Fourier single-pixel imaging is one of the main single-pixel imaging techniques. To improve the imaging efficiency, some of the recent method typically select the low-frequency and discard the high-frequency information to reduce the number of acquired samples. However, sampling only a small amount of low-frequency components will lead to the loss of object details and will reduce the imaging resolution. At the same time, the ringing effect of the restored image due to frequency truncation is significant. In this paper, a new sparse Fourier single-pixel imaging method is proposed that reduces the number of samples explorations while maintaining increased image quality. The proposed method makes a special use of the characteristics of the Fourier spectrum distribution based on which the power of image information decreases gradually from low to high frequencies in the Fourier space. A variable density random sampling matrix is employed to achieve random sampling with Fourier single-pixel imaging technology, followed by the processing of the sparse Fourier spectra using compressive sensing algorithms to recover the high-quality information of the object. The new algorithm can effectively improve the quality of object restoration comparing with the existing Fourier single-pixel imaging methods which only acquire the low-frequency parts. Additionally, considering that the resolution of the system is diffraction limited, super-resolution imaging can also be achieved. Experimental results demonstrate the mainly correctness but also effectiveness of the proposed method.

中文翻译：

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稀疏傅里叶单像素成像

傅里叶单像素成像是主要的单像素成像技术之一。为了提高成像效率，一些最近的方法通常选择低频并丢弃高频信息以减少获取的样本的数量。但是，仅对少量的低频分量进行采样将导致对象细节的丢失，并会降低成像分辨率。同时，由于频率截断，恢复的图像的振铃效果很明显。本文提出了一种新的稀疏傅里叶单像素成像方法，该方法减少了样本探索的次数，同时又保持了较高的图像质量。所提出的方法特别利用了傅立叶频谱分布的特征，基于该特征，图像信息的功率在傅立叶空间中从低频到高频逐渐减小。采用可变密度随机采样矩阵以通过傅立叶单像素成像技术实现随机采样，然后使用压缩感测算法对稀疏傅立叶光谱进行处理，以恢复物体的高质量信息。与仅获取低频部分的现有傅立叶单像素成像方法相比，该新算法可以有效提高物体的恢复质量。另外，考虑到系统的分辨率受衍射限制，也可以实现超分辨率成像。