# Improvements of Computational Ghost Imaging by Using Sequenced Speckle
## 1 Introduction  
Ghost imaging (GI) is a nonlocal technique that retrieves object information by correlating two beams. One beam interacts with the object and is detected by a single-pixel detector, while the other beam, which never interacts with the object, is recorded by a spatially-resolved array detector, such as a CCD camera. The pioneering GI experiments utilized quantum-entangled photons generated through spontaneous parametric down-conversion and reconstructed object images through spatial quantum correlations after point-by-point scanning [1]. Subsequently, GI has been demonstrated with thermal [2; 3; 4; 5] and pseudo-thermal light based on random patterns [6; 7], allowing for the exploration of GI in the classical domain with intensity correlations. While quantum GI generally exhibits superior image quality, its application is limited by the available wavelength range [8; 9; 10]. In contrast, GI based on fluctuating intensity speckle patterns offers greater flexibility in terms of wavelength, even extending to the X-ray regime [11; 12; 13], making it a widely studied and globally recognized method. Speckle patterns typically refer to the intensity distribution resulting from the mutual interference of a set of beams with random wavefronts. Pseudo-thermal GI (PGI) employs scattering of a coherent laser beam by a rotating ground glass diffuser to generate the speckle patterns [14]. On the other hand, computational GI (CGI) replaces the pseudo-thermal source with a deterministic illuminator. The illuminating light beam ismodified using a computer-controlled spatial light modulator (SLM) or digital micromirror device (DMD) [15] before interacting with the object. By predefining speckle patterns with the modulator, GI can be simplified using only a single beam and a single-pixel detector. Recently, speckle fields have been extensively utilized in the study and application of GI, employing both PGI and CGI approaches [16; 17; 18; 19]. Numerous advanced GI schemes with well-designed patterns have been proposed, including phase-shifting sinusoidal patterns [20], Walsh-Hadamard patterns [21], and Gram-Schmidt-processed orthonormal patterns [22]. To further enhance image quality, optimization techniques such as \"Russian Dolls ordering\" [23], \"Zigzag scanning ordering\" [24], \"Cake-cutting strategy\" [25], \"Origami Pattern\" [26], and \"Total variation ascending order\" [27] have been developed to optimize speckle pattern selection and sequence, particularly for Hadamard transform patterns. These strategies offer advantages such as reduced ghost image reconstruction time and improved image quality with less iteration. While it has been demonstrated that well-designed speckle patterns in DMD or SLM-based CGI can enhance image quality and reduce reconstruction time, this approach relies heavily on expensive electronics and beam-shaping devices. Moreover, the limitations of the SLM or DMD, such as the working wavelength and damage threshold, pose constraints on extending the wavelength range or long-distance sensing in PGI. Additionally, commonly used digital devices introduce quantization errors that result in unnecessary noise. Therefore, classical random speckle patterns generated using a rotating ground glass plate hold great potential for practical applications. Investigating the effect of these classical random speckle patterns on ghost image quality is crucial. Several properties of this scheme have been studied in theory and experimentally, including speckle size modulation [14; 16; 17; 18], Schmidt GI [22], GI via sparsity constraint [28], pseudo-inverse GI [29], Bayesian denoising methods [30], and pink noise speckle patterns [31]. These methods have been shown to significantly improve reconstruction efficiency and image quality; however, they often involve complex and time-consuming manipulations of Hadamard matrices compared to random speckles and are limited to CGI. In this work, we propose a method to modulate speckle size and step sequences to enhance image quality.