Single-pixel Compressive Imaging Research Articles

Single-pixel compressive imaging via single photon counting

Single-pixel compressive imaging reconstructs a target scene with many pixels by using a single-pixel detector to measure the power variations as small sequences of sampling patterns are applied. While it boasts remarkable capabilities, its practical applications remain a challenge in the photon-starved regime where signal-to-noise is low. To address this challenge, we propose to combine quantum parametric mode sorting (QPMS) and deep neural networks (DNN) to overcome low signal-to-noise for faithful image construction. We benchmark our approach in a telecom-LiDAR system against that using direct photon counting detection. Our results show that with only 25 sampling patterns (corresponding compression ratio ∼0.043%), QPMS plus DNN give structural similarity index measure and peak signal-to-noise ratio on average above 22 dB and 0.9, respectively, much higher than those with direct detection (DD). The details of our targets from QPMS are more clearly compared with from DD. Notably, such high performance is sustained even in the presence of 500 times stronger in-band background noise, while DD fails. The high efficiency and robust noise rejection promise potential applications in various fields, especially in photon-starving scenarios.

Enhancing Compressive Single-Pixel Imaging With Zig-Zag-Ordered Walsh-Hadamard Light Modulation

Enhancing Compressive Single-Pixel Imaging With Zig-Zag-Ordered Walsh-Hadamard Light Modulation

High-Quality Image Reconstruction Characteristic Function for Single-Pixel Compressive Imaging

High-Quality Image Reconstruction Characteristic Function for Single-Pixel Compressive Imaging

Sequential Subtraction-Based Compressive Single-Pixel Imaging in Complicate Ambient Light

As a special imaging technique, one of the most important advantages of single-pixel imaging (SPI) than conventional imaging method is that it can recover the object image even through turbid medium. In these situations, the noises bring by the turbid medium usually obey special rules in statistics. While in some other applications, SPI is performed in the environment with complicate ambient light, in which no prior information of the environment noise is known. Aiming at this situation, in this work, the frame-by-frame subtraction-based compressive sensing SPI (FFS-CSPI) method with random 0/1 pattern is used to decrease the effect from the unknown ambient light. The noise robustness of the FFS-CSPI method is analyzed and compared with Hadamard CSPI. In simulation and experiment, two kinds of noises, from external light source and from background video, are considered. The results prove that FFS-CSPI with random 0/1 patterns can achieve higher image quality than conventional mean subtraction method and Hadamard CSPI with the same measurement number. Considering the high refresh rate of digital micromirror device when it loads the 0/1 binary patterns, the imaging speed is acceptable. This work will promote the practical applications of SPI in complicated environment.

Single-Pixel Compressive Digital Holographic Encryption System Based on Circular Harmonic Key and Parallel Phase Shifting Digital Holography

An encryption system that combines compressive sensing (CS) and two-step parallel phase shifting digital holography (PPSDH) using double random phase encoding (DRPE) is presented in this paper. The two-step PPSDH is a linear inline holographic scheme and is much suitable for encrypting the 2D/3D information in a single exposure. The distribution of random phase mask (RPM) in the DRPE is implemented using circular harmonic key which increases the security of the encryption process. In this system, the keys used to encrypt are spatial positions of the planes, wavelength, and rotation of the circular harmonics in RPMs, and CS acts as an additional key that makes the system more secure than the conventional optical encryption methods. At the transmission end, two-step PPSDH is applied to encrypt the object information in single hologram. The digital mirror device (DMD) is placed between the object and a single-pixel detector for acquiring fewer hologram measurements. At the receiver end, the single digital hologram is numerically recovered by using a CS optimization problem. The original complex object field is decrypted from the CS recovered holograms by the inversion of two-step PPSDH process with the help of the correct keys. The numerical simulations are presented for complex 2D and 3D objects to test the feasibility of the proposed encryption and decryption system. The proposed method carried out intensity and phase reconstruction of the original object field using single-pixel compressive imaging. The computer simulation results demonstrated that the encrypted information is highly secured with the rotation of the circular harmonic key. The sensitivity of the decrypted intensity and phase images is also studied with variations of the encrypted keys. The obtained results show that the proposed encryption scheme is feasible and has better security performance and robustness.

Dual-color terahertz spatial light modulator for single-pixel imaging

Spatial light modulators (SLM), capable of dynamically and spatially manipulating electromagnetic waves, have reshaped modern life in projection display and remote sensing. The progress of SLM will expedite next-generation communication and biomedical imaging in the terahertz (THz) range. However, most current THz SLMs are adapted from optical alternatives that still need improvement in terms of uniformity, speed, and bandwidth. Here, we designed, fabricated, and characterized an 8 × 8 THz SLM based on tunable liquid crystal metamaterial absorbers for THz single-pixel compressive imaging. We demonstrated dual-color compressive sensing (CS) imaging for dispersive objects utilizing the large frequency shift controlled by an external electric field. We developed auto-calibrated compressive sensing (ACS) algorithm to mitigate the impact of the spatially nonuniform THz incident beam and pixel modulation, which significantly improves the fidelity of reconstructed images. Furthermore, the complementary modulation at two absorption frequencies enables Hadamard masks with negative element values to be realized by frequency-switching, thereby halving the imaging time. The demonstrated imaging system paves a new route for THz single-pixel multispectral imaging with high reliability and low cost.

Transparent Object Reconstruction Based on Compressive Sensing and Super-Resolution Convolutional Neural Network

The detection and reconstruction of transparent objects have remained challenging due to the absence of their features and variations in the local features with variations in illumination. In this paper, both compressive sensing (CS) and super-resolution convolutional neural network (SRCNN) techniques are combined to capture transparent objects. With the proposed method, the transparent object’s details are extracted accurately using a single pixel detector during the surface reconstruction. The resultant images obtained from the experimental setup are low in quality due to speckles and deformations on the object. However, the implemented SRCNN algorithm has obviated the mentioned drawbacks and reconstructed images visually plausibly. The developed algorithm locates the deformities in the resultant images and improves the image quality. Additionally, the inclusion of compressive sensing minimizes the measurements required for reconstruction, thereby reducing image post-processing and hardware requirements during network training. The result obtained indicates that the visual quality of the reconstructed images has increased from a structural similarity index (SSIM) value of 0.2 to 0.53. In this work, we demonstrate the efficiency of the proposed method in imaging and reconstructing transparent objects with the application of a compressive single pixel imaging technique and improving the image quality to a satisfactory level using the SRCNN algorithm.

Re-Ordering of Hadamard Matrix Using Fourier Transform and Gray-Level Co-Occurrence Matrix for Compressive Single-Pixel Imaging in Low Resolution Images

One of the most active research fields in single-pixel imaging is the influence of the sampling basis and its order in the quality of the reconstructed images. This paper presents two new orders, ascending scale (AS) and ascending inertia (AI), of the Hadamard basis and test their performance, using simulation and experimental methods, for low sampling ratios (0.5 to 0.01) in low resolution images (up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$128\,{\times }\,128$ </tex-math></inline-formula> ). These orders were compared with two state-of-the-art orders, cake-cutting (CC) and total gradient (TG), using TVAL3 as the reconstruction algorithm and three noise levels. These newly proposed orders have better reconstructed image quality on the simulation data set (110 images) and achieved structure similarity index values higher than CC order. The experimental data set (2 images) showed that the AS and AI orders performed better with a sampling ratio of 0.5, while for lower sampling ratio the performance of AS, AI and CC was similar. The TG order performed worst in the majority of the cases. Finally, the simulation results present clear evidence that peak signal-to-noise ratio (PSNR) is not a reliable image quality assessment (IQA) metric to assess image reconstruction quality in the context of single pixel imaging.

Single-pixel compressive imaging based on random DoG filtering

As its name implies, compressive sensing aims to bring compression during sampling. However, the deployment of this technique depends on recovering a high fidelity image through a low number of measurements with a simple hardware and fast software. To this end, we introduce an encoding scheme that by filtering the scene acquires information about the image structure. To prepare a set of proposed encoding patterns, at the first step, a filter bank containing a number of Difference of Gaussian (DoG) kernels with different scales is prepared. Then, by randomly selecting the filters from the bank and under-sampling the scene with them at random points, each encoding pattern is constructed. The idea is inspired by the Human Visual System (HVS) that uses a set of size-tuned DoG kernels at each point in the field-of-view. These encoding patterns, which make a set of linearly independent vectors, form the rows of a structured measurement matrix. This matrix allows making relatively well-conditioned dictionaries by different sparsifying bases. The effectiveness of this method is confirmed by simulations and analyses.

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

Single-pixel imaging is an imaging technique that has recently attracted a lot of attention from several areas. This paper presents a study on the influence of the Hadamard basis ordering on the image reconstruction quality, using simulation and experimental methods. During this work, five different orderings, Natural, Walsh, Cake-cutting, High Frequency and Random orders, along with two different reconstruction algorithms, TVAL3 and NESTA, were tested. Also, three different noise levels and compression ratios from 0.1 to 1 were evaluated. A single-pixel camera was developed using a digital micromirror device for the experimental phase. For a compression ratio of 0.1, the Cake-cutting order achieved the best reconstruction quality, while the best contrast was achieved by Walsh order. For compression ratios of 0.5, the Walsh and Cake-cutting orders achieved similar results. Both Walsh and Cake-cutting orders reconstructed the images with good quality using compression ratios from 0.3. Finally, the TVAL3 algorithm showed better image reconstruction quality, in comparison with NESTA, when considering compression ratios from 0.1 to 0.5.

Improved method for compressive single-pixel imaging of a moving object

The traditional compressive imaging method for a moving object has the problem of repeated compressive sampling when the object stops moving or remains stationary. To solve this problem, this paper presents an improved method for compressive imaging in this situation. In contrast to traditional methods, the image is preprocessed before reconstruction. First, the Euclidean distance between the current measurement vector and the previous one is calculated, and then a threshold is used to determine whether the new measurement vector is valid. If the distance is below the threshold, the measurement vector is a repetition of the previous one and is discarded; otherwise, the measurement vector is valid and the measurement value is retained and used for image reconstruction. Theoretical analysis and simulation results show that the proposed method can eliminate the repeated sampling problem caused by a pause in the movement of an object, enabling effective reconstruction of the moving object image.

Single-Pixel Imaging with Origami Pattern Construction.

Single-pixel compressive imaging can recover images from fewer measurements, offering many benefits especially for the imaging modalities where array detection is unavailable. However, the widely used random projections fail to explore internal relations between coding patterns and image reconstruction. Here, we propose a single-pixel imaging method based on a deterministic origami pattern construction that can lead to a more accurate pattern ordering sequence and better imaging quality. It can decrease the sampling ratio, closer to the upper bounds. The experimental realization of this approach is a big step forward towards practical applications.

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.

Single‐pixel compressive imaging based on motion compensation

Compressive sensing (CS) theory enables single-pixel compressive imaging (SPCI) popular in optical remote sensing imaging, since single-pixel imager not only realises the acquisition and recovery of sparse images at the sampling rates significantly below the classical Nyquist rate, but also makes use of special detectors to improve sensitivity, dynamic range, spectral range and so on. However, its requirement of static imaging condition for the time-sequential measurements makes it difficult to apply in remote sensing, since the imaging platform is always in motion relative to the imaging scene. In this study, the authors develop a new method for SPCI on moving platform in optical remote sensing. Instead of ignoring the motion during sampling, the proposed method first builds the compressive sampling model based on motion compensation during sampling, and then reconstructs the image by frame-by-frame recovery method and joint recovery method, respectively, in the framework of CS theory, where the recovery condition is also analysed. To validate the basic principle and the physical feasibility of motion compensation, the authors implement the numerical simulations and optical experiments, where different conditions are exploited sufficiently. In addition, the proposed method for SPCI can be also extended into other applications, such as 360° annular imaging, multi-pixel compressive imaging as well as super-resolution imaging.

Simultaneous spatial, spectral, and 3D compressive imaging via efficient Fourier single-pixel measurements

Single-pixel imaging can capture images using a detector without spatial resolution, which enables imaging in various situations that are challenging or impossible with conventional pixelated detectors. Here we report a compressive single-pixel imaging approach that can simultaneously encode and recover spatial, spectral, and 3D information of the object. In this approach, we modulate and condense the object information in the Fourier space and detect the light signals using a single-pixel detector. The data-compressing operation is similar to conventional compression algorithms that selectively store the largest coefficients of a transform domain. In our implementation, we selectively sample the largest Fourier coefficients, and no iterative optimization process is needed in the recovery process. We demonstrate an 88% compression ratio for producing a high-quality full-color 3D image. The reported approach provides a solution for information multiplexing in single-pixel imaging settings. It may also generate new insights for developing multi-modality computational imaging systems.

Demonstration of acoustic source localization in air using single pixel compressive imaging

Acoustic source localization often relies on large sensor arrays that can be electronically complex and have large data storage requirements to process element level data. Recently, the concept of a single-pixel-imager has garnered interest in the electromagnetics literature due to its ability to form high quality images with a single receiver paired with shaped aperture screens that allow for the collection of spatially orthogonal measurements. Here, we present a method for creating an acoustic analog to the single-pixel-imager found in electromagnetics for the purpose of source localization. Additionally, diffraction is considered to account for screen openings comparable to the acoustic wavelength. A diffraction model is presented and incorporated into the single pixel framework. In this paper, we explore the possibility of applying single pixel localization to acoustic measurements. The method is experimentally validated with laboratory measurements made in an air waveguide.

A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging

Single-pixel imaging is an alternate imaging technique particularly well-suited to imaging modalities such as hyper-spectral imaging, depth mapping, 3D profiling. However, the single-pixel technique requires sequential measurements resulting in a trade-off between spatial resolution and acquisition time, limiting real-time video applications to relatively low resolutions. Compressed sensing techniques can be used to improve this trade-off. However, in this low resolution regime, conventional compressed sensing techniques have limited impact due to lack of sparsity in the datasets. Here we present an alternative compressed sensing method in which we optimize the measurement order of the Hadamard basis, such that at discretized increments we obtain complete sampling for different spatial resolutions. In addition, this method uses deterministic acquisition, rather than the randomized sampling used in conventional compressed sensing. This so-called ‘Russian Dolls’ ordering also benefits from minimal computational overhead for image reconstruction. We find that this compressive approach performs as well as other compressive sensing techniques with greatly simplified post processing, resulting in significantly faster image reconstruction. Therefore, the proposed method may be useful for single-pixel imaging in the low resolution, high-frame rate regime, or video-rate acquisition.

Two-step Holographic Imaging Method based on Single-pixel Compressive Imaging

We propose an experimental holographic imaging scheme combining compressive sensing (CS) theory with digital holography in phase-shifting conditions. We use the Mach-Zehnder interferometer for hologram formation, and apply the compressive sensing (CS) approach to the holography acquisition process. Through projecting the hologram pattern into a digital micro-mirror device (DMD), finally we will acquire the compressive sensing measurements using a photodiode. After receiving the data of two holograms via conventional communication channel, we reconstruct the original object using certain signal recovery algorithms of CS theory and hologram reconstruction techniques, which demonstrated the feasibility of the proposed method.