# Single-Pixel Color Imaging Method with a Compressive Sensing Measurement Matrix
## 1 Introduction  
The rapid development of signal processing technology has caused an increase in people's demand for information. Currently, the large amount of information has challenged integrated information storage and effective transmission of information, and caused immense difficulties for traditional signal processing technology to meet practical demands. In 2004, [PERSON] et al. [1; 2; 3; 4] proposed a simultaneous sampling and compressing theory, called compressive sensing (CS). The proposed new theory has enabled scientists to overcome the compression limit of Shannon-Nyquist sampling theorem. Currently, studies on CS theory and its application have dynamically increased, and the theory has been applied and developed in fields, such as remote sensing [5; 6; 7], modern telecommunications [8; 9; 10], pattern recognition [11], and magnetic resonance imaging [12; 13; 14]. CS has attracted the attention of many scholars and organizations and has been ranked in the top 10 scientific and technological developments in 2017. For example, [PERSON] [15] proposed a network node deployment method using CS. It is applicable to large real-world and unknown networks in which the global approaches are usually unrealizable. But the recovery probabilities for the constructed measurement matrices is not high. [PERSON] et al. [16] proposed a super-resolution method for remote sensing images in the CS framework. The method has a good super-resolution quality and efficiency. But the optimization method can be improved to achieve better image quality. [PERSON] et al. [17] proposed a grid cell firing field detection method using CS. The aim of this study is to present a methodology for unraveling the complete firing field of a grid cell even when it is poorly represented by the recorded spikes. But further experimentation is still needed towards the improvement of sampling process. [PERSON] et al. [18] proposed an image encryption method on CS. But the processingspeed intend to be improved and make the method more proper for real-time encryption fields. Well-known companies, such as Intel, Bell Labs, and Google also applied CS theory in various fields. The single-pixel camera [19; 20] developed by Rice University in the US, is the impressive achievement of CS theory. The system has verified the practical significance of CS theory, and established a new set of imaging systems. Compared with the characteristics of traditional cameras, those of the single-pixel imaging system specifically possess favorable natural conditions. For example, the sampling information required by the single-pixel camera is less than that of traditional imaging equipment, which enables immense development potential in fields such as wireless sensor networks [21], intelligent monitoring, and military affairs. The capability of a single-pixel camera to capture pictures by using a single sensor enables it with immense development space in imaging equipment that require remarkable sensor capability, such as infrared imaging [22] and terahertz imaging [23] equipment, thereby reducing the cost and avoiding the sensor development limitation in the development of imaging techniques. Currently, the single-pixel camera cannot be utilized in practical applications due to its technological limitations. Specifically, the image restoration effect of the single-pixel camera is less efficient than that of traditional cameras because the performance of measurement matrix immensely restrains the restoration effect of the camera. Moreover, the present single-pixel imaging equipment is incapable of collecting and acquiring color information. This condition imposes substantial limitations on the application fields of single-pixel imaging equipment. This study proposes a pseudo-random circulant structure on the basis of Toeplitz matrix, and introduces a method of pseudo-random circulant measurement matrix design based on chaotic sequence. The designed deterministic measurement matrix is applicable for the single-pixel camera, and has better measurement and restoration effects.