Data-driven optimization of modulation matrices for low-sampling-rate single-pixel imaging

Abstract

Single-pixel imaging is a novel optical detection technique based on computational imaging principles. Its core idea is to use a single-pixel detector, which lacks spatial resolution, to acquire high-dimensional scene information through light field modulation and algorithmic reconstruction. However, the fixed arrangement of traditional modulation matrices can introduce redundant features, limiting sampling efficiency and image quality. To address this issue, this paper proposes an optimized modulation matrix—the Convolution Matrix (CM). This matrix replaces the traditional modulation matrix by utilizing its local correlation properties, capturing target information and texture features through convolution, thus reducing redundant information encoding. In addition, a Feature Reconstruction Single-Pixel Imaging Network (FRSPINet) is designed, which integrates an efficient multi-scale attention mechanism. It optimizes high-frequency detail reconstruction by channel-space interactive weight allocation, addressing image degradation issues at low sampling rates. Experimental results show that at a 10 % sampling rate, FRSPINet with the convolution matrix achieves Structural Similarity Index (SSIM) values of 98.1 % and 92.2 % on the MNIST and Fashion MNIST datasets, respectively. On the TFI dataset, the SSIM value is 93.2 %. In practical tests on mini-digits and mini-fashion datasets, the SSIM values between under-sampled and full-sampled reconstructed images are 94.5 % and 87.8 %, respectively. The proposed optimized matrix and image reconstruction network significantly improve image reconstruction quality and provide new insights for research in the field of single-pixel imaging.