Fourier Single-pixel Imaging Research Articles

Learning-based adaptive under-sampling for Fourier single-pixel imaging.

In this Letter, we present a learning-based method for efficient Fourier single-pixel imaging (FSI). Based on the auto-encoder, the proposed adaptive under-sampling technique (AuSamNet) manages to optimize a sampling mask and a deep neural network at the same time to achieve both under-sampling of the object image's Fourier spectrum and high-quality reconstruction from the under-sampled measurements. It is thus helpful in determining the best encoding and decoding scheme for FSI. Simulation and experiments demonstrate that AuSamNet can reconstruct high-quality natural color images even when the sampling ratio is as low as 7.5%. The proposed adaptive under-sampling strategy can be used for other computational imaging modalities, such as tomography and ptychography. We have released our source code.

Efficient Fourier single-pixel imaging based on weighted sorting.

Fourier single-pixel imaging (FSI) has attracted increased attention in recent years with the advantages of a wide spectrum range and low cost. FSI reconstructs a scene by directly measuring the Fourier coefficients with a single-pixel detector. However, the existing sampling method is difficult to balance the noise suppression and image details within a limited number of measurements. Here we propose a new sampling strategy for FSI to solve this problem. Both the generality of the spectral distribution of natural images in the Fourier domain and the uniqueness of the spectral distribution of the target images in the Fourier domain are considered in the proposed method. These two distributions are summed with certain weights to determine the importance of the Fourier coefficients. Then these coefficients are sampled in order of decreasing importance. Both the simulations and experiments demonstrate that the proposed method can capture more key Fourier coefficients and retain more details with lower noise. The proposed method provides an efficient way for Fourier coefficient acquisition.

Fourier Single-Pixel Imaging Via Arbitrary Illumination Patterns

The traditional Fourier single-pixel imaging (FSI) utilizes cosinusoidal (grayscale) illumination patterns to reconstruct the image of an object. In this paper, we propose a universal mechanism in which FSI can be implemented via arbitrary periodic structured illumination not merely cosinusoidal illumination patterns. The proposed theory is verified by numerical simulations and optical experiments. In the experiment, we demonstrate the result of FSI with phase-shifting sawtooth (trapezoid, square) structured illumination modulated by a light projector. Moreover, in order to underline the high efficiency of the proposed mechanism, we perform FSI utilizing binary (square) illumination patterns generated directly by the digital micromirror devices (DMDs). Therefore, this mechanism can promote the high-performance and extensive applications of FSI in various scenarios.

Spatial temporal Fourier single-pixel imaging.

Generally, the imaging quality of Fourier single-pixel imaging (FSI) will severely degrade while achieving high-speed imaging at a low sampling rate (SR). To tackle this problem, a new, to the best of our knowledge, imaging technique is proposed: firstly, the Hessian-based norm constraint is introduced to deal with the staircase effect caused by the low SR and total variation regularization; secondly, based on the local similarity prior of consecutive frames in the time dimension, we designed the temporal local image low-rank constraint for the FSI, and combined the spatiotemporal random sampling method, the redundancy image information of consecutive frames can be utilized sufficiently; finally, by introducing additional variables to decompose the optimization problem into multiple sub-problems and analytically solving each one, a closed-form algorithm is derived for efficient image reconstruction. Experimental results show that the proposed method improves imaging quality significantly compared with state-of-the-art methods.

Image-free active autofocusing with dual modulation and its application to Fourier single-pixel imaging.

Autofocusing is widely used in applications where sharp image acquisition or projection is needed. Here we report an active autofocusing method for sharp image projection. The method works with wide-field structured illumination and single-pixel detection. To find the focus position, the method illuminates the target object with a set of 3-step phase-shifting Fourier basis patterns repeatedly and collects the backscattered light by using a single-pixel detector through a grating. Dual modulation-dynamic modulation by the time-varying structured illumination and static modulation by the grating-embeds the depth information for the target object in the resulting single-pixel measurements. As such, the focus position can be determined by recovering the Fourier coefficients from the single-pixel measurements and searching for the coefficient with the maximum magnitude. High-speed spatial light modulation not only enables rapid autofocusing but also makes the method work even when the lens system is in continuous motion or the focal length of the lens is continuously adjusted. We experimentally validate the reported method in a self-built digital projector and demonstrate the application of the method in Fourier single-pixel imaging.

DCT single-pixel detecting for wavefront measurement

In this work, a checkerboard pattern is used to divide an unknown field into the signal and reference parts, and based on the interference between them, we propose and demonstrate a discrete cosine transform single-pixel imaging (DCT-SPI) technique for measuring the spatial wavefront of an unknown field. Here, the discrete cosine transform (DCT) basis was used for generating the modulation patterns to acquire the spectrum of the wavefront by the phase-shifting technique, and the wavefront to be measured can be retrieved by applying a second-order correlation calculation. We first demonstrate the proposed DCT-SPI can be used for measuring the spatial wavefronts simulated by an amplitude SLM(A-SLM). As compared to the phase-shifting Fourier single-pixel imaging (FSPI) technique, the imaging speed of DCT-SPI is four times faster. In addition, under the RAM capacity limit of a digital micromirror device (DMD), DCT-SPI can realize a higher resolution. Further, we experimentally demonstrate that DCT-SPI can also be used for measuring the phase and amplitude of a dragonfly wing, which suggests it can be applied in the field of quantitative phase imaging with a higher speed and imaging resolution as compared with FSPI.

Polar coordinate Fourier single-pixel imaging.

Traditional single-pixel imaging uses Fourier patterns to modulate objects in the Cartesian coordinate system. The Cartesian Fourier pattern of single-pixel imaging is inappropriate to display in a circular field of view. However, a circular field of view is a widespread form of display in computed optical imaging. Here, circular patterns are adopted to adapt to the circular visual area. The circular patterns are displayed in polar coordinates and derived from two-dimensional Fourier transform in polar coordinates. The proposed circular patterns have improved imaging efficiency significantly from 63.66% to 100%. The proposed polar coordinate Fourier single-pixel imaging is expected to be applied in circular field-of-view imaging and foveated imaging.

Single-pixel color imaging based on a high-performance MAPbI3 perovskite photodetector

Metal halide perovskites with excellent optoelectronic properties show great promise in optical imaging. However, the complex fabrication process of high-density perovskite image sensors limits its development. Herein, we report a simple perovskite color imaging system by combining a single high-performance perovskite photodetector (PD) and the advanced Fourier single-pixel imaging algorithm. We introduce an atomic layer deposition-TiO2 layer and a Spiro-OMeTAD layer to optimize the band energy level arrangement of the perovskite PD, suppressing the dark current and improving the photocurrent of the device, respectively. The optimized perovskite PD with flat spectral response covering all visible wavelength exhibits a high responsivity of 238 mA/W at zero bias, a high special detectivity of 1.13 × 1013 Jones, and a linear dynamic range of 132 dB. In order to bypass the fabrication of the high-density perovskite PD array, we set up a single-pixel imaging system based on an optimized high-performance perovskite PD, demonstrating a high-quality color imaging result. This work provides a perspective for perovskite image sensors and injects vitality into the single-pixel imaging technology.

Fourier Single-Pixel Imaging Based on Adaptive Down-Sampling in Frequency Domain

Fourier Single-Pixel Imaging Based on Adaptive Down-Sampling in Frequency Domain

Full-resolution, full-field-of-view, and high-quality fast Fourier single-pixel imaging.

Fourier single-pixel imaging (FSI) uses Fourier basis patterns for spatial light modulation to acquire the Fourier spectrum of the object image. The object image can be reconstructed via an inverse Fourier transform. However, the Fourier basis patterns are inherently gray scale, which results in the difficulty that the patterns can hardly be generated at a high speed by using a commonly used spatial light modulator-digital micromirrors device. To tackle this problem, fast FSI, which uses upsampled and dithered Fourier basis patterns to approximate the gray scale patterns, has been reported, but the achievable spatial resolution has to be sacrificed in the pattern upsampling process. Here we propose a method that can achieve not only full-resolution but also full-field-of-view and high-quality FSI. The key to the proposed method is to use a new, to the best of our knowledge, error diffusion dithering algorithm combined with two different scanning strategies to generate two sets of binarized Fourier basis patterns for spatial light modulation. As a result, two images with a sub-pixel shift from each other are reconstructed. It results in the final high-quality reconstruction by synthesizing the two images. We experimentally demonstrate the method can produce a high-quality 1024 × 768-pixel and full resolution image with a digital micromirror device with 1024 × 768 micromirrors.

An adaptive and dynamic lens-flare-free single-pixel imaging method for spacecraft docking

Lens flare, the photographic artifact produced by reflecting and scattering a powerful incident light within a camera lens group, can severely degrade image quality and mislead the image-based processing task. Existing solutions typically depend on sophisticated optics design or complex image postprocessing algorithms to reduce lens flare. This paper demonstrates a direct reconstruction of the target feature by single-pixel imaging with a simple optics design and no image postprocessing. A novel sampling strategy is proposed for spacecraft docking, which utilizes Fourier single-pixel imaging methods to capture a specific feature at an ultralow sampling ratio. Simulation and experiments demonstrate that the proposed method can image the feature with a sampling ratio of 4.8% at a video frame rate while almost eliminating the impact of the ring effect. This paper provides a new perspective for achieving lens-flare-free, video-framerate and low-data-throughput imaging in space tasks, which has potential in many imaging-based applications.

Plug-and-Play algorithm for under-sampling Fourier single-pixel imaging

Plug-and-Play algorithm for under-sampling Fourier single-pixel imaging

Multimodality system of x-ray and fluorescence based on Fourier single-pixel imaging for small animals.

.Significance: The multimodality imaging system has become a powerful tool for in-vivo biomedical research. However, a conventional multimodality system generally employs two independent detectors, which is costly and bulky. Meanwhile, the geometric cocalibration and image registration between the imaging modalities are also complicated.Aim: To acquire the multimodality images for small animals with only one visible light sensed single-pixel detector.Approach: The system is built based on a structured detection Fourier single-pixel imaging architecture. A cesium iodide doped with thallium [CsI(Tl)] scintillator plate is placed behind the sample in x-ray imaging, so the x-ray images can be converted to be visible and sensed with the same single-pixel detector as applied in fluorescence imaging.Results: The spatial resolution of x-ray imaging was measured to be 1.81 mm, the sensitivity and the imaging depth of fluorescence imaging was evaluated to be and 4 mm, respectively. In vivo multimodality imaging of a C57BL/6 female mouse bearing tumor targeted with mCherry was carried out.Conclusions: We proposed an x-ray and fluorescence multimodality imaging system for small animals via the structured detection FSI architecture. The system is low cost, with a more compact structure, and free of image registration from different modalities. In vivo multimodality imaging results of a mouse bearing tumor demonstrate its capability for small animal research.

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.

Motion Deblurring for Single-Pixel Spatial Frequency Domain Imaging

The single-pixel imaging technique is applied to spatial frequency domain imaging (SFDI) to bring significant performance advantages in band extension and sensitivity enhancement. However, the large number of samplings required can cause severe quality degradations in the measured image when imaging a moving target. This work presents a novel method of motion deblurring for single-pixel SFDI. In this method, the Fourier coefficients of the reflected image are measured by the Fourier single-pixel imaging technique. On this basis, a motion-degradation-model-based compensation, which is derived by the phase-shift and frequency-shift properties of Fourier transform, is adopted to eliminate the effects of target displacements on the measurements. The target displacements required in the method are obtained using a fast motion estimation approach. A series of numerical and experimental validations show that the proposed method can effectively deblur the moving targets and accordingly improves the accuracy of the extracted optical properties, rendering it a potentially powerful way of broadening the clinical application of single-pixel SFDI.

Fourier single pixel imaging reconstruction method based on the U-net and attention mechanism at a low sampling rate.

There exists the contradiction between imaging efficiency and imaging quality for Fourier single-pixel imaging (FSI). Although the deep learning approaches have solved this problem to some extent, the reconstruction quality at low sampling rate is still not enough to meet the practical requirements. To solve this problem, inspired by the idea of super-resolution, this paper proposes the paralleled fusing of the U-net and attention mechanism to improve the quality of FSI reconstruction at a low sampling rate. This paper builds a generative adversarial network structure to achieve recovery of high-resolution target images from low-resolution FSI reconstruction results under low sampling rate conditions. Compared with conventional FSI and other deep learning methods based on FSI, the proposed method can get better quality and higher resolution results at low sampling rates in simulation and experiments. This approach is particularly important to high-speed Fourier single pixel imaging applications.

Ringing-free fast Fourier single-pixel imaging.

Fourier single-pixel imaging (FSI) allows an image to be reconstructed by acquiring the Fourier spectrum of the image using a single-pixel detector. Fast FSI is typically achieved by acquiring a truncated Fourier spectrum, that is, only low-frequency Fourier coefficients are acquired, with the high-frequency coefficients discarded. However, the truncation of the Fourier spectrum leads to undesirable ringing artifacts in the resulting image. Ringing artifacts produce false edges in the image and reduce the image contrast, resulting in image quality degeneration. The artifact is particularly severe in dynamic FSI, where the sampling ratio is generally ultra-low. We propose an effective and fast deringing algorithm to achieve ringing-free fast FSI. The algorithm eliminates ringing artifacts through 2D sub-pixel shifting and preserves image details through image fusion. Both static and dynamic imaging results demonstrate that the proposed method can reconstruct ringing-free images from under-sampled data in FSI. The deringing algorithm not only provides FSI with the capability of fast high-quality single-pixel imaging but also might prove its applicability in other areas, such as Fourier-based data compression algorithms.

Spatial frequency domain imaging technology based on Fourier single-pixel imaging

.SignificanceOptical properties (absorption coefficient and scattering coefficient) of tissue are the most critical parameters for disease diagnosis-based optical method. In recent years, researchers proposed spatial frequency domain imaging (SFDI) to quantitatively map tissue optical properties in a broad field of contactless imaging. To solve the limitations in wavebands unsuitable for silicon-based sensor technology, a compressed sensing (CS) algorithm is used to reproduce the original signal by a single-pixel detectors. Currently, the existing single-pixel SFDI method mainly uses a random sampling policy to extract and recover signals in the acquisition stage. However, these methods are memory-hungry and time-consuming, and they cannot generate discernible results under low sampling rate. Explorations on high performance and efficiency single-pixel SFDI are of great significance for clinical application.AimFourier single-pixel imaging can reconstruct signals with less time and space costs and has fewer reconstruction errors. We focus on an SFDI algorithm based on Fourier single-pixel imaging and propose our Fourier single-pixel image-based spatial frequency domain imaging method (FSI-SFDI).ApproachFirst, we use Fourier single-pixel imaging algorithm to collect and compress signals and SFDI algorithm to generate optical parameters. Given the basis that the main energy of general image signals is concentrated in the range of low frequency of Fourier frequency domain, our FSI-SFDI uses a circular-sampling scheme to sample data points in the low-frequency region. Then, we reconstruct the image details from these points by optimization-based inverse-FFT method.ResultsOur algorithm is tested on simulated data. Results show that the root mean square error (RMSE) of optical parameters is lower than 5% when the data reduction is 92%, and it can generate discernible optical parameter image with low sampling rate. We can observe that our FSI-SFDI primarily recovers the optical properties while keeping the RMSE under the upper bound of 4.5% when we use an image with resolution as the example for calculation and analysis. Not only that but also our algorithm consumes less space and time for an image with resolution, the signal reconstruction takes only 1.65 ms, and requires less RAM memory. Compared to CS-SFDI method, our FSI-SFDI can reduce the required number of measurements through optimizing algorithm.ConclusionsMoreover, FSI-SFDI is capable of recovering high-quality resolvable images with lower sampling rate, higher-resolution images with less memory and time consumed than previous CS-SFDI method, which is very promising for clinical data collection and medical analysis.

Adaptive Fourier Single-Pixel Imaging Based on Directional Energy Continuity in High Frequencies

Adaptive Fourier Single-Pixel Imaging Based on Directional Energy Continuity in High Frequencies

Multi-Target Tracking Using Windowed Fourier Single-Pixel Imaging.

The single-pixel imaging (SPI) technique enables the tracking of moving targets at a high frame rate. However, when extended to the problem of multi-target tracking, there is no effective solution using SPI yet. Thus, a multi-target tracking method using windowed Fourier single-pixel imaging (WFSI) is proposed in this paper. The WFSI technique uses a series of windowed Fourier basis patterns to illuminate the target. This method can estimate the displacements of K independently moving targets by implementing measurements and calculating windowed Fourier coefficients, which is a measurement method with low redundancy. To enhance the capability of the proposed method, we propose a joint estimation approach for multi-target displacement, which solves the problem where different targets in close proximity cannot be distinguished. Using the independent and joint estimation approaches, multi-target tracking can be implemented with WFSI. The accuracy of the proposed multi-target tracking method is verified by numerical simulation to be less than 2 pixels. The tracking effectiveness is analyzed by a video experiment. This method provides, for the first time, an effective idea of multi-target tracking using SPI.