Ghost images reconstructed from fractional-order moments with thermal light

We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.

High-quality ghost imaging based on undersampled natural-order Hadamard source

Improving the speed of ghost imaging is one of the main ways to leverage its advantages in sensitivity and imperfect spectral regions for practical applications.Because of the proportional relationship between image resolution and measurement time,when the image pixels are large,the measurement time increases,making it difficult to achieve real-time imaging.Therefore,a high-quality ghost imaging method based on undersampled natural-order Hadamard is proposed.This method uses the characteristics of the Hadamard matrix under undersampling conditions where image information can be fully obtained but overlaps,as well as deep learning to extract aliasing information from the overlapping results to obtain the true original image information.We conducted numerical simulations and experimental tests on binary and grayscale objects under undersampling conditions to demonstrate the effectiveness and scalability of this method.This method can significantly reduce the number of measurements required to obtain high-quality image information and advance application promotion.

High-visibility ghost imaging with phase-controlled discrete classical light sources

We take phase modulation to create discrete phase-controlled sources and realize the super-bunching effect by a phasecorrelated method. From theoretical and numerical simulations, we find the space translation invariance of the bunching effect is a key point for the ghost imaging realization. Experimentally, we create the orderly phase-correlated discrete sources which can realize high-visibility second-order ghost imaging than the result with chaotic sources. Moreover, some factors affecting the visibility of ghost image are discussed in detail.

Computational temporal ghost imaging based on complementary modulation

We report an experimental demonstration of temporal ghost imaging in which a digital micromirror device(DMD)and+1/-1 binary modulation have been combined to give an accurate reconstruction of a nonperiodic time object.Compared to the 0/1 modulation,the reconstruction signal can be improved greatly by+1/-1 binary modulation even with half of the measurements.Experimental results show that 0/1 binary temporal objects up to 4 kHz and sinusoidal time objects up to 1 kHz can be reconstructed by this method.The influences of modulation speed and array detector gray levels are also discussed.

Image Reconstruction of Ghost Imaging Based on Improved Generative Adversarial Networks

In this paper, we improve traditional generative adversarial networks (GAN) with reference to residual networks and convolutional neural networks to facilitate the reconstruction of complex objects that cannot be reconstructed by traditional associative imaging methods. Unlike traditional ghost imaging to reconstruct objects from bucket signals, our proposed method can use simple objects (such as EMNIST) as a training set for GAN, and then recognize objects (such as faces) of completely different complexity than the training set. We use traditional ghost imaging and neural network to reconstruct target objects respectively. According to the research results in this paper, the method based on neural network can reconstruct complex objects very well, but the method based on traditional ghost imaging cannot reconstruct complex objects. The research scheme in this paper is of great significance for the reconstruction of complex object-related imaging under low sampling conditions.

Optimization method of Hadamard coding plate inγ‑ray computational ghost imaging

Owing to the constraints on the fabrication ofγ-ray coding plates with many pixels,few studies have been carried out onγ-ray computational ghost imaging.Thus,the development of coding plates with fewer pixels is essential to achieveγ-ray computational ghost imaging.Based on the regional similarity between Hadamard subcoding plates,this study presents an optimization method to reduce the number of pixels of Hadamard coding plates.First,a moving distance matrix was obtained to describe the regional similarity quantitatively.Second,based on the matrix,we used two ant colony optimization arrangement algorithms to maximize the reuse of pixels in the regional similarity area and obtain new compressed coding plates.With full sampling,these two algorithms improved the pixel utilization of the coding plate,and the compression ratio values were 54.2%and 58.9%,respectively.In addition,three undersampled sequences(the Harr,Russian dolls,and cake-cutting sequences)with different sampling rates were tested and discussed.With different sampling rates,our method reduced the number of pixels of all three sequences,especially for the Russian dolls and cake-cutting sequences.Therefore,our method can reduce the number of pixels,manufacturing cost,and difficulty of the coding plate,which is beneficial for the implementation and application ofγ-ray computational ghost imaging.

Ghost imaging-based optical cryptosystem for multiple images using integral property of the Fourier transform

A novel ghost imaging-based optical cryptosystem for multiple images using the integral property of the Fourier transform is proposed.Different from other multiple-image encryption schemes,we mainly construct the modulation patterns related to the plaintext images to realize the encrypted transmission of multiple images.In encryption process,the first image is encrypted by the ghost imaging encryption scheme,and the intensity sequence obtained by the bucket detector is used as the ciphertext.Then modulation patterns of other images are constructed by using the integral property of the Fourier transform and used as the keys.Finally,the ciphertext and keys are transmitted to the receiver to complete the encryption process.During decryption,the receiver uses different keys to decrypt the ciphertext and gets different plaintext images,and decrypted images have no image aliasing problem.Experiments and simulations verify the feasibility,security,and robustness of the proposed scheme.This scheme has high scalability and broad application prospect,which provides a new idea for optical information encryption.

Optical encryption scheme based on spread spectrum ghost imaging

An optical encryption(OE) scheme based on the spread spectrum ghost imaging(SSGI), named as SSGI-OE, is proposed to obtain a high security with a smaller key. In the scheme, the randomly selected row number of a Hadamard matrix of order N is used as the secure key, and shared with the authorized user, Bob, through a private channel. Each corresponding row vector of the order-N Hadamard matrix is then used as the direct sequence code to modulate a speckle pattern for the ghost imaging system, and an image is encrypted with the help of the SSGI. The measurement results from the bucket detector, named as ciphertext, are then transmitted to Bob through a public channel. The illuminating speckle patterns are also shared with Bob by the public channel. With the correct secure key, Bob could reconstruct the image with the aid of the SSGI system, whereas the unauthorized user, Eve, could not obtain any useful information of the encrypted image. The numerical simulations and experimental results show that the proposed scheme is feasible with a higher security and a smaller key. For the 32 × 32 pixels image, the number of bits sent from Alice to Bob by using SSGIOE(M = 1024, N = 2048) scheme is only 0.0107 times over a computational ghost imaging optical encryption scheme.When the eavesdropping ratio(ER) is less than 40%, the eavesdropper cannot acquire any information of the encrypted image. The extreme circumstance for the proposed SSGI-OE scheme is also discussed, where the eavesdropper begins to extract the information when ER is up to 15%.

Defogging computational ghost imaging via eliminating photon number fluctuation and a cycle generative adversarial network

Imaging through fluctuating scattering media such as fog is of challenge since it seriously degrades the image quality.We investigate how the image quality of computational ghost imaging is reduced by fluctuating fog and how to obtain a high-quality defogging ghost image. We show theoretically and experimentally that the photon number fluctuations introduced by fluctuating fog is the reason for ghost image degradation. An algorithm is proposed to process the signals collected by the computational ghost imaging device to eliminate photon number fluctuations of different measurement events. Thus, a high-quality defogging ghost image is reconstructed even though fog is evenly distributed on the optical path. A nearly 100% defogging ghost image is obtained by further using a cycle generative adversarial network to process the reconstructed defogging image.

A probability theory for filtered ghost imaging

Based on probability density functions,we present a theoretical model to explain filtered ghost imaging(FGI)we first proposed and experimentally demonstrated in 2017[Opt.Lett.425290(2017)].An analytic expression for the joint intensity probability density functions of filtered random speckle fields is derived according to their probability distributions.Moreover,the normalized second-order intensity correlation functions are calculated for the three cases of low-pass,bandpass and high-pass filterings to study the resolution and visibility in the FGI system.Numerical simulations show that the resolution and visibility predicted by our model agree well with the experimental results,which also explains why FGI can achieve a super-resolution image and better visibility than traditional ghost imaging.

Principle of subtraction ghost imaging in scattering medium

Scattering medium in light path will cause distortion of the light field,resulting in poor signal-to-noise ratio(SNR)of ghost imaging.The disturbance is usually eliminated by the method of pre-compensation.We deduce the intensity fluctuation correlation function of the ghost imaging with the disturbance of the scattering medium,which proves that the ghost image consists of two correlated results:the image of scattering medium and the target object.The effect of the scattering medium can be eliminated by subtracting the correlated result between the light field after the scattering medium and the reference light from ghost image,which verifies the theoretical results.Our research may provide a new idea of ghost imaging in harsh environment.

Ghost imaging based on the control of light source bandwidth

A scheme to improve the quality in ghost imaging(GI)by controlling the bandwidth of light source(BCGI)is proposed.The theoretical and numerical results show that the reconstruction result with high quality can be obtained by adjusting the bandwidth range of the light source appropriately,and the selection criterion of the bandwidth is analyzed by the power distribution of the imaging target.A proof-of-principle experiment is implemented to verify the theoretical and numerical results.In addition,the BCGI also presents better anti-noise performance when compared with some popular GI methods.

Intensity correlation properties of x-ray beams split with Laue diffraction

Beam splitting is one of the main approaches to achieving x-ray ghost imaging, and the intensity correlation between diffraction beam and transmission beam will directly affect the imaging quality. In this paper, we investigate the intensity correlation between the split x-ray beams by Laue diffraction of stress-free crystal. The analysis based on the dynamical theory of x-ray diffraction indicates that the spatial resolution of diffraction image and transmission image are reduced due to the position shift of the exit beam. In the experimental setup, a stress-free crystal with a thickness of hundredmicrometers-level is used for beam splitting. The crystal is in a non-dispersive configuration equipped with a double-crystal monochromator to ensure that the dimension of the diffraction beam and transmission beam are consistent. A correlation coefficient of 0.92 is achieved experimentally and the high signal-to-noise ratio of the x-ray ghost imaging is anticipated.Results of this paper demonstrate that the developed beam splitter of Laue crystal has the potential in the efficient data acquisition of x-ray ghost imaging.

Lensless ghost imaging through the strongly scattering medium

Lensless ghost imaging has attracted much interest in recent years due to its profound physics and potential applications. In this paper we report studies of the robust properties of the lensless ghost imaging system with a pseudo-thermal light source in a strongly scattering medium. The effects of the positions of the strong medium on the ghost imaging are investigated. In the lensless ghost imaging system, a pseudo-thermal light is split into two correlated beams by a beam splitter. One beam goes to a charge-coupled detector camera, labeled as CCD2. The other beam goes to an object and then is collected in another charge-coupled detector camera, labeled as CCD1, which serves as a bucket detector. When the strong medium, a pane of ground glass disk, is placed between the object and CCD1, the bucket detector, the quality of ghost imaging is barely affected and a good image could still be obtained. The quality of the ghost imaging can also be maintained, even when the ground glass is rotating, which is the strongest scattering medium so far. However, when the strongly scattering medium is present in the optical path from the light source to CCD2 or the object, the lensless ghost imaging system hardly retrieves the image of the object. A theoretical analysis in terms of the second-order correlation function is also provided.

High-order ghost imaging with N-colour thermal light

High-order ghost imaging with thermal light consisting of N different frequencies is investigated. The high-order intensity correlation and intrinsic correlation functions are derived for such N-colour light. It is found that they are similar in form to those for the monochromatic case, thus most of the conclusions we obtained previously for monochromatic Nth-order ghost imaging are still applicable. However, we find that the visibility of the N-colour ghost image depends strongly on the wavelength used to illuminate the object, and increases as this wavelength increases when the test arm is fixed. On the contrary, changes of wavelength in the reference arms do not lead to any change of the visibility.

Handwritten digit recognition based on ghost imaging with deep learning

We present a ghost handwritten digit recognition method for the unknown handwritten digits based on ghost imaging(GI)with deep neural network,where a few detection signals from the bucket detector,generated by the cosine transform speckle,are used as the characteristic information and the input of the designed deep neural network(DNN),and the output of the DNN is the classification.The results show that the proposed scheme has a higher recognition accuracy(as high as 98%for the simulations,and 91%for the experiments)with a smaller sampling ratio(say 12.76%).With the increase of the sampling ratio,the recognition accuracy is enhanced.Compared with the traditional recognition scheme using the same DNN structure,the proposed scheme has slightly better performance with a lower complexity and non-locality property.The proposed scheme provides a promising way for remote sensing.

Resolution and noise in ghost imaging with classical thermal light

The resolution and classical noise in ghost imaging with a classical thermal light are investigated theoretically. For ghost imaging with a Gaussian Schell model source, the dependences of the resolution and noise on the spatial coherence of the source and the aperture in the imaging system are discussed and demonstrated by using numerical simulations. The results show that an incoherent source and a large aperture will lead to a good image quality and small noise.

Correspondence normalized ghost imaging on compressive sensing

Ghost imaging （GI） offers great potential with respect to conventional imaging techniques. It is an open problem in GI systems that a long acquisition time is be required for reconstructing images with good visibility and signal-to-noise ratios （SNRs）. In this paper, we propose a new scheme to get good performance with a shorter construction time. We call it correspondence normalized ghost imaging based on compressive sensing （CCNGI）. In the scheme, we enhance the signal-to-noise performance by normalizing the reference beam intensity to eliminate the noise caused by laser power fluctuations, and reduce the reconstruction time by using both compressive sensing （CS） and time-correspondence imaging （CI） techniques. It is shown that the qualities of the images have been improved and the reconstruction time has been reduced using CCNGI scheme. For the two-grayscale ＂double-slit＂ image, the mean square error （MSE） by GI and the normalized GI （NGI） schemes with the measurement number of 5000 are 0.237 and 0.164, respectively, and that is 0.021 by CCNGI scheme with 2500 measurements. For the eight-grayscale ＂lena＂ object, the peak signal-to-noise rates （PSNRs） are 10.506 and 13.098, respectively using G1 and NGI schemes while the value turns to 16.198 using CCNGI scheme. The results also show that a high-fidelity GI reconstruction has been achieved using only 44% of the number of measurements corresponding to the Nyquist limit for the two-grayscale ＂double-slit＂ object. The qualities of the reconstructed images using CCNGI are almost the same as those from GI via sparsity constraints （GISC） with a shorter reconstruction time.

Efficient implementation of x-ray ghost imaging based on a modified compressive sensing algorithm

Towards efficient implementation of x-ray ghost imaging(XGI),efficient data acquisition and fast image reconstruction together with high image quality are preferred.In view of radiation dose resulted from the incident x-rays,fewer measurements with sufficient signal-to-noise ratio(SNR)are always anticipated.Available methods based on linear and compressive sensing algorithms cannot meet all the requirements simultaneously.In this paper,a method based on a modified compressive sensing algorithm with conjugate gradient descent method(CGDGI)is developed to solve the problems encountered in available XGI methods.Simulation and experiments demonstrate the practicability of CGDGI-based method for the efficient implementation of XGI.The image reconstruction time of sub-second implicates that the proposed method has the potential for real-time XGI.

A FAST CONVERGING SPARSE RECONSTRUCTION ALGORITHM IN GHOST IMAGING

A fast converging sparse reconstruction algorithm in ghost imaging is presented. It utilizes total variation regularization and its formulation is based on the Karush-Kuhn-Tucker (KKT) theorem in the theory of convex optimization. Tests using experimental data show that, compared with the algorithm of Gradient Projection for Sparse Reconstruction (GPSR), the proposed algorithm yields better results with less computation work.