Image quality of compressive single-pixel imaging using different Hadamard orderings

Passive localization and reconstruction of multiple non-line-of-sight objects in a scene with a large visible transmissive window

Passive non-line-of-sight imaging methods have been demonstrated to be capable of reconstructing images of hidden objects. However, current passive non-line-of-sight imaging methods have performance limitations due to the requirements of an occluder and aliasing between multiple objects. In this paper, we propose a method for passive localization and reconstruction of multiple non-line-of-sight objects in a scene with a large visible transmissive window. The analysis of the transport matrix revealed that more redundant information is acquired in a scene with a window than that with an occluder, which makes the image reconstruction more difficult. We utilized the projection operator and residual theory to separate the reconstruction equation of multiple objects into the independent equations of the located objects that can be reconstructed independently by TVAL3 and Split-Bregman algorithms, which greatly reduces the computational complexity of the reconstruction. Our method lays the foundation for multiple objects reconstruction in complex non-line-of-sight scenes.

High-quality coherent ghost imaging of a transmission target

When the test detector of ghost imaging (GI) is a point-like detector and the detector's transverse size is smaller than the transverse coherence length of the light field at the detection plane, this case is corresponding to coherent GI (CGI) and the imaging result recovered by traditional GI (TGI) reconstruction algorithm is usually bad for a transmission target. Here a CGI scheme of a transmission target is proposed and a corresponding CGI reconstruction algorithm is developed to stably recover the target's image. The validity of the proposed method is verified by both simulation and experiments. Both the simulation and experimental results demonstrate that the target's transmission function can be perfectly reconstructed by CGI. We also show that the imaging quality of CGI with a point-like detector is better than that of TGI with a bucket detector if detection noise exists in the sampling process. Performance comparisons between CGI reconstruction and TGI reconstruction are also discussed.

Photon-level single-pixel 3D tomography with masked attention network

Tomography plays an important role in characterizing the three-dimensional structure of samples within specialized scenarios. In the paper, a masked attention network is presented to eliminate interference from different layers of the sample, substantially enhancing the resolution for photon-level single-pixel tomographic imaging. The simulation and experimental results have demonstrated that the axial resolution and lateral resolution of the imaging system can be improved by about 3 and 2 times respectively, with a sampling rate of 3.0 %. The scheme is expected to be seamlessly integrated into various tomography systems, which is conducive to promoting the tomographic imaging for biology, medicine, and materials science.

Optimizing the ordering of the Hadamard masks of ghost imaging suitable for the efficient face reconstruction using the max-projection method

One crucial component of ghost imaging (GI) is the encoded mask. Higher-quality reconstruction at lower sampling rates is still a major challenge for GI. Inspired by deep learning, max-projection method is proposed in the paper to reorder the Hadamard masks for its efficient and rapid reconstruction. The simulations demonstrated that max-projection ordering with only 20 face training images yielded excellent reconstruction outcomes. In noise-free simulations, at an ultralow sampling rate of 5%, the PSNR of the max-projection ordering was 1.1 dB higher than that of the cake-cutting ordering with the best performance in the reference group. In noisy simulations, at ultralow sampling rates, the retrieved images remained almost identical to their noise-free counterparts. Irrespective of the presence or absence of noise, the max-projection ordering guaranteed the highest fidelity of image reconstruction at ultralow sampling rates. The reconstruction time was reduced to mere milliseconds, thereby enabling swift visualization of dynamic phenomena. Accordingly, the max-projection ordering Hadamard matrix offers a promising solution for real-time GI due to its higher reconstruction quality, stronger noise immunity and millisecond reconstruction time.

Block-based compressed sensing for fast optic fiber bundle imaging with high spatial resolution

The resolution of traditional fiber bundle imaging is usually limited by the density and the diameter of the fiber cores. To improve the resolution, compression sensing was introduced to resolve multiple pixels from a single fiber core, but current methods have the drawbacks of excessive sampling and long reconstruction time. In this paper, we present, what we believe to be, a novel block-based compressed sensing scheme for fast realization of high-resolution optic fiber bundle imaging. In this method, the target image is segmented into multiple small blocks, each of which covers the projection area of one fiber core. All block images are independently and simultaneously sampled and the intensities are recorded by a two-dimensional detector after they are collected and transmitted through corresponding fiber cores. Because the size of sampling patterns and the sampling numbers are greatly reduced, the reconstruction complexity and reconstruction time are also decreased. According to the simulation analysis, our method is 23 times faster than the current compressed sensing optical fiber imaging for reconstructing a fiber image of 128 × 128 pixels, while the sampling number is only 0.39%. Experiment results demonstrate that the method is also effective for reconstructing large target images and the number of sampling does not increase with the size of the image. Our finding may provide a new idea for high-resolution real-time imaging of fiber bundle endoscope.

OpenSpyrit: an ecosystem for open single-pixel hyperspectral imaging

This paper describes OpenSpyrit, an open access and open source ecosystem for reproducible research in hyperspectral single-pixel imaging, composed of SPAS (a Python single-pixel acquisition software), SPYRIT (a Python single-pixel reconstruction toolkit) and SPIHIM (a single-pixel hyperspectral image collection). The proposed OpenSpyrit ecosystem responds to the need for reproducibility and benchmarking in single-pixel imaging by providing open data and open software. The SPIHIM collection, which is the first open-access FAIR dataset for hyperspectral single-pixel imaging, currently includes 140 raw measurements acquired using SPAS and the corresponding hypercubes reconstructed using SPYRIT. The hypercubes are reconstructed by both inverse Hadamard transformation of the raw data and using the denoised completion network (DC-Net), a data-driven reconstruction algorithm. The hypercubes obtained by inverse Hadamard transformation have a native size of 64 × 64 × 2048 for a spectral resolution of 2.3 nm and a spatial resolution that is comprised between 182.4 µm and 15.2 µm depending on the digital zoom. The hypercubes obtained using the DC-Net are reconstructed at an increased resolution of 128 × 128 × 2048. The OpenSpyrit ecosystem should constitute a reference to support benchmarking for future developments in single-pixel imaging.

Single-pixel imaging with high spectral and spatial resolution

It has long been a challenge to obtain high spectral and spatial resolution simultaneously for the field of measurement and detection. Here we present a measurement system based on single-pixel imaging with compressive sensing that can realize excellent spectral and spatial resolution at the same time, as well as data compression. Our method can achieve high spectral and spatial resolution, which is different from the mutually restrictive relationship between the two in traditional imaging. In our experiments, 301 spectral channels are obtained in the band of 420-780 nm with a spectral resolution of 1.2 nm and a spatial resolution of 1.11 mrad. A sampling rate of 12.5% for a 64×64p i x e l image is obtained by using compressive sensing, which also reduces the measurement time; thus, high spectral and spatial resolution are realized simultaneously, even at a low sampling rate.

High-precision single-pixel 3D calibration method using pseudo-phase matching

Compressive sensing makes it possible to explore two-dimensional spatial information using a single-point detector. However, the reconstruction of the three-dimensional (3D) morphology using a single-point sensor is largely limited by the calibration. Here we demonstrate a pseudo-single-pixel camera calibration (PSPC) method using pseudo phase matching in stereo, which can perform 3D calibration of low-resolution images with the help of a high-resolution digital micromirror device (DMD) in the system. In this paper, we use a high-resolution CMOS to pre-image the DMD surface and successfully calibrate the spatial position of a single-point detector and the projector with the support of binocular stereo matching. Our system achieved sub-millimeter reconstructions of spheres, steps, and plaster portraits at low compression ratios with a high-speed digital light projector (DLP) and a highly sensitive single-point detector.

Optimized sinusoidal patterns for high-performance computational ghost imaging

Computational ghost imaging (CGI) can reconstruct scene images by two-order correlation between sampling patterns and detected intensities from a bucket detector. By increasing the sampling rates (SRs), imaging quality of CGI can be improved, but it will result in an increasing imaging time. Herein, in order to achieve high-quality CGI under an insufficient SR, we propose two types of novel sampling methods for CGI, to the best of our knowledge, cyclic sinusoidal-pattern-based CGI (CSP-CGI) and half-cyclic sinusoidal-pattern-based CGI (HCSP-CGI), in which CSP-CGI is realized by optimizing the ordered sinusoidal patterns through "cyclic sampling patterns," and HCSP-CGI just uses half of the sinusoidal pattern types of CSP-CGI. Target information mainly exists in the low-frequency region, and high-quality target scenes can be recovered even at an extreme SR of 5%. The proposed methods can significantly reduce the sampling number and real-time ghost imaging possible. The experiments demonstrate the superiority of our method over state-of-the-art methods both qualitatively and quantitatively.

Comparison between Hadamard and canonical bases for in situ wavefront correction and the effect of ordering in compressive sensing

In this work we compare the canonical and Hadamard bases for in situ wavefront correction of a focused Gaussian beam using a spatial light modulator (SLM). The beam is perturbed with a transparent optical element (sparse) or a random scatterer (both prevent focusing at a single spot). The phase corrections are implemented with different basis sizes (N=64,256,1024,4096) and the phase contribution of each basis element is measured with three-step interferometry. The field is reconstructed from the complete 3N measurements, and the correction is implemented by projecting the conjugate phase at the SLM. Our experiments show that in general, the Hadamard basis measurements yield better corrections because every element spans the relevant area of the SLM, thus reducing the noise in the interferograms. In contrast, the canonical basis has the fundamental limitation that the area of the elements is proportional to 1/N, and it requires dimensions that are compatible with the spatial period of the grating. In the case of the random scatterer, we only obtain reasonable corrections with the Hadamard basis and the intensity of the corrected spot increases monotonically with N, which is consistent with fast random changes in phase over small spatial scales. We also explore compressive sensing with the Hadamard basis and find that the minimum compression ratio needed to achieve corrections with similar quality to those that use the complete measurements depends on the basis ordering. The best results are achieved in the case of the Hadamard-Walsh and cake-cutting orderings. Surprisingly, in the case of the random scatterer we find that moderate compression ratios on the order of 10%-20% (N=4096) allow us to recover focused spots, although as expected, the maximum intensities increase monotonically with the number of measurements due to the non-sparsity of the signal.

Compressed ultrahigh-speed single-pixel imaging by swept aggregate patterns

Single-pixel imaging (SPI) has emerged as a powerful technique that uses coded wide-field illumination with sampling by a single-point detector. Most SPI systems are limited by the refresh rates of digital micromirror devices (DMDs) and time-consuming iterations in compressed-sensing (CS)-based reconstruction. Recent efforts in overcoming the speed limit in SPI, such as the use of fast-moving mechanical masks, suffer from low reconfigurability and/or reduced accuracy. To address these challenges, we develop SPI accelerated via swept aggregate patterns (SPI-ASAP) that combines a DMD with laser scanning hardware to achieve pattern projection rates of up to 14.1 MHz and tunable frame sizes of up to 101×103 pixels. Meanwhile, leveraging the structural properties of S-cyclic matrices, a lightweight CS reconstruction algorithm, fully compatible with parallel computing, is developed for real-time video streaming at 100 frames per second (fps). SPI-ASAP allows reconfigurable imaging in both transmission and reflection modes, dynamic imaging under strong ambient light, and offline ultrahigh-speed imaging at speeds of up to 12,000 fps.

Single-pixel imaging using discrete Zernike moments

A novel single-pixel imaging (SPI) technique based on discrete orthogonal Zernike moments is proposed. In this technique, the target object is illuminated by two sets of Zernike basis patterns which satisfy the Zernike polynomials. The Zernike moments of object image are obtained by measuring the reflected light intensities through a single-pixel detector. And the object image is reconstructed by summing the product of Zernike polynomials and detected intensities iteratively. By theoretical and experimental demonstrations, an image with high quality is retrieved under compressive sampling. Moreover, the Zernike illuminating patterns are used for object classification due to the rotation invariant of Zernike moments. By measuring the amplitudes of a few specific Zernike moments through the SPI system, the rotated images with different angles and the same content are classified into the same class on experiment. This classification technique has the advantages of high efficiency and high accuracy due to the high modulation speed and high sensitivity of SPI system.

Single-pixel imaging of a randomly moving object

Single-pixel imaging enjoys advantages of low budget, broad spectrum, and high imaging speed. However, existing methods cannot clearly reconstruct the object that is fast rotating or randomly moving. In this work, we put forward an effective method to image a randomly moving object based on geometric moment analysis. To the best of our knowledge, this is the first work that reconstructs the shape and motion state of the target without prior knowledge of the speed or position. By using the cake-cutting order Hadamard illumination patterns and low-order geometric moment patterns, we obtain a high-quality video stream of the target which moves at high and varying translational and rotational speeds. The efficient method as verified by simulation and experimental results has great potential for practical applications such as Brownian motion microscopy and remote sensing.

Single-pixel imaging with Gao-Boole patterns

Single-pixel imaging (SPI) can perceive the world using only a single-pixel detector, but long sampling times with a series of patterns are inevitable for SPI, which is the bottleneck for its practical application. Developing new patterns to reduce the sampling times might provide opportunities to address this challenge. Based on the Kronecker product of Hadamard matrix, we here design a complete set of new patterns, called Gao-Boole patterns, for SPI. Compared to orthogonal Hadamard basis patterns with elements valued as +1 or -1, our Gao-Boole patterns are non-orthogonal ones and the element values are designed as +1 or 0. Using our Gao-Boole patterns, the reconstructed quality of a target image (N × N pixels) is as high as the Hadamard one but only with half pattern numbers of the Hadamard ones, for both full sampling (N² for Gao-Boole patterns, 2N² for Hadamard basis patterns) and undersampling cases in experiment. Effectively reducing the patterns numbers and sampling times without sacrificing imaging quality, our designed Gao-Boole patterns provide a superior option for structural patterns in SPI and help to steer SPI toward practical imaging application.

Single pixel imaging via unsupervised deep compressive sensing with collaborative sparsity in discretized feature space

Single-pixel imaging (SPI) enables the use of advanced detector technologies to provide a potentially low-cost solution for sensing beyond the visible spectrum and has received increasing attentions recently. However, when it comes to sub-Nyquist sampling, the spectrum truncation and spectrum discretization effects significantly challenge the traditional SPI pipeline due to the lack of sufficient sparsity. In this work, a deep compressive sensing (CS) framework is built to conduct image reconstructions in classical SPIs, where a novel compression network is proposed to enable collaborative sparsity in discretized feature space while remaining excellent coherence with the sensing basis as per CS conditions. To alleviate the underlying limitations in an end-to-end supervised training, for example, the network typically needs to be re-trained as the basis patterns, sampling ratios and so on. change, the network is trained in an unsupervised fashion with no sensing physics involved. Validation experiments are performed both numerically and physically by comparing with traditional and cutting-edge SPI reconstruction methods. Particularly, fluorescence imaging is pioneered to preliminarily examine the in vivo biodistributions. Results show that the proposed method maintains comparable image fidelity to a sCMOS camera even at a sampling ratio down to 4%, while remaining the advantages inherent in SPI. The proposed technique maintains the unsupervised and self-contained properties that highly facilitate the downstream applications in the field of compressive imaging.

High-performance scanning-mode polarization based computational ghost imaging (SPCGI)

Computational ghost imaging (CGI) uses preset patterns and single-pixel detection, breaking through the traditional form of point-to-point imaging. In this paper, based on the Monte Carlo model, a reflective polarization based CGI (PCGI) system has been proposed and constructed under the foggy environments. And the imaging performances of the PCGI at different optical distances have been investigated and analyzed quantitatively. When the targets and the background have a small difference in reflectivity, the difference of polarization characteristics between the targets and the background can help the CGI to remove the interference of scattering light and improve the imaging contrast. Besides, in order to further improve imaging efficiency, a scanning-mode polarization based CGI (SPCGI) has also been proposed, in which the combination of polarization characteristics and the scanning-mode plays an important role to improve the CGI's imaging efficiency and imaging quality.

Secondary Complementary Balancing Compressive Imaging with a Free-Space Balanced Amplified Photodetector

Single-pixel imaging (SPI) has attracted widespread attention because it generally uses a non-pixelated photodetector and a digital micromirror device (DMD) to acquire the object image. Since the modulated patterns seen from two reflection directions of the DMD are naturally complementary, one can apply complementary balanced measurements to greatly improve the measurement signal-to-noise ratio and reconstruction quality. However, the balance between two reflection arms significantly determines the quality of differential measurements. In this work, we propose and demonstrate a simple secondary complementary balancing mechanism to minimize the impact of the imbalance on the imaging system. In our SPI setup, we used a silicon free-space balanced amplified photodetector with 5 mm active diameter which could directly output the difference between two optical input signals in two reflection arms. Both simulation and experimental results have demonstrated that the use of secondary complementary balancing can result in a better cancellation of direct current components of measurements, and can acquire an image quality slightly better than that of single-arm single-pixel complementary measurement scheme (which is free from the trouble of optical imbalance) and over 20 times better than that of double-arm dual-pixel complementary measurement scheme under optical imbalance conditions.

Anti-loss-compression image encryption based on computational ghost imaging using discrete cosine transform and orthogonal patterns

As an emerging imaging technique, computational ghost imaging (CGI) has its unique application in image encryption. However, the long imaging time and high requirement of transmitting data, both in the size of data and vulnerability of lossy compression, limit its application in the practical communications. Using discrete cosine transform to sparse bucket signals of CGI, we here propose a method by transforming the bucket signals from the sensing matrix domain to the space domain, enhancing the ability of the bucket signals (i.e., encrypted image) to resist the lossy compression. Based on the principle of CGI, we first propose to use gradient descent to find an orthogonal matrix as the encryption key, then test the performance of our method at different quality factors and undersampling rates. Both simulations and experimental results demonstrate that our encryption method shows great resistance to the traditional lossy compression methods and has good performance in the undersampling conditions. Our method provides a convenient way to transmit the bucket signals of CGI by the format that involves lossy compression and thus camouflages itself while significantly reducing the amount of data being transmitted.

Ghost panorama using a convex mirror

Computational ghost imaging or single-pixel imaging enables the image formation of an unknown scene using a lens-free photodetector. In this Letter, we present a computational panoramic ghost imaging system that can achieve a full-color panorama using a single-pixel photodetector, where a convex mirror performs the optical transformation of the engineered Hadamard-based circular illumination pattern from unidirectionally to omnidirectionally. To our best knowledge, it is the first time to propose the concept of ghost panoramas and realize preliminary experimentations. It is foreseeable that ghost panoramas will have more advantages in imaging and detection in many extreme conditions (e.g., scattering/turbulence and unconventional spectra), as well as broad application prospects.

Single-pixel imaging: An overview of different methods to be used for 3D space reconstruction in harsh environments

Different imaging solutions have been proposed over the last few decades, aimed at three-dimensional (3D) space reconstruction and obstacle detection, either based on stereo-vision principles using active pixel sensors operating in the visible part of the spectra or based on active Near Infra-Red (NIR) illumination applying the time-of-flight principle, to mention just a few. If extremely low quantum efficiencies for NIR active illumination yielded by silicon-based detector solutions are considered together with the huge photon noise levels produced by the background illumination accompanied by Rayleigh scattering effects taking place in outdoor applications, the operating limitations of these systems under harsh weather conditions, especially if relatively low-power active illumination is used, are evident. If longer wavelengths for active illumination are applied to overcome these issues, indium gallium arsenide (InGaAs)-based photodetectors become the technology of choice, and for low-cost solutions, using a single InGaAs photodetector or an InGaAs line-sensor becomes a promising choice. In this case, the principles of Single-Pixel Imaging (SPI) and compressive sensing acquire a paramount importance. Thus, in this paper, we review and compare the different SPI developments reported. We cover a variety of SPI system architectures, modulation methods, pattern generation and reconstruction algorithms, embedded system approaches, and 2D/3D image reconstruction methods. In addition, we introduce a Near Infra-Red Single-Pixel Imaging (NIR-SPI) sensor aimed at detecting static and dynamic objects under outdoor conditions for unmanned aerial vehicle applications.

Imaging biological tissue with high-throughput single-pixel compressive holography

Single-pixel holography (SPH) is capable of generating holographic images with rich spatial information by employing only a single-pixel detector. Thanks to the relatively low dark-noise production, high sensitivity, large bandwidth, and cheap price of single-pixel detectors in comparison to pixel-array detectors, SPH is becoming an attractive imaging modality at wavelengths where pixel-array detectors are not available or prohibitively expensive. In this work, we develop a high-throughput single-pixel compressive holography with a space-bandwidth-time product (SBP-T) of 41,667 pixels/s, realized by enabling phase stepping naturally in time and abandoning the need for phase-encoded illumination. This holographic system is scalable to provide either a large field of view (~83 mm2) or a high resolution (5.80 μm × 4.31 μm). In particular, high-resolution holographic images of biological tissues are presented, exhibiting rich contrast in both amplitude and phase. This work is an important step towards multi-spectrum imaging using a single-pixel detector in biophotonics.

Imaging reconstruction comparison of different ghost imaging algorithms

As an indirect and computational imaging approach, imaging reconstruction efficiency is critical for ghost imaging (GI). Here, we compare different GI algorithms, including logarithmic GI and exponential GI we proposed, by numerically analysing their imaging reconstruction efficiency and error tolerance. Simulation results show that compressive GI algorithm has the highest reconstruction efficiency due to its global optimization property. Error tolerance studies further manifest that compressive GI and exponential GI are sensitive to the error ratio. By replacing the bucket input of compressive GI with different bucket object signal functions, we integrate compressive GI with other GI algorithms and discuss their imaging efficiency. With the combination between the differential GI (or normalized GI) and compressive GI, both reconstruction efficiency and error tolerance will present the best performance. Moreover, an optical encryption is proposed by combining logarithmic GI, exponential GI and compressive GI, which can enhance the encryption security based on GI principle.