Efficient single-pixel imaging encrypted transmission based on 3D Arnold transformation

Single-pixel imaging(SPI)can transform 2D or 3D image data into 1D light signals,which offers promising prospects for image compression and transmission.However,during data communication these light signals in public channels will easily draw the attention of eavesdroppers.Here,we introduce an efficient encryption method for SPI data transmission that uses the 3D Arnold transformation to directly disrupt 1D single-pixel light signals and utilizes the elliptic curve encryption algorithm for key transmission.This encryption scheme immediately employs Hadamard patterns to illuminate the scene and then utilizes the 3D Arnold transformation to permutate the 1D light signal of single-pixel detection.Then the transformation parameters serve as the secret key,while the security of key exchange is guaranteed by an elliptic curve-based key exchange mechanism.Compared with existing encryption schemes,both computer simulations and optical experiments have been conducted to demonstrate that the proposed technique not only enhances the security of encryption but also eliminates the need for complicated pattern scrambling rules.Additionally,this approach solves the problem of secure key transmission,thus ensuring the security of information and the quality of the decrypted images.

Complex-amplitude Fourier single-pixel imaging via coherent structured illumination

We propose a method of complex-amplitude Fourier single-pixel imaging(CFSI)with coherent structured illumination to acquire both the amplitude and phase of an object.In the proposed method,an object is illustrated by a series of coherent structured light fields,which are generated by a phase-only spatial light modulator,the complex Fourier spectrum of the object can be acquired sequentially by a single-pixel photodetector.Then the desired complex-amplitude image can be retrieved directly by applying an inverse Fourier transform.We experimentally implemented this CFSI with several different types of objects.The experimental results show that the proposed method provides a promising complex-amplitude imaging approach with high quality and a stable configuration.Thus,it might find broad applications in optical metrology and biomedical science.

Resolution-enhanced single-pixel imaging using the Hadamard transform matrix

We propose a single-pixel imaging(SPI)method to achieve a higher-resolution image via the Hadamard transform matrix.Unlike traditional SPI schemes,this new method recovers images by correlating single-pixel signals with synchronized transformed patterns of Hadamard bases that are actually projected onto the digital micromirror device.Each transform pattern is obtained through the inverse Fourier transform of the pattern acquired by Gaussian filtering of each Hadamard basis in the frequency domain.The proposed scheme is based on a typical SPI experimental setup and does not add any hardware complexity,enabling the transformation of Hadamard matrices and image reconstruction through data processing alone.Therefore,this approach could be considered as an alternative option for achieving fast SPI in a diffraction-limited imaging system,without the need for additional hardware.

Fast Fourier single-pixel imaging based on Sierra–Lite dithering algorithm

The single-pixel imaging(SPI) technique is able to capture two-dimensional(2 D) images without conventional array sensors by using a photodiode. As a novel scheme, Fourier single-pixel imaging(FSI) has been proven capable of reconstructing high-quality images. Due to the fact that the Fourier basis patterns(also known as grayscale sinusoidal patterns)cannot be well displayed on the digital micromirror device(DMD), a fast FSI system is proposed to solve this problem by binarizing Fourier pattern through a dithering algorithm. However, the traditional dithering algorithm leads to low quality as the extra noise is inevitably induced in the reconstructed images. In this paper, we report a better dithering algorithm to binarize Fourier pattern, which utilizes the Sierra–Lite kernel function by a serpentine scanning method. Numerical simulation and experiment demonstrate that the proposed algorithm is able to achieve higher quality under different sampling ratios.

Optical encryption of multiple three-dimensional objects based on multiple interferences and single-pixel digital holography

We present an optical encryption method of multiple three-dimensional objects based on multiple interferences and single-pixel digital holography. By modifying the Mach-Zehnder interferometer, the interference of the multiple objects beams and the one reference beam is used to simultaneously encrypt multiple objects into a ciphertext. During decryption, each three-dimensional object can be decrypted independently without having to decrypt other objects. Since the single- pixel digital holography based on compressive sensing theory is introduced, the encrypted data of this method is effectively reduced. In addition, recording fewer encrypted data can greatly reduce the bandwidth of network transmission. Moreover, the compressive sensing essentially serves as a secret key that makes an intruder attack invalid, which means that the system is more secure than the conventional encryption method. Simulation results demonstrate the feasibility of the proposed method and show that the system has good security performance.

Near-Range Large Field-of-View Three-Dimensional Photon-Counting Imaging with a Single-Pixel Si-Avalanche Photodiode

Large field-of-view（FoV） three-dimensional（3 D） photon-counting imaging is demonstrated with a single-pixel single-photon detector based on a Geiger-mode Si-avalanche photodiode. By removing the collecting lens（CL）before the detector, the FoV is expanded to ±10°. Thanks to the high detection efficiency, the signal-to-noise ratio of the imaging system is as high as 7.8 dB even without the CL when the average output laser pulse energy is about 0.45 pJ/pulse for imaging the targets at a distance of 5 m. A 3 D image overlaid with the reflectivity data is obtained according to the photon-counting time-of-flight measurement and the return photon intensity.

Pseudo complementary measurement for traditional single-pixel cameras

A traditional single-pixel camera needs a large number of measurements to reconstruct the object with compressive sensing computation.Compared with the 1/0 matrices in classical measurement,the 1/-1 matrices in the complementary measurement has better property for reconstruction computation and returns better reconstruction results.However,each row of the 1/-1 matrices needs two measurements with the traditional single-pixel camera which results into double measurements compared with the 1/0 matrices.In this paper,we consider the pseudo complementary measurement which only takes the same amount of measurements with the row number of some properly designed 1/0 matrix to compute the total luminous flux of the objective and derives the measurement data of the corresponding 1/-1 matrix in a mathematical way.The numerical simulation and experimental result show that the pseudo complementary measurement is an efficient tool for the traditional single-pixel camera imaging under low measurement rate,which can combine the advantages of the classical and complementary measurements and significantly improve the peak signal-to-noise ratio.

Efficient spectral single-pixel imaging via Morton frequency-domain scanning [Invited]

Single-pixel imaging (SPI) captures two-dimensional images utilizing a sequence of modulation patterns and measurements recorded by a single-pixel detector. However, the sequential measurement of a scene is time-consuming, especially for high-spatial-resolution imaging. Furthermore, for spectral SPI, the enormous data storage and processing time requirements substantially diminish imaging efficiency. To reduce the required number of patterns, we propose a strategy by optimizing a Hadamard pattern sequence via Morton frequency domain scanning to enhance the quality of a reconstructed spectral cube at low sampling rates. Additionally, we expedite spectral cube reconstruction, eliminating the necessity for a large Hadamard matrix. We demonstrate the effectiveness of our approach through both simulation and experiment,achieving sub-Nyquist sampling of a three-dimensional spectral cube with a spatial resolution of 256×256 pixels and181 spectral bands and a reduction in reconstruction time by four orders of magnitude. Consequently, our method offers an efficient solution for compressed spectral imaging.

Dynamic 3D shape reconstruction under complex reflection and transmission conditions using multi-scale parallel single-pixel imaging

Depth measurement and three-dimensional(3D)imaging under complex reflection and transmission conditions are challenging and even impossible for traditional structured light techniques,owing to the precondition of point-to-point triangulation.Despite recent progress in addressing this problem,there is still no efficient and general solution.Herein,a Fourier dual-slice projection with depth-constrained localization is presented to separate and utilize different illumination and reflection components efficiently,which can significantly decrease the number of projection patterns in each sequence from thousands to fifteen.Subsequently,multi-scale parallel single-pixel imaging(MS-PSI)is proposed based on the established and proven position-invariant theorem,which breaks the local regional assumption and enables dynamic 3D reconstruction.Our methodology successfully unveils unseen-before capabilities such as(1)accurate depth measurement under interreflection and subsurface scattering conditions,(2)dynamic measurement of the time-varying high-dynamic-range scene and through thin volumetric scattering media at a rate of 333 frames per second;(3)two-layer 3D imaging of the semitransparent surface and the object hidden behind it.The experimental results confirm that the proposed method paves the way for dynamic 3D reconstruction under complex optical field reflection and transmission conditions,benefiting imaging and sensing applications in advanced manufacturing,autonomous driving,and biomedical imaging.

Arbitrary n-step phase-shifting Fourier single-pixel imaging

In this Letter,we innovatively present general analytical expressions for arbitrary n-step phase-shifting Fourier single-pixel imaging(FSI).We also design experiments capable of implementing arbitrary n-step phase-shifting FSI and compare the experimental results,including the image quality,for 3-to 6-step phase-shifting cases without loss of generality.These results suggest that,compared to the 4-step method,these FSI approaches with a larger number of steps exhibit enhanced robustness against noise while ensuring no increase in data-acquisition time.These approaches provide us with more strategies to perform FSI for different steps,which could offer guidance in balancing the tradeoff between the image quality and the number of steps encountered in the application of FSI.

Single-pixel 3D imaging based on fusion temporal data of single-photon detector and millimeter-wave radar

Recently,there has been increased attention toward 3D imaging using single-pixel single-photon detection(also known as temporal data)due to its potential advantages in terms of cost and power efficiency.However,to eliminate the symmetry blur in the reconstructed images,a fixed background is required.This paper proposes a fusion-data-based 3D imaging method that utilizes a single-pixel single-photon detector and millimeter-wave radar to capture temporal histograms of a scene from multiple perspectives.Subsequently,the 3D information can be reconstructed from the one-dimensional fusion temporal data by using an artificial neural network.Both the simulation and experimental results demonstrate that our fusion method effectively eliminates symmetry blur and improves the quality of the reconstructed images.

Measurable speckle gradation Hadamard single-pixel imaging

The array spatial light field is an effective means for improving imaging speed in single-pixel imaging.However,distinguishing the intensity values of each sub-light field in the array spatial light field requires the help of the array detector or the time-consuming deep-learning algorithm.Aiming at this problem,we propose measurable speckle gradation Hadamard single-pixel imaging(MSG-HSI),which makes most of the refresh mechanism of the device generate the Hadamard speckle patterns and the high sampling rate of the bucket detector and is capable of measuring the light intensity fluctuation of the array spatial light field only by a simple bucket detector.The numerical and experimental results indicate that data acquisition in MSG-HSI is 4 times faster than in traditional Hadamard single-pixel imaging.Moreover,imaging quality in MSG-HSI can be further improved by image stitching technology.Our approach may open a new perspective for single-pixel imaging to improve imaging speed.

Single-pixel wavefront sensing via vectorial polarization modulation[Invited]

The Shack–Hartmann wavefront sensor(SHWFS)is commonly used for its high speed and precision in adaptive optics.However,its performance is limited in low light conditions,particularly when observing faint objects in astronomical applications.Instead of a pixelated detector,we present a new approach for wavefront sensing using a single-pixel detector,which is able to code the spatial position of a light spot array into the polarization dimension and decode the polarization state in the polar coordinate.We propose validation experiments with simple and complex wavefront distortions to demonstrate our approach as a promising alternative to traditional SHWFS systems,with potential applications in a wide range of fields.

Vibration measurement with frequency modulation single-pixel imaging

Single-pixel imaging can reconstruct the image of the object when the light traveling from the object to the detector is scattered or distorted.Most single-pixel imaging methods only obtain distribution of transmittance or reflectivity of the object.Some methods can obtain extra information,such as color and polarization information.However,there is no method that can get the vibration information when the object is vibrating during the measurement.Vibration information is very important,because unexpected vibration often means the occurrence of abnormal conditions.In this Letter,we introduce a method to obtain vibration information with the frequency modulation single-pixel imaging method.This method uses a light source with a special pattern to illuminate the object and analyzes the frequency of the total light intensity signal transmitted or reflected by the object.Compared to other single-pixel imaging methods,frequency modulation single-pixel imaging can obtain vibration information and maintain high signal-to-noise ratio and has potential on finding out hidden facilities under construction or instruments in work.

A detail-enhanced sampling strategy in Hadamard single-pixel imaging

Hadamard single-pixel imaging is an appealing imaging technique due to its features of low hardware complexity and industrial cost.To improve imaging efficiency,many studies have focused on sorting Hadamard patterns to obtain reliable reconstructed images with very few samples.In this study,we propose an efficient Hadamard basis sampling strategy that employs an exponential probability function to sample Hadamard patterns in a direction with high energy concentration of the Hadamard spectrum.We used the compressed-sensing algorithm for image reconstruction.The simulation and experimental results show that this sampling strategy can reconstruct object reliably and preserves the edge and details of images.

Reconstruction algorithm for cross-waveband optical computing imaging

In a single-pixel fast imaging setup,the data collected by the single-pixel detector needs to be processed by a computer,but the speed of the latter will affect the image reconstruction time.Here we propose two kinds of setups which are able to transform non-visible into visible light imaging,wherein their computing process is replaced by a camera integration mode.The image captured by the camera has a low contrast,so here we present an algorithm that can realize a high quality image in near-infrared to visible cross-waveband imaging.The scheme is verified both by simulation and in actual experiments.The setups demonstrate the great potential for single-pixel imaging and high-speed cross-waveband imaging for future practical applications.

Accurate measurement of wall skin friction by single-pixel ensemble correlation

The present work deals with accurately estimating wall-skin friction from near-wall mean velocity by means of PIV measurement.The estimation accuracy relies on the spatial resolution and the precision of the resolved velocity profile inside the viscous sublayer,which is a big challenge for conventional window-based correlation method(K?hler C J,et al.Exp Fluids,2012,52:1641–1656).With the help of single-pixel ensemble correlation,the ensemble-averaged velocity vector can be resolved at significant spatial resolution,thus improving the measurement accuracy.To demonstrate the feasibility of this single-pixel ensemble correlation method,we first study the velocity estimation precision in a case of steady near-wall flow.Synthetic particle images are used to investigate the effect of different image parameters.It is found that the velocity RMS-uncertainty level of the single-pixel ensemble correlation method can be equivalent to the conventional window correlation method once the effective particle number used for the ensemble correlation is large enough.Furthermore,a canonical turbulent boundary layer is synthetically simulated based on velocity statistics resolved by previous Direct Numerical Simulation(DNS)work(Schlatter P,et al.J Fluid Mech,2010,659:116–126).The relative error of wall skin friction coefficient is shown to be one-order smaller than that of the window correlation method.And the optimization strategy to further minimize the measurement uncertainty is discussed in the last part.

Fine edge detection in single-pixel imaging

Typical single-pixel imaging techniques for edge detection are mostly based on first-order differential edge detection operators.In this paper,we present a novel edge detection scheme combining Fourier single-pixel imaging with a second-order Laplacian of Gaussian(LoG)operator.This method utilizes the convolution results of an LoG operator and Fourier basis patterns as the modulated patterns to extract the edge detail of an unknown object without imaging it.The simulation and experimental results demonstrate that our scheme can ensure finer edge detail,especially under a noisy environment,and save half the processing time when compared with a traditional first-order Sobel operator.

Single-pixel imaging with neutrons

Neutron imaging is an invaluable tool for noninvasive analysis in many fields.However,neutron facilities are expensive and inconvenient to access,while portable sources are not strong enough to form even a static image within an acceptable time frame using traditional neutron imaging.Here we demonstrate a new scheme for single-pixel neutron imaging of real objects,with spatial and spectral resolutions of 100 lm and 0.4%at 1A,respectively.Low illumination down to 1000 neutron counts per frame pattern was achieved.The experimental setup is simple,inexpensive,and especially suitable for low intensity portable sources,which should greatly benefit applications in biology,material science,and industry.

Principles and applications of high-speed single-pixel imaging technology

Single-pixel imaging （SPI） technology has garnered great interest within the last decade because of its ability to record high-resolution images using a single-pixel detector. It has been applied to diverse fields, such as magnetic resonance imaging （MRI）, aerospace remote sensing, terahertz photography, and hyperspectral imaging. Compared with conventional silicon-based cameras, single-pixel cameras （SPCs） can achieve image compression and operate over a much broader spectral range. However, the imaging speed of SPCs is governed by the response time of digital mieromirror devices （DMDs） and the amount of com- pression of acquired images, leading to low （ms-level） temporal resolution. Consequently, it is particularly challenging for SPCs to investigate fast dynamic phenomena, which is required commonly in microscopy. Recently, a unique approach based on photonic time stretch （PTS） to achieve high-speed SPI has been reported. It achieves a frame rate far beyond that can be reached with conventional SPCs. In this paper, we first introduce the principles and applications of the PTS technique. Then the basic archi- tecture of the high-speed SPI system is presented, and an imaging flow cytometer with high speed and high throughput is demonstrated experimentally. Finally, the limitations and potential applications of high-speed SPI are discussed.