  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.
