A laguerre-gaussian single-pixel imaging pathing sampling method

Abstract

The present application relates to a kind of Laguerre-Gaussian single-pixel imaging path sampling method.Aiming at the technical problems such as no special sampling strategy, poor undersampling quality, easy to produce annular noise and edge blur of existing Laguerre-Gaussian single-pixel imaging, the present application combines the low-order energy concentration characteristics of Laguerre-Gaussian mode, designs three path sampling strategies of square, circle and triangle, and introduces TVAL3 total variation regularization reconstruction algorithm to form a double optimization scheme of sampling and algorithm.The present application improves the undersampling efficiency by preferentially collecting low-order mode, and the triangular sampling performance is optimal.TVAL3 can suppress noise and retain details, and can still image with high quality at a very low sampling rate of 5%~20%.This method fills the blank of Laguerre-Gaussian single-pixel imaging sampling strategy, can greatly reduce the number of measurements and improve the imaging speed, and is suitable for terahertz, infrared, scattering medium imaging and other scenes, and has good engineering and industrialization application prospect.

Description

Technical Field

[0001] This invention relates to the field of computational single-pixel imaging technology, and more specifically to a Laguerre-Gaussian single-pixel imaging path sampling method. Background Technology

[0002] Single-pixel imaging technology, with its unique advantages such as non-scanning, anti-scattering, and operation in non-visible light bands, has become one of the research hotspots in the field of computational imaging. This technology recovers the complex amplitude information of an object by projecting a modulated light field onto it, combined with intensity detection by a single-pixel detector and subsequent algorithmic reconstruction. This overcomes the limitations of traditional area array imaging detectors in terms of band adaptation and detection sensitivity. Therefore, single-pixel imaging technology has been widely used in terahertz imaging, infrared imaging, spectral imaging, polarization imaging, and scattering medium imaging.

[0003] Sampling strategy is the core factor determining modulation efficiency, data redundancy, and reconstruction quality, and its design and optimization have always been a key research focus in this field. Currently, mature sampling systems have been established for single-pixel imaging on traditional substrates such as Fourier and Hadamard. Fourier single-pixel imaging (FSI) utilizes the low-frequency energy concentration characteristic to design circular, rhomboid, and square paths, significantly improving undersampling efficiency. Hadamard single-pixel imaging (HSI) relies on matrix orthogonality and sparsity to propose random, square, circular, and zigzag sampling methods. In addition, Hadamard single-pixel imaging also employs one-dimensional sorting methods, such as Russian nesting doll order, cake-cutting order, and origami order. For natural images, FSI using circular paths and Hadamard HSI using zigzag paths are considered superior sampling strategies.

[0004] However, most related research focuses on classical substrates, and systematic exploration of sampling strategies for emerging substrates is still lacking. The Laguerre-Gaussian (LG) mode is an orthogonal eigensol of the paraxial wave equation, forming a complete orthogonal basis. Its angular and radial modulation advantages make LG single-pixel imaging uniquely competitive in vortex light and phase imaging, making it an emerging field. Existing LG imaging research mainly focuses on principles and detection methods, while sampling strategies remain a blank. Traditional sequential sampling ignores the energy distribution of LG modes, and undersampling easily leads to the loss of key low-order modes, resulting in a significant decrease in image quality. Traditional Simple Orthogonal Coefficient (SOC) algorithms are prone to distortion problems such as ring noise and edge blurring when processing undersampling data. In contrast, the TVAL3 algorithm in compressed sensing, with its total variational regularization characteristics, exhibits excellent denoising and detail preservation capabilities in sparse signal recovery, making it suitable for LG imaging reconstruction optimization. Summary of the Invention

[0005] (a) Purpose of the invention The purpose of this invention is to overcome the shortcomings of the prior art and provide a Laguerre-Gaussian single-pixel imaging path sampling method to achieve high-quality imaging at extremely low sampling rates of 5% to 20%, fill the gap in LG single-pixel imaging sampling strategies, reduce the number of measurements, and improve imaging speed.

[0006] (II) Technical Solution A Laguerre-Gaussian single-pixel imaging path sampling method includes the following steps: (1) Constructing a path-based sampling strategy Combining the low-order energy concentration characteristics of the LG mode, three path-based sampling methods—square, circular, and triangular—are designed, all centered on the (0,0) mode, prioritizing the acquisition of low-order LG modes to avoid the loss of key information.

[0007] (2) Light field detection and LG complex spectrum acquisition Light intensity signals are acquired by bucket detection, and the complex coefficients of the LG mode are calculated using a four-step phase shift method to complete the undersampled data acquisition.

[0008] (3) Image reconstruction using the TVAL3 algorithm The TVAL3 total variational regularization algorithm is introduced to construct a reconstruction model, which enhances the solution of the Lagrange and alternating direction transformation methods, suppresses ring noise, eliminates edge blurring, and improves the ability to preserve details.

[0009] (4) Output the optimal imaging result At extremely low sampling rates of 5% to 20%, a combination of path sampling and the TVAL3 algorithm is used to output high-quality reconstructed images.

[0010] (III) Inventive Principles In cylindrical coordinates, the light field distribution of the LG mode is as follows: (1) in, Represents polar coordinates. The radius of the light spot is... It is the waist radius. and These are the azimuth index and the radial index, respectively. It is a generalized Laguerre polynomial. Rayleigh length, It is the wave number. It is the ancient Yi phase shift. Also known as the topological charge number. The Laguerre-Gaussian (LG) mode is an eigensol of the paraxial wave equation and can form a complete orthogonal basis. For any complex amplitude object... We can decompose it using the LG model basis, which can be represented as: (2) in and These represent the amplitude and phase distribution of the object in cylindrical coordinates, respectively. The decomposition coefficients of a complex amplitude object in the azimuth angle represent the spiral harmonic decomposition. The decomposition coefficients of an object in the entire LG model include both angular and radial dimensions, i.e., the LG complex spectrum. and All coefficients are complex. In the experiment, only the LG complex spectrum of the object needs to be calculated. The analysis helps to understand the effects of the angular and radial dimensions of the LG model on object reconstruction. and It can be represented as: (3) (4) This is represented as the overlap integral between the object's complex amplitude and a single complex conjugate LG mode. However, in practice, single-pixel detectors only obtain intensity information and lose phase information. To calculate this optically... A four-step phase shift method is required.

[0011] The total light intensity received by the detector after collecting the lens can be expressed as: (5) in This indicates an additional phase shift applied to the LG mode. Let represent the complex amplitude of the reference beam. The four-step phase shift corresponds to four illumination beams with different additional phase shifts. After interacting with the object, the LG spectrum is obtained by detecting four intensity values, which can be expressed as: (6) By obtaining the complex coefficients of each LG mode using the same method, the complex amplitude of the object can be reconstructed using Formula 2. Furthermore, the number of pixels in the image can be arbitrarily adjusted by adjusting the number of pixels in the LG mode.

[0012] Most natural images are sparsity in the Laguerre-Gaussian domain; image information is typically concentrated in the low-frequency region, while subtle details are concentrated in the high-frequency components. Therefore, the orthogonal transform intensity coefficient matrix composed of frequency components is sparse. For example... Figure 2As shown, our analysis of the spectral energy distribution of the 128*128 pixel "Cameraman" image and the "USAF1951" resolution board reveals that most of the energy in the LG mode domain is concentrated in the low-order region, while the information of the higher-order LG coefficients is scarce or even close to zero. Therefore, by projecting only the low-order LG substrate pattern, we can obtain the low-order LG coefficients and directly set the higher-order coefficients to zero, thereby reducing the number of measurements.

[0013] (1) Traditional sequential sampling Traverse all in a fixed order Combinations, typically: Scanning is performed in row or column priority order. This sampling method completely ignores the distribution of pattern importance, and under undersampling conditions, it misses key patterns with equal probability.

[0014] (2) Square sampling by Centered on the target area, expand layer by layer along a square path. The sampling order for each layer is: left edge → top edge → right edge. Define the radius of the square. Sampling order according to Increasing, Same The contents are sorted according to the rules mentioned above.

[0015] (3) Circular sampling Centered at (0,0), according to the radius of the circle Layered, within the same radius layer, according to polar angle Sequential sampling.

[0016] (4) Triangle sampling By hierarchical parameters Sampling from smallest to largest, within each layer according to Decreasing (or increasing) order, and maintaining symmetry.

[0017] In the image reconstruction process of LG single-pixel imaging, the reconstruction algorithm is the key link to realize the restoration of the object's complex amplitude information from the LG complex spectral coefficients. Its solution logic and regularization characteristics directly determine the quality of the reconstructed image. Especially in undersampling scenarios, the algorithm's ability to suppress noise and restore details will be further amplified.

[0018] This technique introduces the Tval3 algorithm, which, based on total variational regularization, effectively handles image reconstruction problems in single-pixel imaging. In single-pixel imaging, the goal is to reconstruct a high-dimensional image from low-dimensional measurement data. This process can be represented by the following mathematical model: (7) in, This represents a one-dimensional arrangement of measurement coefficients; Represents a row rearrangement of a one-dimensional sequence based on an orthogonal basis; This represents a one-dimensional arrangement of the objects to be tested. The Tval3 algorithm is applicable to any structured real or complex basis. It is specifically designed to solve optimization problems with total variational regularization, and its objective function is: (8) in, express Total variation, express Paradigm. By introducing the enhanced Lagrangian method, the objective function can be written as: (9) in, and It is a Lagrange multiplier. and These are regularization parameters associated with the penalty term for each constraint, and the objective function is finally solved using an alternating direction transformation method.

[0019] (iv) Main advantages of the present invention The above-described technical solution of the present invention has the following advantages: (1) Filling the technological gap: For the first time, a path-based sampling scheme for LG single-pixel imaging was proposed, solving the problem of the lack of a dedicated sampling strategy in this field.

[0020] (2) Excellent undersampling performance: Path sampling has a much better imaging quality than traditional sequential sampling at extremely low sampling rates (5%~20%). Combined with the TVAL3 algorithm, it effectively eliminates ring noise and edge blurring, significantly improving image clarity and resolution.

[0021] (3) High practicality: It greatly reduces the number of measurements and improves imaging speed. It is suitable for terahertz, infrared, scattering media, biomedical, industrial inspection and other scenarios. Attached Figure Description

[0022] Figure 1 This is a flowchart of the path-based sampling imaging process based on the Laguerre-Gaussian pattern described in this method; Figure 2 These are the LG mode amplitude spectra of grayscale and binary images; Figure 3 These are different sampling paths of the LG mode described in this method; Figure 4 This is a schematic diagram of the imaging device described in this method; Figure 5 These are experimental reconstruction results of the USAF1951 resolution test target obtained by sampling from different paths at low sampling rates. Detailed Implementation

[0023] To make the technical solution, advantages and objectives of the present invention clearer, the method flow is described in conjunction with specific examples and the technical solution of the present invention is further explained with reference to the accompanying drawings.

[0024] Experimental setup such as Figure 4 A He-Ne laser with a wavelength of 632.8 nm was used as the light source. The laser beam was modulated into horizontally polarized light by a polarizer to maximize the efficiency of the SLM. It then passed through a spatial filtering system consisting of an objective lens, a pinhole, and lens L1 to generate a high-quality Gaussian beam. Simultaneously, the beam was expanded to a suitable size to completely cover the working area of ​​the SLM. Holograms of different LG modes and a reference beam, encoded using a checkerboard pattern, were loaded onto the SLM. The modulated interference field was projected onto the transmissive object through a 4f system consisting of lenses L2 and L3. An iris aperture was used in the 4f system to filter the first-order diffraction light from the SLM. Finally, a single-pixel detector collected the detection signal. The output signal of the photodetector was acquired by a data acquisition card as the detection value and used with the LG mode for object reconstruction. The SLM used in the experiment had 1024*1024 pixels. The hologram on the SLM used checkerboard encoding, with half of the pixels used to modulate the LG mode and the other half used to modulate the reference beam. The collected light intensity information is used to calculate the LG complex spectral coefficients using a four-step phase-shifting method. The collected LG complex coefficients are then input into the TVAL3 total variational regularization reconstruction model to finally achieve target imaging.

[0025] Figure 5 The experimental reconstruction results of the USAF1951 resolution test target using different sampling paths at low sampling rates are shown. It can be seen that at an extremely low sampling rate of 5%, the reconstructed image from traditional sequential sampling only reflects a small amount of target information. In contrast, the square, circular, and triangular sampling strategies utilize pattern space information more efficiently, clearly restoring the core features of the target, intuitively verifying the significant impact of sampling strategies on LGSI imaging performance. Furthermore, the comparison between Figures (d) and (e) demonstrates the optimization effect of the TVAL3 algorithm compared to the traditional SOC algorithm in image reconstruction. Figure (f) shows the magnified details of the line pairs within the dashed bounding box of the target object at a 20% sampling rate. Among the three sampling strategies, triangular sampling yields the richest image reconstruction details and the most complete information restoration, exhibiting the best imaging performance compared to the other two strategies. The comparison also reveals that the TVAL3 algorithm excels in improving LGSI image reconstruction performance, with the reconstructed image resolution significantly superior to the traditional SOC algorithm. Figure (g) shows the normalized intensity spectrum curves. These results demonstrate the significant differences between different methods, and the conclusions are verified through quantization.

[0026] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A Laguerre-Gaussian single-pixel imaging path sampling method, characterized in that, Includes the following steps: Combining the low-order energy concentration characteristics of the Laguerre-Gaussian (LG) mode, three path-based sampling strategies—square, circular, and triangular—are constructed to prioritize the acquisition of low-order LG modes. The LG complex spectral coefficients are calculated from the acquired light intensity signals using a four-step phase-shifting method. The TVAL3 total variational regularization algorithm is introduced into image reconstruction to suppress ring noise and improve detail preservation. At extremely low sampling rates of 5%-20%, high-quality imaging results are output after path sampling and optimization by the TVAL3 algorithm.

2. The Laguerre-Gaussian single-pixel imaging path sampling method according to claim 1, characterized in that: In the design of the LG pattern sampling strategy, square sampling expands layer by layer with a square radius, circular sampling is layered with a radial radius, and triangular sampling is based on layer parameters. Sampling is performed layer by layer from smallest to largest, with radial exponents used within each layer. Decreasing order, while maintaining angular indices. Symmetrical sampling prioritizes the acquisition of low-order LG modes; all three path-based sampling methods outperform traditional sequential sampling, with triangular sampling showing the best performance under undersampling conditions; the TVAL3 algorithm, constrained by total variational regularization, employs enhanced Lagrangian and alternating direction transformation methods for solving the problem, significantly outperforming the traditional SOC algorithm. It can achieve clear, noise-free image reconstruction under undersampling conditions during LG single-pixel imaging; the combination of triangular sampling and the TVAL3 algorithm at extremely low sampling rates of 5%-20% can more effectively utilize information in the mode space, more effectively suppress imaging noise, preserve image structural details, optimize sampling error robustness, and achieve high-quality imaging compared to the original sequential sampling and traditional SOC inverse transformation algorithm.

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