I just read on ArXiv.org that L. Bian and his colleagues made a cool comparison between several ways of performing single-pixel imaging. They have tested the performance on several recovery procedures, some quite familiar but others not so well stablished. I find both Table 1 and Fig. 7 extremely interesting. One sums up really well the different reconstruction approaches that can be used in single-pixel imaging (with or without using Compressive Sensing). The figure points out one thing that experience has told me: every problem you try to solve usually needs an specific solver if you want to get good and fast results (which is extremely important when you start to work with BIG objects, as I plan to write soon here).

Experimental comparison of single-pixel imaging algorithms,

L. Biam et al, last revised 24 Oct 2017, https://arxiv.org/abs/1707.03164

(featured image extracted from Fig.7 of the manuscript)

Abstract:

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.