because the computational time for one step is significantly reduced by the cubic of the ratio of numbers of randomly updating variables to all the variables. The customized method shows superior performance to the straightforward implementation in terms of the quality of sensors and the computational time.

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arXiv2020

Data-driven sparse sensor placement based on A-optimal design of experiment with ADMM

The present study proposes a sensor selection method based on the proximal splitting algorithm and the A-optimal design of experiment using the alternating direction method of multipliers (ADMM) algorithm. The performance of the proposed method was evaluated with a random sensor problem and compared with the previously proposed methods such as the greedy method and the convex relaxation. The performance of the proposed method is better than an existing method in terms of the A-optimality criterion. In addition, the proposed method requires longer computational time than the greedy method but it is quite shorter than the convex relaxation in large-scale problems. The proposed method was applied to the data-driven sparse-sensor-selection problem. A data set adopted is the NOAA OISST V2 mean sea surface temperature set. At the number of sensors larger than that of the latent state variables, the proposed method showed similar and better performances compared with previously proposed methods in terms of the A-optimality criterion and reconstruction error.

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arXiv2020

A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problem, which consists of a regularization term(s) and a data-fidelity term(s). The methods have to handle a regularization term(s) and a data-fidelity term(s) simultaneously in one objective function, and so we need to carefully control the hyperparameter(s) that balances these terms. However, the setting of such hyperparameters is often a troublesome task because their suitable values depend strongly on the regularization terms adopted and the noise intensities on a given observation. Our proposed method is formulated as a convex optimization problem, where we utilize a novel hybrid regularization technique named Hybrid Spatio-Spectral Total Variation (HSSTV) and incorporate data-fidelity as hard constraints. HSSTV has a strong ability of noise and artifact removal while avoiding oversmoothing and spectral distortion, without combining other regularizations such as low-rank modeling-based ones. In addition, the constraint-type data-fidelity enables us to translate the hyperparameters that balance between regularization and data-fidelity to the upper bounds of the degree of data-fidelity that can be set in a much easier manner. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem. Through comprehensive experiments, we illustrate the advantages of the proposed method over various HS image restoration methods including state-of-the-art ones.

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arXiv2020

On The Synergy Between Nonconvex Extensions of The Tensor Nuclear Norm for Tensor Recovery

Low-rank tensor recovery has attracted much attention among various tensor recovery approaches. A tensor rank has several definitions, unlike the matrix rank--e.g. the CP rank and the Tucker rank. Many low-rank tensor recovery methods are focused on the Tucker rank. Since the Tucker rank is nonconvex and discontinuous, many relaxations of the Tucker rank have been proposed, e.g., the tensor nuclear norm, weighted tensor nuclear norm, and weighted tensor Schatten-$p$ norm. In particular, the weighted tensor Schatten-p norm has two parameters, the weight and $p$, and the tensor nuclear norm and weighted tensor nuclear norm are special cases of these parameters. However, there has been no detailed discussion of whether the effects of the weighting and $p$ are synergistic. In this paper, we propose a novel low-rank tensor completion model using the weighted tensor Schatten-$p$ norm to reveal the relationships between the weight and $p$. To clarify whether complex methods such as the weighted tensor Schatten-$p$ norm are necessary, we compare them with a simple method using rank-constrained minimization. It was found that the simple methods did not outperform the complex methods unless the rank of the original tensor could be accurately known. If we can obtain the ideal weight, $p = 1$ is sufficient, although it is necessary to set $p<1$ when using the weights obtained from observations. These results are consistent with existing reports.

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arXiv2019

TrendNets: Mapping Emerging Research Trends From Dynamic Co-Word Networks via Sparse Representation

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.

cs.DL↗

arXiv2019

Convolutional-Sparse-Coded Dynamic Mode Decomposition and Its Application to River State Estimation

This work proposes convolutional-sparse-coded dynamic mode decomposition (CSC-DMD) by unifying extended dynamic mode decomposition (EDMD) and convolutional sparse coding. EDMD is a data driven analysis method for describing a nonlinear dynamical system with a linear time-evolution equation. Compared with existing EDMD methods, CSC-DMD has an advantage of reflecting spatial structure of the target. As an example, the proposed method is applied to river bed shape estimation from the water surface observation. The estimation problem is reduced to sparsity-aware restoration with a hard constraint, which is given by the CSC-DMD prediction, where the algorithm is derived by the primal-dual splitting method. A time series set of water surface and bed shape measured through an experimental river setup is used to train and test the system. From the result, the significance of the proposed method is verified.

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arXiv2019

Efficient Constrained Signal Reconstruction by Randomized Epigraphical Projection

This paper proposes a randomized optimization framework for constrained signal reconstruction, where the word "constrained" implies that data-fidelity is imposed as a hard constraint instead of adding a data-fidelity term to an objective function to be minimized. Such formulation facilitates the selection of regularization terms and hyperparameters, but due to the non-separability of the data-fidelity constraint, it does not suit block-coordinate-wise randomization as is. To resolve this, we give another expression of the data-fidelity constraint via epigraphs, which enables to design a randomized solver based on a stochastic proximal algorithm with randomized epigraphical projection. Our method is very efficient especially when the problem involves non-structured large matrices. We apply our method to CT image reconstruction, where the advantage of our method over the deterministic counterpart is demonstrated.

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arXiv2017

Efficient Constrained Tensor Factorization by Alternating Optimization with Primal-Dual Splitting

Tensor factorization with hard and/or soft constraints has played an important role in signal processing and data analysis. However, existing algorithms for constrained tensor factorization have two drawbacks: (i) they require matrix-inversion; and (ii) they cannot (or at least is very difficult to) handle structured regularizations. We propose a new tensor factorization algorithm that circumvents these drawbacks. The proposed method is built upon alternating optimization, and each subproblem is solved by a primal-dual splitting algorithm, yielding an efficient and flexible algorithmic framework to constrained tensor factorization. The advantages of the proposed method over a state-of-the-art constrained tensor factorization algorithm, called AO-ADMM, are demonstrated on regularized nonnegative tensor factorization.

math.NA↗

arXiv2017

Fast Singular Value Shrinkage with Chebyshev Polynomial Approximation Based on Signal Sparsity

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.

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arXiv2015

Discrete-Valued Control by Sum-of-Absolute-Values Optimization

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.

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