Single-pixel imaging of a translational object.

Image-free tracking methods based on single-pixel detectors (SPDs) can track a moving object at a very high frame rate, but they rarely can achieve simultaneous imaging of such an object. In this study, we propose a method for simultaneously obtaining the relative displacements and images of a translational object. Four binary Fourier patterns and two differential Hadamard patterns are used to modulate one frame of the object and then modulated light signals are obtained by SPD. The relative displacements and image of the moving object can be gradually obtained along with the detection. The proposed method does not require any prior knowledge of the object and its motion. The method has been verified by simulations and experiments, achieving a frame rate of 3332 Hz to acquire relative displacements of a translational object at a spatial resolution of 128 × 128 pixels using a 20000-Hz digital micro-mirror device. This proposed method can broaden the application of image-free tracking methods and obtain spatial information about moving objects.

High-quality compressed sensing imaging with limited detector bits using sparse measurements and multiple dithers.

High-flux measurement characteristics of compressed sensing (CS) imaging causes the imaging system prone to be disturbed by quantization. To realize high-quality CS imaging with limited detector bits, an improved imaging method combining sparse measurements and multiple dithers is proposed to reduce the dynamic range of the measured signals and increase that of effective detection. Simulations and experiments show that compared with traditional CS imaging, the proposed system decreases reconstruction errors caused by quantization distortions and may reduce the required number of detector bits to 1. The effects of detector noise and system parameters are discussed to validate the feasibility and performance of this method.

Single-pixel compressive imaging based on the transformation of discrete orthogonal Krawtchouk moments.

A single-pixel compressive imaging technique that uses differential modulation based on the transformation of discrete orthogonal Krawtchouk moments is proposed. In this method, two sets of Krawtchouk basis patterns are used to differentially modulate the light source, then the Krawtchouk moments of the target object are acquired from the light intensities measured by a single-pixel detector. The target image is reconstructed by applying an inverse Krawtchouk moment transform represented in the matrix form. The proposed technique is verified by both computational simulations and laboratory experiments. The results show that this technique can retrieve an image from compressive measurements and the real-time reconstruction. The background noise can be removed by the differential measurement to realize the excellent image quality. Moreover, the proposed technique is especially suitable for the single-pixel imaging application that requires the extraction of the characteristics at the region-of-interest.

Pile-up effect in an infrared single-pixel compressive LiDAR system.

Compressive sensing (CS) has been used in LiDAR systems utilizing one single-photon-counting avalanche diode. We demonstrate an unexpected grayscale inversed image of an object at an unchosen depth, which appears in the reconstruction of the infrared single-pixel LiDAR system due to the pile-up effect. A correction algorithm and the sparse measurement are proposed and experimentally verified to effectively reduce the photon pile-up influence, so that the negative images can be completely removed. The correction methods in this research can improve the accuracy and the flexibility of the single-pixel LiDAR systems employing detectors with a low maximum light count.

A High-Speed Imaging Method Based on Compressive Sensing for Sound Extraction Using a Low-Speed Camera.

This paper reports an efficient method for sound extraction from high-speed light spot videos reconstructed from the coded light spot images captured with a low-speed camera based on compressive sensing, but at the expense of consuming time. The proposed method first gets the high-speed video of the light spot that is illuminated on the vibrating target caused by sound. Then the centroid of the light spot is used to recover the sound. Simulations of the proposed method are carried out and experimental results are demonstrated. The results show that high-speed videos with a frame rate of 2000 Hz can be reconstructed with a low-speed (100 Hz) charge-coupled device (CCD) camera, which is randomly modulated by a digital micro-mirror device (DMD) 20 times during each exposure time. This means a speed improvement of 20 times is achieved. The effects of synchronization between CCD image recording and DMD modulation, the optimal sampling patterns of DMD, and sound vibration amplitudes on the performance of the proposed method are evaluated. Using this compressive camera, speech (counting from one to four in Chinese) was recovered well. This has been confirmed by directly listening to the recovered sound, and the intelligibility value (0⁻1) that evaluated the similarity between them was 0.8185. Although we use this compressive camera for sound detection, we expect it to be useful in applications related to vibration and motion.

Quantum limit of photon-counting imaging based on compressed sensing.

We experimentally demonstrate that the sensitivity of photon-counting imaging can be improved by 2 orders of magnitude with the compressed sensing (CS) theory. The maximum sensitivity of CS imaging under the quantum limit, which is approximately 1 photon in each pixel during one measurement, is quantitatively obtained through theoretical derivation and proved experimentally. The influences of dark noise and shot noise on photon-counting imaging are also studied to confirm the fundamental constrains on the imaging sensitivity of different imaging methods, which can guide the effort for further enhancing the ultra-weak light imaging ability.

Evaluation criterion of thermal light ghost imaging based on the receiver operating characteristic analysis.

The performances of different thermal ghost imaging (GI) algorithms are compared in an experiment of computational GI using a digital micromirror device. Here we present a rather different evaluation criterion named receiver operating characteristic (ROC) analysis that serves as the performance of merit for the quantitative comparison. A ROC curve is created by plotting the true positive rate against the false positive rate at various threshold settings. Both theoretical analysis and experimental results demonstrate that the ROC curve and the area under the curve are better and more intuitive indicators of the performance of the GI, compared with conventional evaluation methods. Additionally, for examining gray-scale objects, the calculation of the volume under the ROC surface is analyzed and serves as a performance metric. Our scheme should attract general interest and open exciting prospects for ROC analysis in thermal GI.

Edge detection based on gradient ghost imaging.

We present an experimental demonstration of edge detection based on ghost imaging (GI) in the gradient domain. Through modification of a random light field, gradient GI (GGI) can directly give the edge of an object without needing the original image. As edges of real objects are usually sparser than the original objects, the signal-to-noise ratio (SNR) of the edge detection result will be dramatically enhanced, especially for large-area, high-transmittance objects. In this study, we experimentally perform one- and two-dimensional edge detection with a double-slit based on GI and GGI. The use of GGI improves the SNR significantly in both cases. Gray-scale objects are also studied by the use of simulation. The special advantages of GI will make the edge detection based on GGI be valuable in real applications.

Iterative denoising of ghost imaging.

We present a new technique to denoise ghost imaging (GI) in which conventional intensity correlation GI and an iteration process have been combined to give an accurate estimate of the actual noise affecting image quality. The blurring influence of the speckle areas in the beam is reduced in the iteration by setting a threshold. It is shown that with an appropriate choice of threshold value, the quality of the iterative GI reconstructed image is much better than that of differential GI for the same number of measurements. This denoising method thus offers a very effective approach to promote the implementation of GI in real applications.

Complementary compressive imaging for the telescopic system.

Conventional single-pixel cameras recover images only from the data recorded in one arm of the digital micromirror device, with the light reflected to the other direction not to be collected. Actually, the sampling in these two reflection orientations is correlated with each other, in view of which we propose a sampling concept of complementary compressive imaging, for the first time to our knowledge. We use this method in a telescopic system and acquire images of a target at about 2.0 km range with 20 cm resolution, with the variance of the noise decreasing by half. The influence of the sampling rate and the integration time of photomultiplier tubes on the image quality is also investigated experimentally. It is evident that this technique has advantages of large field of view over a long distance, high-resolution, high imaging speed, high-quality imaging capabilities, and needs fewer measurements in total than any single-arm sampling, thus can be used to improve the performance of all compressive imaging schemes and opens up possibilities for new applications in the remote-sensing area.

Lensless ghost imaging with sunlight.

An experiment demonstrating lensless ghost imaging (GI) with sunlight has been performed. A narrow spectral line is first filtered out and its intensity correlation measured. With this true thermal light source, an object consisting of two holes is imaged. The realization of lensless GI with sunlight is a step forward toward the practical application of GI with ordinary daylight as the source of illumination.

Adaptive compressive ghost imaging based on wavelet trees and sparse representation.

Compressed sensing is a theory which can reconstruct an image almost perfectly with only a few measurements by finding its sparsest representation. However, the computation time consumed for large images may be a few hours or more. In this work, we both theoretically and experimentally demonstrate a method that combines the advantages of both adaptive computational ghost imaging and compressed sensing, which we call adaptive compressive ghost imaging, whereby both the reconstruction time and measurements required for any image size can be significantly reduced. The technique can be used to improve the performance of all computational ghost imaging protocols, especially when measuring ultra-weak or noisy signals, and can be extended to imaging applications at any wavelength.

High-speed secure key distribution over an optical network based on computational correlation imaging.

We present a protocol for an optical key distribution network based on computational correlation imaging, which can simultaneously realize privacy amplification and multiparty distribution. With current technology, the key distribution rate could reach hundreds of Mbit/s with suitable choice of parameters. The setup is simple and inexpensive, and may be employed in real networks where high-speed long-distance secure communication is required.

Protocol based on compressed sensing for high-speed authentication and cryptographic key distribution over a multiparty optical network.

We present a protocol for the amplification and distribution of a one-time-pad cryptographic key over a point-to-multipoint optical network based on computational ghost imaging (GI) and compressed sensing (CS). It is shown experimentally that CS imaging can perform faster authentication and increase the key generation rate by an order of magnitude compared with the scheme using computational GI alone. The protocol is applicable for any number of legitimate user, thus, the scheme could be used in real intercity networks where high speed and high security are crucial.

Thermal light optical coherence tomography for transmissive objects.

We report an experimental demonstration of optical coherence tomography for transmissive objects utilizing second-order correlation ghost imaging with thermal light. To evaluate the longitudinal resolution of our system, the concept of the imaging longitudinal coherence length is introduced, which is more accurate for judging the image quality of ghost imaging with unequal optical paths than the conventional point-to-point longitudinal coherence length. Our work should help clarify our understanding of the longitudinal coherence of thermal light, as well as provide a scheme for performing optical coherence tomography on objects that are not highly reflective.