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.

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

The paper presents a deep learning-aided iterative detection algorithm for massive overloaded multiple-input multiple-output (MIMO) systems where the number of transmit antennas $n(\gg 1)$ 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 as the trainable projected gradient-detector (TPG-detector). The trainable internal parameters like step size parameters can be optimized with standard deep learning techniques such as back propagation and stochastic gradient descent algorithms. This approach referred to as data-driven tuning brings notable advantages of the proposed scheme such as fast convergence. The main iterative process of the TPG-detector consists of matrix-vector product operations that require $O(m n)$-time for each iterative step. In addition, the number of trainable parameters in the TPG-detector is independent of the number of antennas $n$ and $m$. These features of the TPG-detector lead to its fast and stable training process and reasonable scalability to large systems. The numerical simulations show that the proposed detector achieves comparable detection performance to those of the known algorithms for massive overloaded MIMO channels, e.g., the state-of-the-art IW-SOAV detector, with lower computation cost.