# Parallel Ghost Imaging with Extra Large Field of View and High Pixel Resolution
## 2 Experimental Methods and Results  
We adopt the ghost imaging model from a classical perspective, so entangled photons are unnecessary. The imaging process of ghost imaging is as follows: the light emitted by the light source is divided into two identical beams in the object arm and the reference arm after passing through the modulator and beam splitter. The sample is placed on the object arm, and a bucket detector without spatial resolution, i.e., a single pixel detector, is used to receive the object arm signal. No object is placed in the reference arm, and the light is directly directed onto the detector with spatial resolution. The object arm has an object but no spatial resolution, and the reference arm has spatial resolution but no object. Neither of them can obtain object information alone, but by correlating the two, object images can be obtained. Based on this, ghost imaging, also known as correlation imaging,is a non-local imaging method that decouples detection from imaging. Ghost imaging is meaningful in the field of X-rays because of its non-local nature. We can transfer the high ionizing radiation dose required for high-resolution and large field of view imaging of objects to the air of the reference arm to bear, thereby achieving low-dose imaging. In this work, we further explore the non-local properties of ghost imaging, decoupling the size of the reference arm detector from the imaging field of view, thus achieving parallel ghost imaging with both extra large FOV and high resolution. The ghost imaging system is a linear system, and the model for collecting data can be expressed as  
\[Ax=b \tag{1}\]  
where \(A\in R^{m\times n}\) is the matrix formed by the speckle patterns, which are vectorized. In the experiment, \(m\) measurements are made, each with a speckle pattern containing \(n\) pixels. \(x\in R^{n\times 1}\) is the target image we seek to reconstruct, also expressed as a vector. \(b\in R^{m\times 1}\) is the sequence of single-pixel signals collected by the bucket detector. All ghost imaging algorithms aim to extract as much information about the object \(x\) as possible from the speckle patterns \(A\) and the bucket signals \(b\). In parallel ghost imaging, each pixel of the position-sensitive detector is treated as a bucket detector, allowing tens of thousands of single-pixel ghost imaging measurements to be performed simultaneously. PGI employs a Total Variation Augmented Lagrangian Alternating Direction Method (TVAL3) based on compressed sensing [27], which is a method for solving the unknown image iteratively from the underdetermined system of linear equations. TVAL3 [28] introduces prior knowledge of the signal to significantly reduce the number of measurements and lower the dose. The natural image prior used in TVAL3 is total variation (TV) regularization, which is based on the statistical sparsity of image gradients in natural images. TVAL3 can be simplified as follows:  
\[Min||c||_{l_{0}}\] \[s.t.Dx=c;\] \[Ax=b \tag{2}\]  
where \(Ax=b\) is the measurement model of ghost imaging, \(D\) is the transformation matrix that converts the object image \(x\) to \(c\), and the \(l_{0}\)-norm computes the number of non-zero elements in \(c\). The goal is to minimize this measure to find a sparse solution. As the \(l_{0}\)-norm is a non-convex function and difficult to solve directly, the \(l_{1}\)-norm is often used as an approximation. TVAL3 requires far fewer measurements than other methods to achieve comparable reconstruction quality, and it converges faster than most linear iterative methods. It is currently one of the most powerful ghost imaging algorithms and has been validated through numerous experiments. We have established an experimental platform at the X-ray imaging and biomedical application beamline BL13 HB [29] of the Shanghai Synchrotron Radiation Facility (SSRF) to implement parallel ghost imaging within the computational ghost imaging framework.