  One of the most active research fields in single-pixel imaging is the
influence of the sampling basis and its order in the quality of the
reconstructed images. This paper presents two new orders, ascending scale (AS)
and ascending inertia (AI), of the Hadamard basis and test their performance,
using simulation and experimental methods, for low sampling ratios (0.5 to
0.01). These orders were compared with two state-of-the-art orders,
cake-cutting (CC) and total gradient (TG), using TVAL3 as the reconstruction
algorithm and three noise levels. These newly proposed orders have better
reconstructed image quality on the simulation data set (110 images) and
achieved structure similarity index values higher than CC order. The
experimental data set (2 images) showed that the AS and AI orders performed
better with a sampling ratio of 0.5, while for lower sampling ratio the
performance of AS, AI and CC was similar. The TG order performed worst in the
majority of the cases. Finally, the simulation results present clear evidence
that peak signal-to-noise ratio (PSNR) is not a reliable image quality
assessment (IQA) metric to assess image reconstruction quality in the context
of single pixel imaging.
