Ghost imaging (GI), as an non-local imaging technique, can retrieve the image of an object by intensity correlation between two correlated beams. In this process, one beam that interacts with the object is collected by a detector without spatial resolution, and this optical path is called the test arm. In the reference arm, the other beam carries no object information and is collected by a multi-pixel detector. GI was confirmed in an experiment for the first time by using entangled photon pairs in 1995 [1]. Subsequently, the thermal source and pseudo-thermal source were also be used to realize GI [2], [3], [4], which broke through the limitation of entangled source and promoted the development of GI. Later, the spatial light modulator (SLM), digital projector and digital micro-mirror device (DMD) were used to produce the preset random light source in computational ghost imaging (CGI) which removed the reference arm [5], [6], [7], [8], [9]. Compared with traditional GI, CGI can be realized with only one single-pixel detector, which greatly simplified the settings of GI.

In recent years, ghost imaging (GI) has paid attention to the practical applications. In this process, the noise cannot be avoided. In fact, regardless of traditional GI or CGI, their imaging quality is largely affected by the noise. To address this issue, many algorithms have been proposed to reduce the negative impact of the noise, such as compressed sensing [10], differential operation [11], pseudo-inverse operation [12], deep learning [13], [14], [15], etc. It is noted that wavelet transform (WT), as a signal processing algorithm, can be used for compression [16] and denoising [17]. Based on the characteristics of WT, some studies used the light source processed by WT to irradiate the object [18], [19] in CGI system, and proved the improvement of the resolution. More recently, some studies have introduced WT into the light source modulation in CGI system, which effectively reduced the sampling times [20], [21], [22]. However, to our knowledge, no clear-cut result about the anti-noise property of GI when WT is considered. In this paper, the anti-noise performance of CGI system using wavelet threshold denoising (WTD) on the preset reference speckle patterns (RWGI) is investigated. In this process, the light source noise and the path noise are considered, and another method implemented as a contrast is to use WTD on the light source (LWGI). The simulation and experimental results show that the RWGI exhibits strong robustness against the light source noise. Comparing RWGI with LWGI, RWGI achieves higher signal to noise ratio (SNR) under the path noise. To explain the reason why RWGI has better anti-noise performance, We take the case of different path noise conditions as an example to consider the changes of the decline rate of the correlation coefficients between the speckle patterns (CCSP) on the object plane. In addition, it is noted that the SNR of CGI with orthogonal modulation is improved compared to that of CGI with random speckle pattern [23], [24]. Therefore, the RWGI with orthogonal modulation is considered, and the simulation results show that our method also improves the SNR of CGI with orthogonal modulation.