The commonly used ghost imaging technique can be used to obtain the reflectivity of a reflective object, but leaves the phase distribution of the reflection coefficient not retrieved. To reconstruct the phase of a reflective object, we propose a kind of generalized reflective ghost diffraction (GD) scheme, in which the reference screens are inserted into the reference path of the standard reflective GD setup. With the help of the three-step phase-shifting method, we provide an algorithm to reconstruct the phase distribution of the reflective object. The applicability of this theoretical proposal is demonstrated via numerical simulations. The effects of the transverse coherence of the Gaussian Schell-model source on the phase reconstruction are also discussed.

To solve the problem of poor quality in ghost imaging via sparsity constraints (GISC) multispectral image reconstruction with correlation operations and compressed sensing algorithms under low sampling rate detection conditions, we propose an end-to-end deep-learning-based method. Based on the U-Net, Res2Net-SE-Conv is employed instead of convolutional blocks to extract local and global image features at a more fine-grained level while adaptively adjusting the channel feature response. The two-dimensional contextual transformer is constructed to fully use contextual correlation information to enhance the effectiveness of feature representations. We employ the two-dimensional contextual transformer in the decoder part, dubbed CoT-Unet, to reconstruct the desired 3D cube. The results show that compared with U-Net, TSA-Net based on spatial-spectral self-attention, the PSNR of reconstructed images by the CoT-Unet is improved by 5 dB and 3 dB, respectively, SSIM is improved by 0.23 and 0.07, and SAM is decreased by 0.06 and 0.58. Compared with conventional algorithms such as DGI and CS, our method significantly improves the quality of reconstructed images. Furthermore, the comparison results at 10%, 20%, and 30% sampling rates show that our approach has the best quality in reconstructing GISC multispectral images at low sampling rates.

Current ghost imaging phase reconstruction schemes require either complex optical systems, iterative algorithms, Fourier transform steps, or entangled photon pairs. These factors may increase the difficulty of system design, lead to phase retrieval errors, or result in excessive time consumption. To tackle this challenge, we propose a five-step phase-shifting method that eliminates the need for complex optical systems, Fourier transform steps, entangled photon pairs, or iterative algorithms. Using five specifically designed incoherent sources, we can generate five distinct ghost imaging patterns. Subsequently, the phase information of the object can be calculated from these five speckle patterns. Additionally, we offer a detailed theoretical explanation for choosing the five-step phase-shifting method over the more commonly used three-step or four-step phase-shifting methods. We demonstrate the applicability of this theoretical proposal through numerical simulations involving two types of complicated objects. The results illustrate that the phase information of the complex object can be successfully and quantitatively reconstructed.

The conventional approach to phase reconstruction in Reflective Ghost Imaging (RGI) typically involves the introduction of three reference screens into the reference path, deeming the Fourier transform step indispensable. However, this method introduces complexity to the system and raises concerns regarding potential errors in phase retrieval. In response to these challenges, we advocate for adopting the Five-Step Phase-Shifting (FSPS) method in the RGI system. This method presents two key advantages over traditional approaches: (1) It streamlines the phase reconstruction process by eliminating the requirement for a Fourier inverse transform. (2) It avoids the need to insert objects into the reference optical path, simplifying the computation of reference optical path intensity and enabling seamless application to Computational Ghost Imaging (CGI), overcoming the constraints of Dual-Arm Ghost Imaging (DAGI). We substantiate the theoretical proposition through numerical simulations involving two intricate objects. Furthermore, our discussion delves into exploring the influence of varying reflective angles on the phase reconstruction performance.

The Coded Aperture Snapshot Spectral Compressive Imaging (CASSI) system modulates three-dimensional hyperspectral images into two-dimensional compressed images in a single exposure. Subsequently, three-dimensional hyperspectral images (HSI) can be reconstructed from the two-dimensional compressed measurements using reconstruction algorithms. Among these methods, deep unfolding techniques have demonstrated excellent performance, with RDLUF-MixS^2 achieving the best reconstruction results. However, RDLUF-MixS^2 requires extensive training time, taking approximately 14 days to train RDLUF-MixS^2-9stg on a single RTX 3090 GPU, making it computationally expensive. Furthermore, RDLUF-MixS^2 performs poorly on real data, resulting in significant artifacts in the reconstructed images. In this study, we introduce the Dense-spatial Spectral-attention Transformer (DST) into the Proximal Gradient Descent Unfolding Framework (PGDUF), creating a novel approach called Proximal Gradient Descent Unfolding Dense-spatial Spectral-attention Transformer (PGDUDST). Compared to RDLUF-MixS^2, PGDUDST not only surpasses the network reconstruction performance limit of RDLUF-MixS^2 but also achieves faster convergence. PGDUDST requires only 58% of the training time of RDLUF-MixS^2-9stg to achieve comparable reconstruction results. Additionally, PGDUDST significantly alleviates the artifact issues caused by RDLUF-MixS^2 in real experimental data, demonstrating superior performance and producing clearer reconstructed images.