Single pixel imaging at high resolution with sampling based on image maps

Single-pixel imaging (SPI) suffers from the trade-off between the image acquisition speed limited by the modulation frequency of digital micromirror devices (DMD), the acceptable compression ratio of the measured signals and the computational complexity of image reconstruction. For this reason, the usually reported resolution of optical SPI does not exceed $256 \times 256$ pixels, falling far below the standard of classical imaging. We have recently proposed a SPI framework, which shows promising results in capturing images at the full resolution of the DMD, i.e. $1024 \times 768$ pixels, within a fraction of a second. The compression ratio is on the order of 0.4%. Furthermore, for images with a limited field of view (FOV), the quality of the image reconstruction is greatly improved as compared to other SPI protocols. We use uniquely designed non-adaptive, binary sampling patterns, which allow us to both extract the spatial information of the image from a compressive single-pixel measurement and to easily determine empty regions of the image at the same time. To this end, the sampling patterns are derived from multiple complete partitionings of the image area, which are further called image maps. We have previously proposed a single example of image partitioning. In the present paper, we introduce another partitioning which puts a special focus on the central area of the image to further enhance the quality of reconstruction in this region. We use the differential Fourier domain regularized inversion (D-FDRI) to initially reconstruct the images, followed by an iterative algorithm, which determines the FOV and corrects the mean values of pixels in all partitioning regions. The proposed framework allows us to sample and reconstruct images at the resolution of $1024 \times 768$ within the time of 0.3 s.