  In typical single-pixel detection multiplexing, an unknown object is
sequentially illuminated with intensity patterns: the total signal is summed
into a single-pixel detector and is then demultiplexed to retrieve the object.
Because of measurement noise, the retrieved object differs from the ground
truth by some error quantified by the signal-to-noise ratio (SNR). In
situations where the noise only arises from the photon counting process, it has
not been made clear if single-pixel detection multiplexing leads to a better
SNR than simply scanning the object with a focused intensity spot - a modality
known as raster scanning. This study theoretically assesses the SNR associated
with certain types of single-pixel detection multiplexing, and compares it with
raster scanning. In particular, we show that, under photon noise, when the
positive intensity modulation is based on Hadamard or Cosine patterns,
single-pixel detection multiplexing does not systematically improve the SNR as
compared to raster scanning. Instead, it only improves the SNR on object pixels
at least $k$ times brighter than the object mean signal $\bar{x}$, where $k$ is
a constant that depends on the modulation scheme.
