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.

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.

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. Plug-and-play (PnP) is a promising approach for the video SCI reconstruction because it can leverage both the observation model and denoising methods for videos. This paper proposes a deep unfolding-based method for tuning noise level parameters in PnP-based video SCI, which significantly affects the reconstruction accuracy. For the training of the parameters, we prepare training data from the densely annotated video segmentation (DAVIS) 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 significantly improve the reconstruction accuracy and exhibit a non-monotonic pattern, which is different from the assumptions in the conventional convergence analyses of PnP-based algorithms.

Error Analysis of Douglas-Rachford Algorithm for Linear Inverse Problems: Asymptotics of Proximity Operator for Squared Loss

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. In this paper, we firstly 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. The analysis shows that the output of the proximity operator can be characterized with a scalar random variable in the large system limit. Moreover, we investigate the asymptotic behavior of the Douglas-Rachford algorithm, which is one of the famous proximal splitting methods. From the asymptotic result, we can predict the evolution of the mean-square-error (MSE) in the algorithm for large-scale linear inverse problems. Simulation results demonstrate that the MSE performance of the Douglas-Rachford algorithm can be well predicted by the analytical result in compressed sensing with the $\ell_{1}$ optimization.