arXiv subjects

Ryo Hayakawa

Publications and source records attributed to Ryo Hayakawa.

10 recordsLinked to original sources

arXiv2026

Reconstruction of Piecewise-Constant Sparse Signals for Modulo Sampling

Modulo sampling is a promising technology to preserve amplitude information that exceeds the observable range of analog-to-digital converters during the digitization of analog signals. Since conventional methods typically reconstruct the original signal by estimating the differences of the residual signal and computing their cumulative sum, each estimation error inevitably propagates through subsequent time samples. In this paper, to eliminate this error-propagation problem, we propose an algorithm that reconstructs the residual signal directly. The proposed method takes advantage of the high-frequency characteristics of the modulo samples and the sparsity of both the residual signal and its difference. Simulation results show that the proposed method reconstructs the original signal more accurately than a conventional method based on the differences of the residual signal.

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arXiv2025

Approximate Proximal Operators for Analog Compressed Sensing Using PN-junction Diode

In order to realize analog compressed sensing, the paper considers approximate proximal operators of the $\ell_1$ and minimax concave penalty (MCP) regularization functions. Specifically, we propose to realize the approximate functions by an electric analog circuit using forward voltage-current (V-I) characteristics of the PN-junction diodes. To confirm the validity of the proposed approach, we employ the proposed approximate proximal operators for the $\ell_1$ and MCP regularization functions in compressed sensing with the proximal gradient method. The sparse reconstruction performance of the algorithms using the proposed approximate proximal operators is demonstrated via computer simulations taking into account the impact of additive noise introduced by analog devices.

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arXiv2025

Loss Function Design for Deep Unfolded Sparse Signal Recovery: Supervised and Unsupervised Learning

This paper investigates the impact of loss function design in deep unfolding techniques for sparse signal recovery algorithms. We focus on deep unfolded versions of the fundamental iterative shrinkage thresholding algorithm (ISTA) and the iterative hard thresholding algorithm (IHT). To obtain a guideline for the loss function design, we examine the effect of supervised learning using mean squared error and unsupervised learning using the objective function of the original optimization problem. Our simulation results reveal that the effect of loss function design significantly depends on the convexity of the optimization problem. For convex $\ell_1$-regularized problems, supervised-ISTA achieves better final recovery accuracy but fails to minimize the original objective function, whereas we empirically observe that unsupervised-ISTA converges to a nearly identical solution as conventional ISTA but with accelerated convergence. Conversely, for nonconvex $\ell_0$-regularized problems, both supervised-IHT and unsupervised-IHT converge to better local minima than the original IHT, showing similar performance under the training conditions regardless of the loss function employed. However, when the test conditions differ from the training conditions, our results suggest that unsupervised learning offers better robustness to distribution mismatch. These findings provide valuable insights into the design of effective deep unfolded networks for sparse signal recovery applications.

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arXiv2025

Optimization-Based Image Restoration under Implementation Constraints in Optical Analog Circuits

Optical analog circuits have attracted attention as promising alternatives to traditional electronic circuits for signal processing tasks due to their potential for low-latency and low-power computations. However, implementing iterative algorithms on such circuits presents challenges, particularly due to the difficulty of performing division operations involving dynamically changing variables and the additive noise introduced by optical amplifiers. In this study, we investigate the feasibility of implementing image restoration algorithms using total variation regularization on optical analog circuits. Specifically, we design the circuit structures for the image restoration with widely used alternating direction method of multipliers (ADMM) and primal dual splitting (PDS). Our design avoids division operations involving dynamic variables and incorporate the impact of additive noise introduced by optical amplifiers. Simulation results show that the effective denoising can be achieved in terms of peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) even when the circuit noise at the amplifiers is taken into account.

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arXiv2025

Asymptotics of Proximity Operator for Squared Loss and Performance Prediction of Nonconvex Sparse Signal Recovery

Proximal splitting-based convex optimization is a promising approach to linear inverse problems because we can use some prior knowledge of the unknown variables explicitly. An understanding of the behavior of the optimization algorithms would be important for the tuning of the parameters and the development of new algorithms. In this paper, we first analyze the asymptotic property of the proximity operator for the squared loss function, which appears in the update equations of some proximal splitting methods for linear inverse problems. Our analysis shows that the output of the proximity operator can be characterized with a scalar random variable in the large system limit. Moreover, we apply the asymptotic result to the prediction of optimization algorithms for compressed sensing. Simulation results demonstrate that the MSE performance of the Douglas-Rachford algorithm can be well predicted in compressed sensing with the $\ell_{1}$ optimization. We also examine the behavior of the prediction for the case with nonconvex smoothly clipped absolute deviation (SCAD) and minimax concave penalty (MCP) regularization.

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arXiv2025

Depth-Aided Color Image Inpainting in Quaternion Domain

In this paper, we propose a depth-aided color image inpainting method in the quaternion domain, called depth-aided low-rank quaternion matrix completion (D-LRQMC). In conventional quaternion-based inpainting techniques, the color image is expressed as a quaternion matrix by using the three imaginary parts as the color channels, whereas the real part is set to zero and has no information. Our approach incorporates depth information as the real part of the quaternion representations, leveraging the correlation between color and depth to improve the result of inpainting. In the proposed method, we first restore the observed image with the conventional LRQMC and estimate the depth of the restored result. We then incorporate the estimated depth into the real part of the observed image and perform LRQMC again. Simulation results demonstrate that the proposed D-LRQMC can improve restoration accuracy and visual quality for various images compared to the conventional LRQMC. These results suggest the effectiveness of the depth information for color image processing in quaternion domain.

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arXiv2025

Noise Variance Estimation Using Asymptotic Residual in Compressed Sensing

In compressed sensing, measurements are typically contaminated by additive noise, and therefore, information about the noise variance is often needed to design algorithms. In this paper, we propose a method for estimating the unknown noise variance in compressed sensing problems. The proposed method, called asymptotic residual matching (ARM), estimates the noise variance from a single measurement vector on the basis of the asymptotic result for the $\ell_{1}$ optimization problem. Specifically, we derive the asymptotic residual corresponding to the $\ell_{1}$ optimization and show that it depends on the noise variance. The proposed ARM approach obtains the estimate by comparing the asymptotic residual with the actual one, which can be obtained by empirical reconstruction without the information on the noise variance. For the proposed ARM, we also propose a method to choose a reasonable parameter based on the asymptotic residual. Simulation results show that the proposed noise variance estimation outperforms several conventional methods, especially when the problem size is small. We also show that, by using the proposed method, we can tune the regularization parameter of the $\ell_{1}$ optimization to achieve good reconstruction performance, even when the noise variance is unknown.

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arXiv2025

Deep Unfolding-Aided Parameter Tuning for Plug-and-Play-Based Video Snapshot Compressive Imaging

Snapshot compressive imaging (SCI) captures high-dimensional data efficiently by compressing it into two-dimensional observations and reconstructing high-dimensional data from two-dimensional observations with various algorithms. The plug-and-play (PnP) method is a promising approach for the video SCI reconstruction because it can leverage both observation models and denoising methods for videos. Since the reconstruction accuracy significantly depends on the choice of noise level parameters, this paper proposes a deep unfolding-based method for tuning these parameters in PnP-based video SCI. For the training of the parameters, we prepare training data from the densely annotated video segmentation dataset, reparametrize the noise level parameters, and apply the checkpointing technique to reduce the required memory. Simulation results show that the trained noise level parameters via the proposed approach exhibit a non-monotonic pattern, which is different from the assumptions in the conventional convergence analyses of PnP-based algorithms. These findings provide new insights into both the application of deep unfolding and the theoretical basis of PnP algorithms.

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arXiv2022

Asymptotic Performance Prediction for ADMM-Based Compressed Sensing

In this paper, we propose a method to predict the asymptotic performance of the alternating direction method of multipliers (ADMM) for compressed sensing, where we reconstruct an unknown structured signal from its underdetermined linear measurements. The derivation of the proposed method is based on the recently developed convex Gaussian min-max theorem (CGMT), which can be applied to various convex optimization problems to obtain its asymptotic error performance. Our main idea is to analyze the convex subproblem in the update of ADMM iteratively and characterize the asymptotic distribution of the tentative estimate obtained at each iteration. However, since the original CGMT cannot be used directly for the analysis of the iterative updates, we intuitively assume an extended version of CGMT in the derivation of the proposed method. Under the assumption, the result shows that the update equations in ADMM can be decoupled into a scalar-valued stochastic process in the asymptotic regime with the large system limit. From the asymptotic result, we can predict the evolution of the error (e.g., mean-square-error (MSE) and symbol error rate (SER)) in ADMM for large-scale compressed sensing problems. Simulation results show that the empirical performance of ADMM and its prediction are close to each other in sparse vector reconstruction and binary vector reconstruction.

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arXiv2019

Trainable Projected Gradient Detector for Massive Overloaded MIMO Channels: Data-driven Tuning Approach

This paper presents a deep learning-aided iterative detection algorithm for massive overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas $n$ is larger than that of receive antennas $m$. Since the proposed algorithm is based on the projected gradient descent method with trainable parameters, it is named the trainable projected gradient-detector (TPG-detector). The trainable internal parameters, such as the step-size parameter, can be optimized with standard deep learning techniques, i.e., the back propagation and stochastic gradient descent algorithms. This approach is referred to as data-driven tuning, and ensures fast convergence during parameter estimation in the proposed scheme. The TPG-detector mainly consists of matrix-vector product operations whose computational cost is proportional to $m n$ for each iteration. In addition, the number of trainable parameters in the TPG-detector is independent of the number of antennas. These features of the TPG-detector result in a fast and stable training process and reasonable scalability for large systems. Numerical simulations show that the proposed detector achieves a comparable detection performance to those of existing algorithms for massive overloaded MIMO channels, e.g., the state-of-the-art IW-SOAV detector, with a lower computation cost.

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