Single pixel imaging based on semi-continuous wavelet transform

Single pixel imaging is a novel imaging technique, and it becomes a focus of research in recent years due to its advantages such as high lateral resolution and high robustness to noise. Imaging speed is one of the critical shortcomings, which limits the further development and applications of this technique. In this paper, we focus on the issues of imaging efficiency of a single pixel imaging system. We propose semi-continuous wavelet transform (SCWT) protocol and introduce the protocol into the single pixel imaging system. The proposed protocol is something between continuous wavelet transform and discrete wavelet transform, which allows the usage of those smooth (usually non-orthogonal, and they have advantages in representing smooth signals compressively, which can improve the imaging speed of single pixel imaging) wavelets and with limited numbers of measurements. The proposed imaging scheme is studied, and verified by simulations and experiments. Furthermore, a comparison between our proposed scheme and existing imaging schemes are given. According to the results, the proposed SCWT scheme is proved to be effective in reconstructing a image compressively.