Single-pixel panoramic imaging method based on Walsh-Hadamard base

Abstract

The invention discloses a single pixel panoramic imaging (SPPI) method based on a Walsh-Hadamard (W-H) base. The SPPI technology is widely applied to the fields of automatic driving, pipeline detection, low-altitude economy and the like, and according to a traditional scheme, although efficient panoramic perception is achieved through combination of a convex mirror and an imaging algorithm, the algorithm efficiency and precision still need to be optimized. According to the invention, a W-H orthogonal basis optimization panoramic annular modulation mode is introduced, and the SPPI technology is improved on one-dimensional and two-dimensional imaging algorithms. The method mainly comprises the following steps: 1) constructing a two-dimensional orthogonal ring modulation framework by adopting a W-H orthogonal basis to replace a random mode; 2) building a panoramic imaging system based on a passive modulation single-pixel camera; and 3) improving a single-pixel panoramic imaging model based on two-dimensional W-H base orthogonality and a V2DALM algorithm, and optimizing the panoramic imaging adaptation capability of the algorithm. According to the method, the imaging speed and quality are considered, and the optimal SPPI scheme can be selected for different application scene requirements such as high fidelity, high speed and speed-fidelity balance.

Description

Technical Field

[0001] This invention belongs to the field of computational imaging technology, and specifically designs a single-pixel panoramic imaging (SPPI) method based on the Walsh-Hadamard (WH) basis, with a particular focus on the radial / angular sampling rate independent control mechanism of single-pixel panoramic imaging. Background Technology

[0002] Single-pixel imaging technology uses a single-pixel detector to acquire images through time-domain coding and statistical calculation. Its core advantages are high system flexibility, low cost, and wide range of applications.

[0003] SPPI is a new branch of single-pixel imaging methods that has been developed in recent years. It can achieve 360° panoramic capture by introducing convex mirrors, providing new application scenarios for single-pixel imaging technology of polarized structure type patterns, and showing great application potential in fields such as intelligent navigation, pipeline inspection and drone obstacle avoidance.

[0004] However, its traditional panoramic solution has a dimensional compression defect: merging the radial and angular information of the circular panorama into a one-dimensional vector results in the loss of two-dimensional structural information, which limits the degree of freedom of sampling. During reconstruction, only the overall sampling rate can be adjusted, and it is impossible to independently optimize the resolution of a certain dimension.

[0005] The aforementioned shortcomings can lead to resource waste: when the clarity of one dimension needs to be improved while the requirements of another dimension have already been met, traditional solutions can only meet the imaging requirements of the dimension to be optimized by increasing the total sampling rate, which is undoubtedly redundant for the other dimension.

[0006] In addition, the compressed sensing algorithm relied upon by traditional single-pixel panoramic reconstruction schemes has high computational resource requirements, resulting in poor real-time performance and making it difficult to meet the needs of large-size, high-resolution scenes.

[0007] Furthermore, the signal energy of small modulation units in the logarithmic polarized panoramic modulation structure is more affected in a uniform noise environment. The local undersampling problem caused by traditional random modulation will make these small modulation unit regions more sensitive to noise, resulting in obvious visual disturbances during reconstruction and thus affecting the imaging quality.

[0008] Therefore, there is an urgent need to develop efficient single-pixel panoramic reconstruction algorithms and optimize panoramic modulation modes.

[0009] It is noted that the WH orthogonal basis (Hadamard basis based on Walsh sorting) consists of only +1 and -1. Its orthogonality allows it to achieve efficient signal reconstruction through matrix addition and subtraction operations. Moreover, compared with random modulation patterns, the modulation pattern based on the WH basis achieves global complementary distribution of signal energy through uniform modulation across the entire domain. Even if some measurements are disturbed, the signal integrity can still be restored through redundant information.

[0010] Furthermore, WH's binary characteristics not only ensure equalization of pixel modulation weights (avoiding the loss of low-weight pixel information in multi-level modulation), but also make it compatible with the maximum modulation rate of digital micromirror devices (DMDs), maximizing the modulation speed.

[0011] From the perspective of reconstruction steps, optimizing the Hadamard pattern sequence and improving the single-pixel reconstruction algorithm can further improve imaging efficiency and quality, which has precedents in related studies. Summary of the Invention

[0012] In view of this, this invention improves the original SPPI scheme based on the total variation (TV) one-dimensional compressed sensing algorithm by introducing WH orthogonal basis to optimize the modulation mode of SPPI, and supplements and improves the panoramic imaging mathematical model of the WH-based two-dimensional orthogonal algorithm and two-dimensional compressed sensing algorithm, and proposes an SPPI scheme based on the WH-based two-dimensional algorithm.

[0013] Compared to the traditional SPPI scheme based on random illumination mode, each scheme has significant improvements in imaging quality, noise resistance, and reconstruction speed. In particular, the two-dimensional panoramic imaging scheme, including schemes based on orthogonal algorithms and V2DALM algorithms, can provide a two-dimensional sampling strategy. That is, while keeping the total sampling rate constant, the specific values ​​of the radial / angular sampling rate can be flexibly determined to achieve better imaging reconstruction quality and noise resistance as needed.

[0014] The technical solution adopted in this invention mainly includes the following steps: A. A panoramic ring modulation framework is constructed by replacing the random mode with a WH orthogonal basis, noise interference is suppressed by global uniform energy distribution, and the resolution in the radial and angular directions is flexibly set; B. A panoramic imaging device based on a passively modulated single-pixel camera is built by using a convex mirror, a digital micromirror device (DMD), and a single-pixel detector; C. An improved single-pixel two-dimensional imaging algorithm (based on the orthogonal and V2DALM algorithms of the two-dimensional WH basis) is adopted and the panoramic imaging adaptation capability of the algorithm is optimized so that it supports independent adjustment of the radial / angular sampling rate, and adapts to different panoramic scene requirements with a two-dimensional sampling strategy.

[0015] Step A includes the following steps:

[0016] Let the required radial and angular resolutions for modulation be P and Q, respectively. The two-dimensional coded information is represented in logarithmic polar coordinates as: In the Cartesian system, the region corresponding to the non-collection target is designed as a central blind hole with radius r0, and the outer radius of the p-th ring is r. p The center radius is (where the radius of the center of the first ring is set to...) The polar angle is θ. q The variational polar radius is ξ p The increasing coefficient is ε, and the mapping relationship is as follows:

[0017] Let the m-th term of the M-th order Hadamard polynomial of Walsh sort be... ( Given a set of integers, and considering the non-negativity of optical modulation intensity in the real world, a "positive" correction is applied to the WH sequence:

[0018] Design of a one-dimensional WH ring modulation pattern: When it is necessary to measure a panoramic target of P×Q, the total number of samplings is s (S=P×Q), and each measurement corresponds to an L. S (L S For a positive WH polynomial sequence of order ≥S), to reduce redundancy, only the first S terms of the sequence are taken as the logarithmic polar coordinate information of a two-dimensional modulation pattern corresponding to a single measurement sequence, and it is converted into a ring modulation pattern by equations (1)-(2).

[0019] Design of a two-dimensional WH ring modulation pattern: When the total number of full samplings in the radial and angular directions are P and Q times respectively, each measurement in the radial and angular directions corresponds to an L. P (L P A sequence of positive WH polynomials of order ≥P and an L Q (L Q For a positive WH polynomial sequence of order ≥Q), to reduce redundancy, only the first P terms and the first Q terms of each sequence are taken as single measurement sequences, and they are encoded radially and angularly to obtain the logarithmic polar coordinate information of the modulation pattern. The logarithmic polar coordinate information of the modulation pattern is then converted into a ring modulation pattern by equations (1)-(2).

[0020] It is worth noting that the two-dimensional orthogonal algorithm requires P and Q to be powers of 2, while the one-dimensional and two-dimensional compressed sensing algorithm (TV / V2DALM) has no such restriction.

[0021] The specific steps for step B are as follows:

[0022] Optical path design: The convex mirror serves as a panoramic reflector, reflecting 360° panoramic light to the lens system; the lens group collimates and focuses the panoramic annular reflected light, making it clearly imaged on the target surface of the digital micromirror device; the DMD pre-stores annular modulation patterns, the center of which is strictly aligned with the optical center of the reflected light from the convex mirror; the intensity signal of the reflected light, spatially modulated by the DMD, is synchronously acquired by a single-pixel detector to obtain the measured intensity.

[0023] It is worth noting that, in order to reduce the interference of stray light reflected from the blind zone (non-target area with radius r0) of the convex mirror center on the modulation signal, a low-reflectivity film can be coated on the central area of ​​the convex mirror. At the same time, in order to improve imaging accuracy, the lens system, DMD and single-pixel detector are integrated into a closed dark box, retaining only the panoramic information incident window, which effectively suppresses ambient light noise. It is necessary to strictly ensure that the center of the DMD modulation pattern is aligned with the optical focus of the convex mirror, otherwise it will cause distortion of the reconstructed image. In addition, the DMD reflected modulation spot must cover the center of the effective photosensitive surface of the single-pixel detector. If the detector does not capture the intensity extreme area (such as the edge attenuation area), it will lead to a decrease in the accuracy of the reconstructed information.

[0024] Data Acquisition Process: During data acquisition, in order to suppress transient noise (mainly from power fluctuations and environmental interference), a multiple resampling strategy is implemented for a single DMD modulation pattern, and a stable intensity value is extracted through median filtering. If an FPGA synchronization module is configured, the DMD refresh and detector exposure window can be driven to achieve hardware-level timing alignment, eliminating intensity drift caused by photoelectric response delay.

[0025] The specific steps for step C are as follows:

[0026] Preparing Measurement Matrix Information: One-Dimensional Measurement Matrix: After T samplings, the equivalent measurement matrix using T single measurement sequences is represented as W′. T×S Each row corresponds to a modulation pattern; similarly, the two-dimensional measurement matrix: when radial sampling T P Second-rate Angular sampling T Q Second-rate When, the corresponding radial and angular measurement matrices are respectively expressed as

[0027] Intensity sequence: A series of reflected light intensity signals after spatial modulation by the DMD are synchronously acquired by a single-pixel detector to form an intensity sequence (where the one-dimensional scheme is B). T×1 The two-dimensional scheme is ).

[0028] The one-dimensional and two-dimensional compressed sensing algorithms, which substitute matrix information and intensity sequences, are expressed as follows: Among them, the reconstruction results are due to the non-uniformity of the unit size in the logarithmic polar coordinate system. The uneven intensity satisfies the following relationship with the panoramic information O: G is the gradient calculation matrix. It is the l1 norm. It is a cyclic difference matrix (defined by total variational regularization), reconstructed Solve optimization problems using the TV and V2DALM methods.

[0029] Similarly, the two-dimensional intensity information is substituted into the orthogonal reconstruction algorithm to calculate the panoramic information o: Attached Figure Description

[0030] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below, wherein:

[0031] Figure 1 A diagram of the SPPI experimental setup described in the first embodiment of the present invention.

[0032] Figure 2 This is a schematic diagram of the panoramic information to be imaged in the first embodiment of the present invention.

[0033] Figure 3 This is a schematic diagram of a ring-shaped panoramic target in the first embodiment of the present invention.

[0034] Figure 4 Two schematic diagrams of the modulation patterns described in the embodiments of the present invention are provided.

[0035] Figure 5 A schematic diagram of the panoramic information reconstruction procedure of V2DALM in the first embodiment of the present invention.

[0036] Figure 6 This is a schematic diagram comparing the single-pixel panoramic image recovered according to the method in the first embodiment of the present invention with that of a traditional scheme. Detailed Implementation

[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0038] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways than those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0039] In this embodiment, the SPPI experimental setup is as follows: Figure 1 As shown ((a) is an overview diagram of the SPPI experimental principle, and (b) and (c) are schematic diagrams of the optical information propagation in SPPI), Figure 2 The panoramic information is displayed on a flexible LED screen and surrounded by a convex mirror (150mm radius). The convex mirror (25mm radius of curvature) reflects the panoramic information, and the field of view is obtained by an optical lens system (ideally reflecting a ring-shaped panoramic target such as...). Figure 3 (As shown).

[0040] One-dimensional TV modulation pattern design (taking a resolution of P=64, Q=256, and a sampling rate of 50% as an example): Each sampling (a total of 8192(T) samplings), a single row vector is extracted from the 16384-order WH matrix and its first 16384 (P×Q) elements are truncated. The reshape function of Matlab is used to reorganize it into 64×256 two-dimensional logarithmic polar coordinate information. Then, the annular modulation pattern (a total of 8192 modulation patterns, with the corresponding measurement matrix being W′) is obtained through equations (1)-(2). 8192×16384 ).

[0041] Two-dimensional V2DALM modulation pattern design (taking a resolution of P=64, Q=256, radial sampling rate of 50%, and angular sampling rate of 70% as an example): Each sampling (total 32 (T P )×179(T Q (Sampling) A single row vector is extracted from a 64th-order Hadamard matrix, and its first 64 (P) elements are truncated as radial encoding. A single row vector is extracted from a 256th-order Hadamard matrix, and its first 256 (Q) elements are truncated as angular encoding. Encoding the radial and angular directions respectively yields two-dimensional logarithmic polar coordinate information. Then, through mapping relationships, the annular modulation pattern is obtained (a total of 5728 modulation patterns, corresponding to the measurement matrix W′). 32×64 and W′ 179×256 ).

[0042] Two-dimensional orthogonal modulation pattern design (taking a resolution of P=64, Q=256, radial sampling rate of 30%, and angular sampling rate of 30% as an example, because the imaging effect of the orthogonal scheme is greatly affected by the increase of the sampling rate under the interference of actual noise, and can only reconstruct approximate panoramic information at a low sampling rate): Each sampling (total 19 (T P )×76(T Q(Sampling) A single row vector is extracted from the 64th order Hadamard matrix and its first 64 (P) elements are truncated as radial encoding. A single row vector is extracted from the 256th order Hadamard matrix and its first 256 (Q) elements are truncated as angular encoding. The two-dimensional logarithmic polar coordinate information can be obtained by encoding the radial and angular directions respectively. Then, the annular modulation pattern (a total of 1444 modulation patterns, the corresponding measurement matrix is ​​W′) is obtained through equation (1)-(2). 19×64 and W′ 76×256 ).

[0043] The design of the circular panoramic modulation pattern directly determines the upper limit of the reconstructed image resolution. Here, a modulation pattern sequence of 64×256 is used, which corresponds to an upper limit of 64×256 resolution for the reconstructed panoramic result.

[0044] Circular panoramic modulation mode (e.g.) Figure 4 As shown, (a) and (b) are the modulation modes of the one-dimensional and two-dimensional schemes, respectively. The modulation light is pre-stored on the DMD (model DLP6500, refresh rate set to 2.5Hz) and collected using a single-pixel photodetector (model HAMAMATSU S2281, operating rate set to 20Hz).

[0045] A multiple resampling strategy is implemented for a single DMD modulation pattern: within a single DMD modulation period, each ring pattern is loaded and maintained at a stable exposure time of 0.4 seconds. During this period, the single-pixel detector synchronously acquires 8 intensity values ​​at a sampling interval of 50 milliseconds to form an original intensity sequence. Finally, the stable intensity values ​​are extracted as the intensity corresponding to each modulation mode to obtain the intensity sequence.

[0046] Based on the modulation pattern design in the example, the one-dimensional and two-dimensional intensity sequences (including V2DALM and orthogonal schemes) are obtained as follows: B 8192×1 B 32×179 B 19×76 )

[0047] Intensity information B 8192×1 and measurement matrix W′ 8192×16384 The data is fed into the TV algorithm to input the intensity information B. 32×179 and measurement matrix W′ 32×64 and W′ 179×256 Data is substituted into the V2DALM algorithm with two-dimensional modulation improvement (algorithm program as follows) Figure 5 As shown), the intensity information B 19×76 and measurement matrix W′ 19×64 and W′ 76×256 The data can be substituted into the orthogonal reconstruction algorithm to obtain the results.

[0048] Reconstruction result intensity correction: The final panoramic reconstruction result is as follows Figure 6 As shown in the figure ((a), (b) and (c) are the reconstruction results of the two-dimensional V2DALM, the orthogonal scheme and the one-dimensional TV scheme based on the WH basis, respectively, and (d) is the reconstruction result of the traditional one-dimensional TV scheme).

Claims

1. A single-pixel panoramic imaging method based on the Walsh-Hadamard basis, characterized in that: It features a panoramic single-pixel imaging mechanism with independent radial / angular sampling rate control; under the condition of keeping the total sampling rate constant, the sampling density in the radial and angular directions can be freely configured, thereby realizing the free distribution of modulation energy in two dimensions and the selective and efficient reconstruction of radial and angular structural information; even at a low total sampling rate, the ability to reconstruct panoramic information can be significantly improved by optimizing the two-dimensional sampling allocation.

2. The method according to claim 1, characterized in that... The imaging process includes the following steps: (1) A panoramic ring modulation framework is constructed by replacing random modes with Walsh-Hadamard orthogonal bases. Noise interference is suppressed by globally uniform energy distribution, and flexible settings for radial and angular resolution are achieved. Specifically, this includes: (1a) Set the radial and angular resolutions to P and Q according to the modulation requirements, establish the mathematical relationship between the Cartesian coordinate system and the logarithmic polar coordinate system, so that the logarithmic polar coordinate encoded information can be converted into a ring modulation pattern. (1b) Design one-dimensional Walsh-Hadamard ring modulation pattern log-polar coordinate encoding information, that is, for a panoramic target with a resolution of P×Q, from L s (L s Extract single-row vectors from a Walsh-Hadamard matrix of order ≥S, S=P×Q, truncate the first S elements and reassemble them into log-polar coordinate encoded information of order P×Q; (1c) Design two-dimensional Walsh-Hadamard ring modulation pattern logarithmic polar coordinate encoding information, i.e., from radial LP(L P ≥P) order and angular direction L Q (L Q Row vectors are extracted from the Walsh-Hadamard matrix of order ≥Q. The first P and first Q terms are truncated and then encoded in the radial and angular directions respectively to obtain two-dimensional log-polar coordinate encoded information. (2) A panoramic imaging system based on a passively modulated single-pixel camera is constructed using convex mirrors, digital micromirror devices, and single-pixel detectors, specifically including: (2a) Optical path design: The convex mirror reflects the 360° panoramic light to the lens system, the lens system focuses the reflected light onto the target surface of the digital micromirror device, the digital micromirror device pre-stores the ring modulation pattern and the center of the pattern is aligned with the optical center of the reflected light from the convex mirror, and the single pixel detector collects the intensity signal of the reflected light modulated by the digital micromirror device. (2b) Data Acquisition: One of the following methods shall be used: Synchronization method: Timing alignment is achieved by synchronously controlling the refresh of the digital micromirror device and the exposure of the detector, so that the sampling and modulation refresh of the single-pixel detector are kept at the same frequency and the intensity value is obtained. Asynchronous method: The modulation pattern of a single digital micromirror device is repeatedly sampled multiple times, and then a stable intensity value is extracted by median filtering; (3) An improved single-pixel two-dimensional imaging algorithm supporting independent adjustment of radial / angular sampling rates is used to complete the imaging of panoramic targets, specifically including: (3a) Construct the measurement matrix: Based on the dimensions of the measurement matrix, use one of the following methods: One-dimensional measurement matrix: After T samplings, the measurement matrix equivalent to using T single measurement sequences is denoted as W′. T×S Each row corresponds to a modulation pattern; Two-dimensional measurement matrix: when radial sampling T P Second-rate Angular sampling T Q Second-rate When, the corresponding radial and angular measurement matrices are denoted as follows: (3b) Acquiring the intensity sequence: The one-dimensional scheme yields the following intensity sequence: The intensity matrix is ​​obtained by the two-dimensional scheme. (3c) The total variation (TV) one-dimensional compressed sensing algorithm is used to reconstruct panoramic information from the one-dimensional measurement data; Panoramic information reconstruction is performed on two-dimensional measurement data using the two-dimensional variational augmented Lagrange multiplier (V2DALM) algorithm and the two-dimensional orthogonal algorithm, where the two-dimensional orthogonal algorithm requires P and Q to be powers of 2.

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