  Single-pixel imaging (SPI) is a novel technique capturing 2D images using a
photodiode, instead of conventional 2D array sensors. SPI owns high
signal-to-noise ratio, wide spectrum range, low cost, and robustness to light
scattering. Various algorithms have been proposed for SPI reconstruction,
including the linear correlation methods, the alternating projection method
(AP), and the compressive sensing based methods. However, there has been no
comprehensive review discussing respective advantages, which is important for
SPI's further applications and development. In this paper, we reviewed and
compared these algorithms in a unified reconstruction framework. Besides, we
proposed two other SPI algorithms including a conjugate gradient descent based
method (CGD) and a Poisson maximum likelihood based method. Both simulations
and experiments validate the following conclusions: to obtain comparable
reconstruction accuracy, the compressive sensing based total variation
regularization method (TV) requires the least measurements and consumes the
least running time for small-scale reconstruction; the CGD and AP methods run
fastest in large-scale cases; the TV and AP methods are the most robust to
measurement noise. In a word, there are trade-offs between capture efficiency,
computational complexity and robustness to noise among different SPI
algorithms. We have released our source code for non-commercial use.
