Single‐pixel compressive imaging based on motion compensation

Abstract

Compressive sensing (CS) theory enables single-pixel compressive imaging (SPCI) popular in optical remote sensing imaging, since single-pixel imager not only realises the acquisition and recovery of sparse images at the sampling rates significantly below the classical Nyquist rate, but also makes use of special detectors to improve sensitivity, dynamic range, spectral range and so on. However, its requirement of static imaging condition for the time-sequential measurements makes it difficult to apply in remote sensing, since the imaging platform is always in motion relative to the imaging scene. In this study, the authors develop a new method for SPCI on moving platform in optical remote sensing. Instead of ignoring the motion during sampling, the proposed method first builds the compressive sampling model based on motion compensation during sampling, and then reconstructs the image by frame-by-frame recovery method and joint recovery method, respectively, in the framework of CS theory, where the recovery condition is also analysed. To validate the basic principle and the physical feasibility of motion compensation, the authors implement the numerical simulations and optical experiments, where different conditions are exploited sufficiently. In addition, the proposed method for SPCI can be also extended into other applications, such as 360° annular imaging, multi-pixel compressive imaging as well as super-resolution imaging.