Fourier Single-pixel Imaging Research Articles

Two-step Fourier single-pixel imaging for secure and efficient hidden information transmission

In the rapidly evolving field of optical information security, single-pixel imaging (SPI) has emerged as a promising technique for hidden information transmission. However, traditional SPI methods face significant challenges, including the need for excessive modulation patterns and the vulnerability of encrypted information during transmission. Furthermore, the field lacks efficient methods to reconstruct both plaintext and ciphertext images from the same set of single-pixel measurements. Here, we propose a novel and efficient encryption strategy for Fourier single-pixel imaging (FSPI) that addresses these critical challenges. Our approach integrates two key innovations: a two-step Fourier-total variation conjugate gradient descent (F-TVCGD) method and a dual-key decryption mechanism. The F-TVCGD method significantly reduces the number of modulation patterns required for image reconstruction, enhancing efficiency and minimizing data redundancy. Our dual-key mechanism enables the reconstruction of both plaintext and ciphertext images from a single set of single-pixel measurements using different decryption keys, significantly enhancing security without compromising efficiency. The incorporation of Fourier symmetric patterns improves the convergence robustness of the symmetric gradient descent (SGD) algorithm, leading to superior performance under challenging conditions such as sparse sampling and noise attacks. Numerical simulations and optical experiments validate our method's improvements in both accuracy and security compared to traditional approaches. Our findings demonstrate that the proposed F-TVCGD and SGD strategies effectively address the challenges of excessive modulation patterns and information vulnerability in FSPI.

Adaptive sampling strategy for Fourier single-pixel imaging

Fourier single-pixel imaging is a technique that utilizes Fourier bases as illumination patterns to capture images. While the use of orthogonal bases enhances the imaging quality compared with other methods of single pixel imaging, the slow imaging speed has hindered its broader application. Acquiring only low-frequency Fourier coefficients enables capturing a significant portion of image information at low sampling ratio, thereby enhancing imaging speed. Nevertheless, truncating frequencies results in a loss of image detail and a decrease in picture quality. To address this challenge, this paper introduces an adaptive sampling strategy for Fourier single-pixel imaging, allowing for customized sampling distributions for each specific object. The sampling distribution is dynamically generated based on the acquired Fourier coefficients during the acquisition process, eliminating the need for prior information. Through extensive simulations and experimental analysis, this approach has demonstrated its ability to capture more complex image details at equivalent sampling ratios.

Fourier single-pixel imaging based on sampling prediction from intermediate frequencies

The imaging quality of Fourier single pixel imaging (FSI) is determined by the number of samples, therefore higher image quality requires more sampling times. Common low-frequency sampling methods compromise high-frequency signals to reduce the number of samples, but this will reduce the resolution of the reconstructed image. The recent adaptive sampling methods can reconstruct high-quality images with low sampling ratio, but the calculation of sampling trajectories is a time-consuming process. To improve imaging efficiency, we propose a fast sampling method based on intermediate frequency prediction for FSI. This method utilizes the continuity and directionality of important frequency distributions in the Fourier spectrum, according to which regions of important high-frequency components can be quickly predicted by firstly identifying important frequency components on the intermediate frequency ring. The simulation and experiment results demonstrated our method is 9 times faster than existing adaptive sampling methods in predicting sampling trajectories while maintaining similar image reconstruction quality for an image of 256 × 256 pixels under 5% sampling ratio. In addition, our method can efficiently sample important spectral components of images that has different frequency distributions, which proves that this method has the potential for wide applications.

Uniform-sampling foveated Fourier single-pixel imaging

Inspired by the retina of human eye, foveated imaging is an effective way to achieve high imaging quality and high imaging efficiency. However, with an inherent property of nonuniformity, advantages of foveated imaging cannot be played well due to the confliction with many theories having uniform properties. Thus, an innovative concept “uniform-sampling foveated imaging” is proposed to break the barrier of foveated imaging and uniform imaging. In this work, the concept is used as a uniform-sampling foveated Fourier single-pixel imaging (UFFSI) to achieve high imaging quality and high imaging efficiency of single-pixel imaging (SPI). First, by flexibly using the proposed three kinds of foveated pattern structures of foveated SPI, namely, “circular structure” via log-polar transformation, “rectangular structure” via log-rectilinear transformation and “rotating-rectangle structure” via log-rectilinear-rotation transformation, the total data number is reduced radically by the data redundancy reduction only requiring high resolution (HR) on regions of interest (ROIs). Next, by a nonuniform weight distribution processing based on the innovative concept of “uniform-sampling foveated imaging”, nonuniform sampling is transformed into uniform sampling to obtain the same uniform optical power as the uniform HR FSI, thus, sparse spectrum property and fast Fourier transform of FSI are used accurately and directly to obtain high imaging quality with further reduced measurements and fast reconstruction. Experimentally, in a large-scale scene, at an ultralow sampling ratio of 0.78 % referring to uniform HR FSI with 1024 × 768 pixels, by using UFFSI with 89 % reduction of data redundancy, ROI has a significantly better imaging quality with around 3.3times reduction in reconstruction time. We hope this work can provide a breakthrough point for future foveated imaging and real-time SPI in real life.

Isotropic and anisotropic edge detection based on Fourier single pixel imaging

In this paper, we propose a novel edge detection scheme based on Fourier single pixel imaging, capable of realizing both isotropic and anisotropic edge detection. In the scheme, we use a series of specific designed sinusoidal speckle patterns to illuminate the object. The corresponding total intensity of reflective light is then measured by a bucket detector. By performing the inverse Fourier transformation on the bucket detection results, an isotropic or anisotropic edge image of the object could be reconstructed directly. Simulation and experimental results demonstrate that our scheme can capture the isotropic or anisotropic edge images of the object with both direct and indirect line of sight to the object. Our scheme offers the advantages of achieving a clear and high-quality isotropic or anisotropic edge image with only one imaging reconstruction computing operation from sub-Nyquist measurements, which significantly reduces the number of measurements required for single pixel imaging. In addition, our scheme provides the benefits of achieving the single pixel anisotropic edge imaging, allowing one to decide the edges in an arbitrary direction to disappear while preserving the edges in other directions.

Low-sampling high-quality Hadamard and Fourier single-pixel imaging through automated optimization neural network

In this manuscript, an automated optimization neural network is applied in Hadamard single-pixel imaging (H-SPI) and Fourier single-pixel imaging (F-SPI) to improve the imaging quality at low sampling ratios which is called AO-Net. By projecting Hadamard or Fourier basis illumination light fields onto the object, a single-pixel detector is used to collect the reflected light intensities from object. The one-dimensional detection values are fed into the designed AO-Net, and the network can automatically optimize. Finally, high-quality images are output through multiple iterations without pre-training and datasets. Numerical simulations and experiments demonstrate that AO-Net outperforms other existing widespread methods for both binary and grayscale images at low sampling ratios. Specially, the Structure Similarity Index Measure value of the binary reconstructed image can reach more than 0.95 when the sampling ratio is less than 3%. Therefore, AO-Net holds great potential for applications in the fields of complex environment imaging and moving object imaging.

Partial hard occluded target reconstruction of Fourier single pixel imaging guided through range slice

Fourier single pixel imaging utilizes pre-programmed patterns for laser spatial distribution modulation to reconstruct intensity image of the target through reconstruction algorithms. The approach features non-locality and high anti-interference performance. However, Poor image quality is induced when the target of interest is occluded in Fourier single pixel imaging. To address the problem, a deep learning-based image inpainting algorithm is employed within Fourier single pixel imaging to reconstruct partially obscured targets with high quality. It applies a distance-based segmentation method to segment obscured regions and the target of interest. Additionally, it utilizes an image inpainting network that combines multi-scale sparse convolution and transformer architecture, along with a reconstruction network that integrates Channel Attention Mechanism and Attention Gate modules to reconstruct complete and clear intensity images of the target of interest. The proposed method significantly expands the application scenarios and improves the imaging quality of Fourier single pixel imaging. Simulation and real-world experimental results demonstrate that the proposed method exhibits the high inpainting and reconstruction capacity in the conditions of hard occlusion and down-sampling.

Self-adaptive sampling for Fourier single-pixel imaging using probability estimation

Self-adaptive sampling for Fourier single-pixel imaging using probability estimation

Denoised single-pixel imaging in a Fourier acquisition mode.

The degradation of imaging quality caused by environmental noise during Fourier single pixel imaging (FSPI) is a big problem. In this paper, we propose simple and efficient denoised single-pixel imaging schemes by using linear filters to reduce the impact. Two filters, such as an average filter and Gaussian filter, are employed, and their corresponding schemes are named SCH-A and SCH-G, respectively. The experimental and simulation results show that both schemes can effectively reduce the impact of environmental noise and have greater robustness in comparison with those using the deringing SPI and conventional SPI. Compared with SCH-A, the reconstructed image by SCH-G keeps more details and edges. With the increase of template size, SCH-A and SCH-G have better filtering effects with the same variance. Meanwhile, the larger the template size is, the better filtering effect SCH-A has. This conclusion is also applicable to SCH-G under the same variance.

Vector-guided Fourier single-pixel imaging.

The Fourier single-pixel imaging technique exhibits great potential for compressive imaging. However, the utilization of low sampling ratio can introduce unwanted ringing artifacts, thereby compromising the fidelity of reconstructed image detail. To address this issue, Vector guided Fourier single-pixel imaging (V-FSI) has been proposed. We analyze the statistical properties in the edge vector field derived from images with low sampling ratio. Based on this information, a tailored sampling map is designed to acquire the significant high-frequency components for image reconstruction. Experimental results demonstrate the remarkable effectiveness of the proposed V-FSI method in enhancing image quality. Notably, V-FSI exhibits exceptional capabilities in perceiving and preserving the details of the objects, particularly for objects characterized by pronounced periodicity and directionality.

High-resolution iterative reconstruction at extremely low sampling rate for Fourier single-pixel imaging via diffusion model.

The trade-off between imaging efficiency and imaging quality has always been encountered by Fourier single-pixel imaging (FSPI). To achieve high-resolution imaging, the increase in the number of measurements is necessitated, resulting in a reduction of imaging efficiency. Here, a novel high-quality reconstruction method for FSPI imaging via diffusion model was proposed. A score-based diffusion model is designed to learn prior information of the data distribution. The real-sampled low-frequency Fourier spectrum of the target is employed as a consistency term to iteratively constrain the model in conjunction with the learned prior information, achieving high-resolution reconstruction at extremely low sampling rates. The performance of the proposed method is evaluated by simulations and experiments. The results show that the proposed method has achieved superior quality compared with the traditional FSPI method and the U-Net method. Especially at the extremely low sampling rate (e.g., 1%), an approximately 241% improvement in edge intensity-based score was achieved by the proposed method for the coin experiment, compared with the traditional FSPI method. The method has the potential to achieve high-resolution imaging without compromising imaging speed, which will further expanding the application scope of FSPI in practical scenarios.

Physics-informed and simulation-driven optimization for binary Fourier single-pixel imaging.

Binary patterns are used in fast Fourier single-pixel imaging (FSI) technology to increase the imaging speed at the expense of spatial resolution or image quality. In this Letter, we propose a method for optimizing the image quality-speed trade-off that is informed by physical principles and driven by data from simulations. To compensate for the quantization error induced by binary dithering, convolution kernels are proposed and optimized for both low and high spatial frequencies. The proposed method has been demonstrated to work in both simulation and experiments. Other single-pixel imaging (SPI) techniques may also benefit from this approach.

FSPI-R&D: Joint reconstruction and detection to enhance the object detection precision of Fourier Single-Pixel Imaging

FSPI-R&D: Joint reconstruction and detection to enhance the object detection precision of Fourier Single-Pixel Imaging

S2O-FSPI: Fourier single pixel imaging via sampling strategy optimization

It is necessary to artificially set the sampling strategy of Fourier single-pixel imaging (FSPI) to obtain more useful information of the image under the assumption that the image information is mainly concentrated in the low-frequency part of the spatial frequency domain. However, due to the empiricism sampling strategy, it is easy to sample the spatial frequencies with low contribution to image reconstruction, resulting in a waste of sampling resources. To solve this problem, a one-stage FSPI reconstruction network with sampling strategy optimization is designed to obtain the efficient sampling strategy and improve the reconstruction quality. The proposed one-stage FSPI reconstruction network contains the sampling strategy optimization module and reconstruction module, which are jointly trained to obtain high-quality reconstructed results and efficient sampling strategy simultaneously. Experiments and numerical simulations demonstrate the effectiveness of the proposed method. Moreover, the geometric topology of the optimal sampling strategy for FSPI reconstruction trained on various categories of datasets is summarized. It is found that the dataset with similar categories have the similar geometric topology of the optimal sampling strategy, which provides support for sampling strategy selection in subsequent Fourier single-pixel imaging studies.

Image denoising and deringing for fourier single-pixel imaging based on upgraded weighted nuclear norm minimization

Single-pixel imaging techniques have been extensively studied because of the low requirements for the detector resolution and the low equipment cost. However, a large amount of noise and ringing commonly occur in the reconstructed images via previous single-pixel imaging methods at ultra-low sampling rates, which limits the real applications. In this paper, a novel Fourier single-pixel imaging method is proposed to reconstruct high-quality single-pixel imaging images at ultra-low sampling rates, which involves the stages of Fourier single-pixel imaging, block matching, upgraded weight nuclear norm minimization, and aggregation. To decrease the computational burden while important image details, block matching and aggregation are employed for the blocks divided from the low-quality image reconstructed by Fourier single-pixel imaging. To adapt the proposed upgraded weight nuclear norm minimization to different contaminated images, an adaptive scheme for the iterative regularization parameter is proposed to update the traditional weight nuclear norm minimization. Experimental results indicate that the proposed Fourier single-pixel imaging method based on upgraded weight nuclear norm minimization exhibits the capacity to reliably and effectively reconstruct high-quality images for single-pixel imaging at low sampling rates, even at the sampling rate of 1 %. Experimental results also demonstrate that the proposed method performs better image reconstruction than some existing single-pixel imaging.

Periodic Inverted Micropyramid-Si/Graphene Self-Powered Photodiode With Excellent Current Stability for Fourier Single-Pixel Imaging

Periodic Inverted Micropyramid-Si/Graphene Self-Powered Photodiode With Excellent Current Stability for Fourier Single-Pixel Imaging

Fast object imaging and classification based on circular harmonic Fourier moment detection.

Limited by the number of illumination fields and the speed of a spatial light modulator, single-pixel imaging (SPI) cannot realize real-time imaging and fast classification of an object. In this paper, we proposed the circular harmonic Fourier single-pixel imaging (CHF-SPI) for the first time to realize fast imaging and classification of objects. The light field distribution satisfies the circular harmonic Fourier formula, and the light intensity values of the single-pixel detector are equivalent to the circular harmonic Fourier moments. Then the target can be reconstructed under low sampling ratio by inverse transformation. Through simulation and experimental verification, clear imaging can be performed at a sampling ratio of 0.9%. In addition, circular harmonic Fourier moments are used to construct multi-distortion invariant to classify objects with rotation and scale change. The scale change multiples of objects can be calculated and the objects can be classified by using 10 light fields. It is of great significance to classify objects quickly without imaging.

An edge detail enhancement strategy based on Fourier single-pixel imaging

In this study, we propose an edge detection scheme based on Fourier single-pixel imaging, which extracts edges directly from the Fourier spectrum of the target object. The numerical simulations and experimental results show that the edges extracted by the proposed scheme have a better signal-to-noise ratio (SNR) than those extracted by the phase-shift sinusoidal pattern scheme. Furthermore, we investigate the effect of edge extraction in the case of undersampling and propose a plug-and-play edge detection algorithm to enhance the image. Our work combines Fourier single-pixel imaging with edge detection to extract the edges of a target object without imaging, providing a new idea for edge detection techniques.

Fourier Single-Pixel Imaging Based on Online Modulation Pattern Binarization

Down-sampling Fourier single-pixel imaging is typically achieved by truncating the Fourier spectrum, where exclusively the low-frequency Fourier coefficients are extracted while discarding the high-frequency components. However, the truncation of the Fourier spectrum can lead to an undesired ringing effect in the reconstructed result. Moreover, the original Fourier single-pixel imaging necessitated grayscale Fourier basis patterns for illumination. This requirement limits imaging speed because digital micromirror devices (DMDs) generate grayscale patterns at a lower refresh rate. In order to solve the above problem, a fast and high-quality Fourier single-pixel imaging reconstruction method is proposed in the paper. In the method, the threshold binarization of the Fourier base pattern is performed online to improve the DMD refresh rate, and the reconstruction quality of Fourier single-pixel imaging at a low-sampling rate is improved by generating an adversarial network. This method enables fast reconstruction of target images with higher quality despite low-sampling rates. Compared with conventional Fourier single-pixel imaging, numerical simulation and experimentation demonstrate the effectiveness of the proposed method. Notably, this method is particularly significant for fast Fourier single-pixel imaging applications.

Optical multiple-image authentication method based on Fourier single-pixel imaging and multiple logistic maps.

As a promising technique, the spatial information of an object can be acquired by employing active illumination of sinusoidal patterns in the Fourier single-pixel imaging. However, the major challenge in this field is that a large number of illumination patterns should be generated to record measurements in order to avoid the loss of object details. In this paper, an optical multiple-image authentication method is proposed based on sparse sampling and multiple logistic maps. To improve the measurement efficiency, object images to be authenticated are randomly sampled based on the spatial frequency distribution with smaller size, and the Fourier sinusoid patterns generated for each frequency are converted into binarized illumination patterns using the Floyd-Steinberg error diffusion dithering algorithm. In the generation process of the ciphertext, two chaotic sequences are used to randomly select spatial frequency for each object image and scramble all measurements, respectively. Considering initial values and bifurcation parameters of logistic maps as secret keys, the security of the cryptosystem can be greatly enhanced. For the first time to our knowledge, how to authenticate the reconstructed object image is implemented using a significantly low number of measurements (i.e., at a very low sampling ratio less than 5% of Nyquist limit) in the Fourier single-pixel imaging. The experimental results as well as simulations illustrate the feasibility of the proposed multiple-image authentication mechanism, which can provide an effective alternative for the related research.