Differential real-time single-pixel imaging with Fourier domain regularization -- applications to VIS-IR imaging and polarization imaging

The speed and quality of single-pixel imaging (SPI) are fundamentally limited by image modulation frequency and by the levels of optical noise and compression noise. In an approach to come close to these limits, we introduce a SPI technique, which is inherently differential, and comprises a novel way of measuring the zeroth spatial frequency of images and makes use of varied thresholding of sampling patterns. With the proposed sampling, the entropy of the detection signal is increased in comparison to standard SPI protocols. Image reconstruction is obtained with a single matrix-vector product so the cost of the reconstruction method scales proportionally with the number of measured samples. A differential operator is included in the reconstruction and following the method is based on finding the generalized inversion of the modified measurement matrix with regularization in the Fourier domain. We demonstrate $256 \times 256$ SPI at up to $17~$Hz at visible and near-infrared wavelength ranges using two polarization or spectral channels. A low bit-resolution data acquisition device with alternating-current-coupling can be used in the measurement indicating that the proposed method combines improved noise robustness with a differential removal of the direct current component of the signal.