Apodized Fourier single-pixel imaging by changing the contrast of patterns using Norton-Beer functions

Abstract

Single-pixel imaging (SPI) has attracted a lot of attention in the last two decades, not only for its imaging ability using a low-level or non-visible light but also for imaging through scattering media. As a special method, Fourier SPI (FSI) projects sinusoids on the object and measures Fourier spectrum using a single-pixel detector. As the information of many natural objects is concentrated in lower frequencies in Fourier space, fewer measurements are required for imaging these objects using FSI. However, the sub-sampling of the Fourier space causes ringing artifacts in the retrieved images. In this paper, we propose changing the contrast of different sinusoids based on Norton-Beer (NB) functions and show its ability to reduce ringing artifacts (‘apodized’ FSI). This method is investigated using one- and two-dimensional simulations by implementing NB profiles in low-pass and band-pass modes. In this way, the two modes of apodized imaging and edge enhancement are performed during the measuring process. The feasibility of these modes is experimentally proved for a simple and real object. Furthermore, different ways of using varying-contrast patterns are compared with common post-process apodization. We believe that our study can be interesting for both SPI and image processing communities.