  The usually reported pixel resolution of single pixel imaging (SPI) varies
between $32 \times 32$ and $256 \times 256$ pixels falling far below imaging
standards with classical methods. Low resolution results from the trade-off
between the acceptable compression ratio, the limited DMD modulation frequency,
and reasonable reconstruction time, and has not improved significantly during
the decade of intensive research on SPI. In this paper we show that image
measurement at the full resolution of the DMD, which lasts only a fraction of a
second, is possible for sparse images or in a situation when the field of view
is limited but is a priori unknown. We propose the sampling and reconstruction
strategies that enable us to reconstruct sparse images at the resolution of
$1024 \times 768$ within the time of $0.3~$s. Non-sparse images are
reconstructed with less details. The compression ratio is on the order of $0.4
\%$ which corresponds to an acquisition frequency of $7~$Hz. Sampling is
differential, binary, and non-adaptive, and includes information on multiple
partitioning of the image which later allows us to determine the actual field
of view. Reconstruction is based on the differential Fourier domain regularized
inversion (D-FDRI). The proposed SPI framework is an alternative to both
adaptive SPI, which is challenging to implement in real time, and to classical
compressive sensing image recovery methods, which are very slow at high
resolutions.
