Uniform-sampling foveated Fourier single-pixel imaging

Inspired by the retina of human eye, foveated imaging is an effective way to achieve high imaging quality and high imaging efficiency. However, with an inherent property of nonuniformity, advantages of foveated imaging cannot be played well due to the confliction with many theories having uniform properties. Thus, an innovative concept "uniform-sampling foveated imaging" is proposed to break the barrier of foveated imaging and uniform imaging. In this work, the concept is used as a uniform-sampling foveated Fourier single-pixel imaging (UFFSI) to achieve high imaging quality and high imaging efficiency of single-pixel imaging (SPI). First, by flexibly using the proposed three kinds of foveated pattern structures of foveated SPI, namely, "circular structure" via log-polar transformation, "rectangular structure" via log-rectilinear transformation and "rotating-rectangle structure" via log-rectilinear-rotation transformation, the total data number is reduced radically by the data redundancy reduction only requiring high resolution (HR) on regions of interest (ROIs). Next, by a nonuniform weight distribution processing based on the innovative concept of "uniform-sampling foveated imaging", nonuniform sampling is transformed into uniform sampling to obtain the same uniform optical power as the uniform HR FSI, thus, sparse spectrum property and fast Fourier transform of FSI are used accurately and directly to obtain high imaging quality with further reduced measurements and fast reconstruction. Experimentally, in a large-scale scene, at an ultralow sampling ratio of 0.78 % referring to uniform HR FSI with 1024 x 768 pixels, by using UFFSI with 89 % reduction of data redundancy, ROI has a significantly better imaging quality with around 3.3times reduction in reconstruction time. We hope this work can provide a breakthrough point for future foveated imaging and real-time SPI in real life.