Underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization

Abstract

The invention provides an underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization, and the method comprises the following steps: reconstructing the original echo data of an underwater single-photon laser radar into a superposed photon number sequence corresponding to X * Y pixel points, the superposed photon number sequence corresponding to each pixel point is generated by carrying out photon number superposition based on a time bin lattice on multiple laser pulse echo signals received at the position of the pixel point, and the number M of laser pulses for carrying out photon number superposition on each pixel point is the same; performing depth-reflectivity estimation based on modal fusion on the superposed photon number sequence of each pixel point to obtain a depth map and a reflectivity map of the underwater target; and optimizing the depth map and the reflectivity map of the underwater target based on a collaborative variational imaging optimization strategy. By using the method provided by the invention, the high-quality reconstructed image of the underwater target can be quickly obtained.

Description

Technical Field

[0001] The present application belongs to the field of single-photon laser radar imaging technology, and relates to an underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization. Background Art

[0002] With the deepening of ocean exploration, long-distance, high-resolution imaging of underwater slow-moving targets has become a basic technology supporting many other ocean detection technologies and has received great attention. In traditional underwater target detection technology, optical detection is affected by the light attenuation and low contrast of the underwater imaging environment, resulting in reduced image quality; the current mainstream acoustic detection faces limitations in sound wave propagation speed and resolution, as well as signal attenuation and distortion caused by the inhomogeneity of seawater media, which greatly affects reliability and practicality.

[0003] The emergence of single-photon LiDAR provides a new approach for underwater detection and becomes an effective way to detect targets in weak light and high light attenuation intensity environments. Currently, single-photon LiDAR systems using scanning imaging are capable of single-photon detection of slow-moving underwater targets in terms of hardware. However, with the improvement of detection capability brought by photon-level detection sensitivity, photon events caused by noise inevitably lead to an increase in noise points and randomness in detection. In addition, the information loss caused by severe light attenuation greatly interferes with the selection and reconstruction of target information, ultimately affecting the detection results. Therefore, robust imaging algorithms are indispensable for improving the detection accuracy of single-photon detection systems.

[0004] According to the differences in imaging mechanisms, data processing methods and technical implementation, the existing single-photon lidar imaging algorithms are mainly divided into two categories: imaging methods based on neural networks and imaging algorithms based on traditional modeling methods. Among them, imaging algorithms based on modeling methods have low computing requirements and flexible parameter adjustment, and have been widely used. Among the more commonly used imaging algorithms based on traditional modeling methods, non-fixed pixel scanning time reconstruction methods are represented by methods such as first-photon algorithms and first-photon group algorithms that reconstruct targets based on "first-principle" photon information. For example, Peng Xiao et al. proposed a first-photon algorithm (Peng X, Zhao XY, Li LJ, et al. First-photon imaging via a hybrid penalty [J]. Photonics Research, 2020, 8(3): 325-330.) The target image is reconstructed based on the arrival time and echo intensity of the first photon. However, this algorithm easily identifies strong noise as the target reflection signal, which is not applicable to complex environments, especially those with low signal-to-noise ratio. For example, Chinese invention patent CN112305560A proposes a single-photon lidar imaging algorithm based on the first-photon group, but its criterion for screening the first-photon group is greatly affected by the statistical characteristics of the echo signal. Therefore, it has poor adaptability to complex environments, especially underwater environments, and requires manual parameter adjustment for different detection environments and detection processes. In addition, the detection time required to achieve reconstruction of the same underwater target under different conditions is not fixed. Although the fixed pixel acquisition time reconstruction method sacrifices a certain degree of flexibility and resource efficiency, it is suitable for standardized rapid imaging due to its consistency and ease of processing. However, the existing fixed pixel acquisition time reconstruction method uses median filtering, which ignores the inherent spatiotemporal connection of single photon data and the distribution characteristics of the signal, and also loses a large amount of edge information and high-frequency components. In an underwater environment with severe backscattering, the non-local spatial pixel filtering with excellent filtering performance also loses its robustness. Summary of the invention

[0005] The purpose of this application is to provide an underwater single-photon lidar target reconstruction method based on modal fusion and collaborative variational imaging optimization, which can make full use of the different statistical characteristics of single-photon accumulation corresponding to noise and scene information in the echo signal, and can efficiently complete the target reconstruction task under a variety of challenging imaging conditions without manual parameter adjustment. The method includes the following steps:

[0006] The original echo data of the underwater single-photon laser radar is reconstructed into a superimposed photon number sequence corresponding to X×Y pixel points, wherein the superimposed photon number sequence corresponding to each pixel point is generated by superimposing the photon number of multiple laser pulse echo signals received at its location based on the time bin grid, and the number of laser pulses M for superimposing the photon number of each pixel point is the same;

[0007] The depth-reflectivity estimation based on modal fusion is performed on the superimposed photon number sequence of each pixel point to obtain the depth map and reflectivity map of the underwater target;

[0008] The depth map and reflectivity map of underwater targets are optimized based on the collaborative variational imaging optimization strategy.

[0009] Furthermore, for the superimposed photon number sequence of any pixel point, depth-reflectivity estimation based on modal fusion is performed, including the following steps:

[0010] Use a sliding window of preset length to slide stepwise on the superimposed photon number sequence of the pixel point with a time bin as a step length to intercept multiple candidate groups;

[0011] Select the candidate group with the largest number of photons as the group where the target signal is located;

[0012] Determine the underwater target depth corresponding to the pixel point based on the time bin number corresponding to the maximum value element in the group where the target signal is located, and

[0013] The reflectivity of the underwater target corresponding to the pixel is determined based on the sum of the number of photons in the group where the target signal belongs.

[0014] Preferably, the underwater target is a slow-moving target, and the lower limit of M is 5 times and / or the length of the sliding window is between 5 time bins and 9 time bins.

[0015] Preferably, the underwater single-photon lidar target reconstruction method based on modal fusion and collaborative variational imaging optimization also includes a signal-noise separation operation based on the statistical characteristics of the photon number distribution on the superimposed photon number sequence of each pixel point, and the signal-noise separation operation includes at least one of a mask operation and a matched filter.

[0016] Furthermore, the mask operation is specifically:

[0017]

[0018] Where x and y are the horizontal and vertical coordinates of the pixel point, B and B masked are the superimposed photon number sequences before and after the mask operation, j is the index in the time axis direction, and BlindBin is the length of the mask.

[0019] Preferably, the following steps are further performed before performing the mask operation:

[0020] Performing a photon number superposition operation based on N laser pulses and a depth estimation on the original echo data, wherein N is less than or equal to M;

[0021] The length of the BlindBin is determined based on the result of the pre-estimation of the depth.

[0022] Furthermore, the matched filtering is specifically:

[0023] B MF (x,y,j)=B(x,y,j)*h(j),

[0024] Wherein, h(j) is the pulse response determined based on the pulse width and waveform of the laser pulse, B MF is the superposition photon number sequence after matched filtering.

[0025] Furthermore, the collaborative variational imaging optimization strategy includes performing a Wiener-Hopf adaptive filtering operation, a total variational deconvolution operation, and a morphological reconstruction operation of fusing global features with local features on the depth map and / or reflectivity map.

[0026] Furthermore, the Wiener-Hopf adaptive filtering operation is performed by the following formula:

[0027]

[0028] Among them, D noisy , R noisy are the depth map and reflectivity map before adaptive filtering, D Wiener-Hopf , R Wiener-Hopf They are the depth map and reflectivity map after adaptive filtering, H D , H R are the impulse response functions of the Wiener-Hopf filter corresponding to the depth map and reflectivity map, respectively. k and l are the neighboring pixels of pixel x and y. are the noise powers of the depth map and reflectivity map, respectively, are the local variances of the depth map and reflection intensity map at pixel x and y respectively.

[0029] Furthermore, the total variation deconvolution operation is performed by the following formula:

[0030]

[0031] Among them, I Wiener-Hopf is the depth map D before the total variation deconvolution operation Wiener-HopfOr reflectivity map R Wiener-Hopf ,

[0032] I deconvTV is the depth map or reflectivity map after the total variation deconvolution operation, I is the image variable to be optimized in the iterative optimization process, λ is the regularization parameter of the data fidelity term, τ is the regularization parameter of the total variation term, is the image gradient operator, ||·||2 is the L2 norm, ||·||1 is the L1 norm, PSF is the point spread function, and σ is the standard deviation of the Gaussian beam.

[0033] Furthermore, the morphological reconstruction operation includes edge detection and morphological closing operation, distance transformation and morphological reconstruction, and connected region processing and image enhancement performed sequentially.

[0034] Furthermore, the edge detection and morphological closing operation are performed by the following formula:

[0035] E closed =close(C(I deconvTV ),S(N)),

[0036] Among them, C(I deconvTV ) is the image I deconvTV Extract edges, close represents the morphological closing operation, S(N) is the neighborhood of pixels in the image, E closed It is the edge map obtained by edge detection and morphological closing operation.

[0037] Furthermore, the distance transformation and morphological reconstruction are performed by the following formula:

[0038]

[0039] Where W(~Eclosed) is E closed The distance transform of the complement of , max(·) is the normalization operation, Reconstruct() is the morphological reconstruction function, I Reconstructed is the image after morphological reconstruction.

[0040] Furthermore, the connected region processing and image enhancement are performed by the following formula:

[0041]

[0042] Among them, LabelImg==p represents the connected area marked as p, mode(·) is the value of all pixels in the statistical area, ∪ is all connected areas, num is the number of connected areas, For image clarity processing, I final Depth map or reflectivity map generated for final optimization.

[0043] Preferably, the image sharpening process is performed using a trained Real-ESRGAN model.

[0044] The embodiment of the present application provides an underwater single-photon lidar target reconstruction method based on modal fusion and collaborative variational imaging optimization, which makes full use of the difference in the statistical characteristics of the time distribution of noise and scene information photons in the echo signal of the single-photon lidar, separates the target signal and estimates the flight time and reflection intensity from the single-photon sequence accumulated by multiple laser pulses, further improves the total variational smoothing constraint, adds adaptive filtering and global morphological constraint structure to deconvTV, and dynamically adjusts the filtering parameters to better maintain the image edges and textures while suppressing abnormal pixels, protect the naturalness and visual details of the image, so as to quickly obtain high-quality reconstructed images of underwater targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 A schematic diagram of the system architecture of an underwater single-photon laser radar;

[0046] Figure 2 A flowchart of an underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization provided according to an embodiment of the present application;

[0047] Figure 3A A schematic diagram of the data structure of the original echo signal of the underwater single-photon laser radar provided according to an embodiment of the present application;

[0048] Figure 3B A schematic diagram of a superposition photon number sequence provided according to some specific embodiments;

[0049] Figure 4 A schematic diagram of a superimposed photon number sequence of each pixel point of three-dimensional reconstruction provided according to an embodiment of the present application;

[0050] Figure 5 A flowchart of a depth-reflectivity estimation operation based on modal fusion provided according to an embodiment of the present application;

[0051] Figure 6 A depth map and a reflectivity map obtained after depth-reflectivity estimation according to an embodiment of the present application;

[0052] Figure 7 A flowchart of an underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization provided according to an embodiment of the present application;

[0053] Figure 8 A schematic diagram of the layout of an experimental water pool provided according to specific embodiment 1 of the present application;

[0054] Fig. 9 A front view of an underwater target provided according to specific embodiment 1 of the present application;

[0055] Fig.10 A three-dimensional structural diagram of an underwater target provided according to specific embodiment 1 of the present application;

[0056] Fig.11 A schematic diagram of underwater propagation of a laser pulse provided according to specific embodiment 1 of the present application;

[0057] Fig. 12A The underwater target reconstruction result using 50 laser pulses provided in the specific embodiment 1 of the present application;

[0058] Fig. 12B The underwater target reconstruction result using 500 laser pulses provided in the specific embodiment 1 of the present application;

[0059] Fig.13A Reconstruction results for underwater targets using the peak algorithm;

[0060] Fig. 13B Reconstruction results for underwater targets using the cross-correlation algorithm;

[0061] Fig. 13C Reconstruction results for underwater targets using the first-photon algorithm;

[0062] Fig.13D Reconstruction results for underwater targets using the first photon group algorithm;

[0063] Fig.14 A schematic diagram of an underwater target provided according to specific embodiment 2 of the present application;

[0064] Fig.15A This is the underwater target reconstruction result of 32 pixels / 10 laser pulses provided in specific embodiment 2 of the present application;

[0065] Fig. 15B The underwater target reconstruction result of 64 pixels / 10 laser pulses provided in specific embodiment 2 of the present application;

[0066] Fig. 15C This is the underwater target reconstruction result of 128 pixels / 20 laser pulses provided in specific embodiment 2 of the present application. DETAILED DESCRIPTION

[0067] Hereinafter, the present application will be further described based on preferred embodiments with reference to the accompanying drawings.

[0068] In the description of the embodiments of the present application, it should be noted that if the terms "upper", "lower", "inside", "outside", etc. indicate an orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship in which the products of the embodiments of the present application are usually placed when in use, it is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application. In addition, in the description of the present application, in order to distinguish different units, the words first, second, etc. are used in this specification, but these are not limited by the order of manufacture, nor can they be understood as indicating or implying relative importance, and their names may be different in the detailed description and claims of the present application.

[0069] The vocabulary in this specification is used to illustrate the embodiments of the present application, but is not intended to limit the present application. It should also be noted that, unless otherwise clearly specified and limited, the terms "disposed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection, a direct connection, an indirect connection through an intermediate medium, or a connection between the two elements. For those skilled in the art, the specific meanings of the above terms in this application can be specifically understood.

[0070] In order to clearly illustrate the technical solution provided in this application, the implementation method of target reconstruction using underwater single-photon lidar is first introduced.

[0071] <1. Introduction to Scanning Imaging Single Photon LiDAR Technology>

[0072] Figure 1 This is a system architecture diagram of an underwater single-photon lidar. The system is a scanning imaging underwater single-photon lidar rather than a staring imaging method. The reason is that for complex and changeable underwater environments, the scanning system can adapt to different detection needs by adjusting the scanning mode and speed, which is especially important for changeable underwater environments.

[0073] like Figure 1As shown in the figure, the optical part of the system is mainly composed of FPGA (Field-Programmable Gate Array), laser, galvanometric scanner, Single-Photon Avalanche Diode (SPAD), Time-Correlated Single Photon Counting (TCSPC), and optical devices such as beam expander, open hole mirror, optical filter and lens, which are arranged in a sealed cabin. Among them, FPGA is connected to the host controller through a sealed port to provide a trigger signal to the laser. The laser pulse generated by the laser after triggering is expanded to a suitable diameter through the beam expander, and under the control of the galvanometric scanner, it is emitted into a propagation medium such as water through a sapphire glass window to achieve point-by-point scanning of the target.

[0074] The photon signal reflected from the target is reflected by the aperture mirror, the lens converges the light beam, and the stray light is filtered by the optical filter, and then enters the single-photon avalanche diode, which converts the optical signal into a detection signal in the form of an electrical signal and sends it to the time-correlated single-photon counter.

[0075] The time-correlated single-photon counter simultaneously receives the detection signal from the single-photon avalanche diode and the synchronization signal of the laser, thereby obtaining the flight time of each single photon. The above flight time information is transmitted to the FPGA. The FPGA obtains the time histogram (Time Histogram) corresponding to each scanning point by counting the number of photons received in each time period (generally expressed in time bins in picoseconds or nanoseconds). After the time histogram (Time Histogram) corresponding to each scanning point is sent to the host as the original echo data, the underwater target image can be reconstructed through various target reconstruction algorithms.

[0076] In addition, if Figure 1 As shown, the system also includes modules such as a power supply and a heat exchanger to realize power supply and heat dissipation for system equipment.

[0077] After obtaining the above raw echo data, various target reconstruction algorithms can be used to process it to reconstruct the depth map and reflectivity map of the underwater target. The depth map can reflect whether there is a target in the scanning area and the distance between each position of the target and the system, and the reflectivity map reflects the reflection intensity information of each location of the target.

[0078] It should be emphasized that the number of laser pulses emitted at the same position is often closely related to the technical route adopted by the target reconstruction algorithm. This is because the measurement principle of single-photon lidar determines that information such as the depth of a certain position of the target is represented by the statistical characteristics of photons returned by multiple laser pulses. Therefore, for different algorithms, the number of laser pulses emitted at the same position required to meet the accuracy requirements may vary from a few times to hundreds or even thousands of times, which will significantly affect the amount of data that needs to be processed and the speed of target reconstruction.

[0079] In addition, when certain algorithms are used for scanning and target reconstruction, the number of laser pulses emitted at different positions may not be the same. For example, Chinese invention patent CN112305560A discloses a single-photon laser radar rapid imaging method based on the first photon group. The technical route of this method is: continuously emit laser pulses to the same position, and after each emission, find an area that can satisfy the existence of N photon counts in the ε time neighborhood from the collected photon counting results. If it cannot be found, continue to emit laser pulses to the position until the area is found for the first time (called the first photon group), and then the corresponding number of emission pulses Num and the counting time of N photons {t1, t2, ..., t N}; according to the characteristic that the Gaussian function can approximate the time waveform of the laser pulse echo, {t1, t2, ..., t N} is used as the estimated value of the flight time of the pulse signal emitted to the position, and then the estimated value of the depth corresponding to the position is obtained; according to the properties of the Poisson random process, -ln(1-N / Num) is used as the estimated value of the reflection intensity information of the underwater target at this position.

[0080] The above method has the following problems in the process of underwater target detection and data processing:

[0081] 1) This method needs to judge whether the first photon group is received based on the N-ε condition (also known as the μ-ε condition) for screening the first photon group. Therefore, it completely judges whether the target echo appears based on the statistical characteristics of the collected photon counts. In order to screen out the first photon group at a certain position, the number of laser pulses that need to be emitted at that position is not fixed, which not only causes the single-photon laser radar to scan different positions of underwater targets at different times, but also in some harsh underwater environments, the number of pulses that need to be emitted may exceed the time allowed for actual measurement, which undoubtedly greatly prolongs the data processing time and fails to meet the needs of rapid imaging of slow-moving underwater targets;

[0082] 2) Whether the N-ε condition (also known as μ-ε) used to screen the first photon group is set reasonably will have a fundamental impact on the estimation result: the larger N is and the smaller ε is, the more tightly the definition of the first signal photon group is restricted, and a large number of very concentrated photon counts must appear to obtain the first signal photon group. This results in higher robustness to noise (because the probability that the noise just happens to gather to meet the N-ε condition is smaller), but it obviously requires more accumulation time to obtain the first signal photon group that meets the N-ε condition, which will undoubtedly lead to an increase in the number of laser pulses Num for screening the first photon group, reducing the efficiency of the entire method. On the contrary, if N is increased and ε is reduced, the probability of noise meeting the N-ε condition and being unrecognized as the first photon group will undoubtedly increase.

[0083] Obviously, each time the measurement of underwater targets is carried out, it is necessary to reset the values ​​of N and ε based on prior knowledge according to the actual underwater environment, laser characteristics and underwater target reflection characteristics, and then repeatedly optimize according to the measurement results. Otherwise, it is very easy to have problems such as too long measurement time or too high misrecognition rate. At the same time, this method completely estimates the echo flight time and reflection intensity of underwater targets based on the probability model, and the physical image is not clear, especially when the first photon group is screened incorrectly, the estimation of the target echo flight time and reflection intensity will be completely meaningless.

[0084] It can be seen that the optimization of the target reconstruction algorithm and the improvement of the hardware system complement each other and jointly determine the speed and accuracy of the target reconstruction. To this end, the present application improves the existing target reconstruction algorithm based on underwater single-photon lidar, and proposes an underwater single-photon lidar target reconstruction method based on modal fusion and collaborative variational imaging optimization. This method can effectively utilize the basic characteristics of the different distributions of noise and scene information photons in the echo signal in the time histogram to decompose the pulse accumulated single-photon original signal, and use the optimization strategy to enhance the target depth and reflectivity image. At the same time, there is no need to manually adjust the parameters during each measurement to ensure that the effective photon flight time information can be captured. Therefore, it can meet the needs of fast and high-precision target reconstruction of slow-moving targets in various underwater environments.

[0085] <2. Framework of this application method>

[0086] Figure 2 The flowchart of the underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization provided by the present application is shown. As shown in the figure, the method includes the following steps:

[0087] Step 100, reconstructing the original echo data of the underwater single-photon laser radar into a superimposed photon number sequence corresponding to X×Y pixel points;

[0088] Step 200, performing depth-reflectivity estimation based on modal fusion on the superimposed photon number sequence of each pixel point to obtain a depth map and a reflectivity map of the underwater target;

[0089] Step 300: Optimize the depth map and reflectivity map of the underwater target based on the collaborative variational imaging optimization strategy.

[0090] Among them, step 100 is used to generate a superimposed photon number sequence corresponding to each pixel point on a two-dimensional plane; step 200 estimates the depth and reflectivity by comprehensively considering the statistical characteristics and peak characteristics of the superimposed photon number sequence of each pixel point, thereby preliminarily generating a two-dimensional depth map and reflectivity map; step 300 improves the accuracy and stability of underwater target image reconstruction by collaboratively optimizing the total variation deconvolution algorithm of the existing image and morphological reconstruction.

[0091] The above steps are described in detail below in conjunction with the accompanying drawings and preferred implementations.

[0092] <3. Reconstruction of original echo data>

[0093] Figure 3A FIG. 4 shows the data structure of the original echo obtained by scanning an underwater target by an underwater single-photon laser radar system in some embodiments, such as Figure 3A As shown, when an area of ​​X pixels in the horizontal direction and Y pixels in the vertical direction is scanned, X×Y rows of echo data can be obtained, wherein the element value of any row corresponds to the number of photons received at each time bin when multiple laser pulses are emitted at the location of a certain pixel.

[0094] Without loss of generality, for a pixel x,y,(x∈[1,X]&y∈[1,Y]), each laser pulse emitted to it intercepts the first Z time bins, and the time bin sequence corresponding to each laser pulse can be obtained Correspondingly, the number of photons received by the point during each laser pulse irradiation can be expressed as the following M photon number sequences of length Z:

[0095]

[0096] …,

[0097]

[0098] The above M sequences are arranged head to tail to form the echo data of a pixel point. The echo data of each pixel point are arranged in rows to obtain Figure 3A Raw echo data shown.

[0099] Since the imaging principle of single-photon lidar determines that the sequence of received photon numbers obtained by a single laser pulse cannot reflect the characteristics of the target, especially due to optical attenuation and other reasons, some laser pulses may have no photons returned at all. Therefore, only through multiple laser pulse measurements can a statistical distribution of photon arrival times with actual physical significance be generated.

[0100] In an embodiment of the present application, after acquiring the above echo data, the echo data of each pixel is subjected to photon number superposition based on a time bin to obtain a superimposed photon number sequence corresponding to each pixel.

[0101] Specifically, for any pixel x, y, the elements corresponding to the same time bin in the M photon number sequences are superimposed one by one, for example:

[0102] For the first time bin make

[0103] For the second time bin make

[0104] By analogy, we can get the superimposed photon number sequence corresponding to each pixel point (x, y):

[0105]

[0106] Figure 3B The superimposed photon number sequence at two pixels is shown as an example. After obtaining the superimposed photon number sequence corresponding to each pixel point (x, y), further, it can be Figure 4 As shown, it is reconstructed according to a data structure of X pixels in the horizontal direction and Y pixels in the vertical direction, and finally an array of X×Y×Z dimensions is obtained.

[0107] It should be noted that in the embodiments of the present application, the number M of laser pulses used for photon count stacking of each pixel point is the same. Using the same number of laser pulses for photon count superposition can effectively avoid the problem of uncertain data processing time caused by the existing first-photon group method that needs to use the N-ε criterion to screen in the random sub-pulse measurement results, and is more suitable for the requirements of rapid imaging of underwater slow-moving targets. In addition, as analyzed in the previous article, since the single-photon laser radar collects and counts energy as low as a single photon, the photon counting result of a single pulse generally cannot show a clear difference between the distribution of the echo signal and the distribution of the noise signal, and it may even appear that the counting result of the noise signal in some time bins is higher than the true echo signal. However, with the By accumulating the results of multiple pulse measurements, the probability distribution characteristics of the echo signal (such as Gaussian distribution) will be continuously strengthened through superposition. At the same time, the noise signal randomly distributed in each measurement will show a probability distribution characteristic that is more in line with the random distribution as the number of pulses is superimposed. Finally, the signal-noise is continuously strengthened according to their respective probability distribution characteristics, that is, the signal-to-noise ratio of the photon number sequence obtained after superposition is improved. Therefore, after superimposing the measurement results of a certain number of pulses, there must be an area with the most concentrated photon counts. At this time, it is only necessary to search and further process the area with the most concentrated photon counts to obtain the reflection intensity and time information of the echo signal, thereby effectively avoiding the problem of reduced efficiency or increased false recognition rate when N and ε are set improperly in the first photon method.

[0108] <4. Depth-reflectivity estimation based on modal fusion>

[0109] After obtaining the superimposed photon number sequence of each pixel point through step 100, the depth and reflectivity of each pixel point can be estimated through step 200. Figure 5 The figure shows a process of estimating the depth and reflectivity of any pixel point x, y in a specific embodiment.

[0110] like Figure 5 As shown, first, in step 221, the corresponding superposition photon number sequence is read Then, through step 222 to step 224, a window with a length of W bins is set, with a step length of 1 bin, and the superposition photon number sequence is continuously slid from the starting position and W elements are intercepted at each sliding position to obtain multiple candidate groups. Where i represents the position of each slide.

[0111] Obviously, when i=1,

[0112] Then, in step 226, the number of photons in each candidate group is summed, and the candidate group with the largest sum is determined as the group where the target signal is located. And extract the time bin information corresponding to each element in the group through step 227

[0113] As analyzed above, when multiple laser pulse measurement results are superimposed, the signal-to-noise ratio of the superimposed photon number sequence has been significantly improved. Obviously, the area where the photon count distribution corresponding to the sliding window retrieval result is most concentrated is very likely to be the area corresponding to the true echo signal of the underwater target at that location. At the same time, the sum of the number of photons in this group also reflects the reflection intensity of the laser pulse of the underwater target at the corresponding position of the pixel point with a high probability. Therefore, the retrieval results can be used to quickly estimate the depth and reflectivity of the location.

[0114] Specifically, in step 228, the flight time of the echo signal can be obtained by searching for the peak value of the photon number in the group where the target signal is located, that is, selecting the τth element with the largest number of photons from the group where the target signal is located, and binning its corresponding time. Determined as the flight time T of the photon reflected from the target x,y By performing peak judgment in the group of target signals obtained by sliding statistics, the influence of some noise extreme values ​​on flight time judgment when the peak method is directly used can be effectively avoided, and the accuracy of depth estimation can be effectively improved.

[0115] At the same time, the sum of the number of photons in the group where the target signal is located also reflects with great probability the reflection intensity of the underwater target for the laser pulse at the corresponding position of the pixel point. Therefore, in step 229, the values ​​of all elements in the group where the target signal is located are superimposed to obtain N x,y This method of superimposing the results of multiple pulse measurements and then superimposing the photon count values ​​in the area with the most concentrated photon count distribution to obtain the reflectivity is obviously more physically meaningful than the method of determining the reflection intensity of the first photon group based on the ratio of a specified photon number N to a random number of experiments Num.

[0116] The above T x,y 、N x,y The depth and reflectivity of the pixel point x and y are represented respectively. For example, in step 230, the flight time can be further converted into the distance D between the underwater target at the position x and y and the single photon laser radar by the following formula: x,y :

[0117] D x,y =c×T x,y / 2,

[0118] Here, c represents the speed of light in water.

[0119] By repeatedly executing step 200 for each pixel, the depth and reflectivity corresponding to each pixel can be obtained, such as Figure 6 As shown, after arranging each pixel according to its position, a depth map D of the target scene with a size of X×Y pixels can be initially obtained. noisy (x,y) and reflectivity map R noisy (x,y), where x∈[1,X],y∈[1,Y].

[0120] <V. Cooperative Variational Imaging Optimization Strategy>

[0121] Due to the complexity of light attenuation in the underwater environment, there is still some information missing and noise interference in the above-mentioned preliminary reconstructed depth map and reflectivity map. To this end, in an embodiment of the present application, through step 300, the depth map and reflectivity map of the target scene are further optimized using a collaborative variational imaging optimization strategy. The core idea is to use the idea of ​​total variation smoothing constraints, through adaptive filtering operations and total variation deconvolution operations (Total Variation deconvolution, deconvTV) under global morphological constraints, while suppressing abnormal pixels, better maintain image edges and textures, and protect the naturalness and visual details of the image.

[0122] 5-1) Wiener-Hopf adaptive filtering operation:

[0123] The depth map D of the target scene is obtained by step 200. noisy and reflectivity map R noisy ,Using Wiener-Hopf adaptive filtering, the filtering parameters are adaptively adjusted with the help of the local statistical characteristics of the image. The behavior of the filter will be different in different areas of the image, thereby removing abnormal pixel values ​​while retaining edges and details, providing a clean pixel environment for subsequent smoothing constraint operations.

[0124] Specifically, for the initially obtained depth map D noisy and reflectivity map R noisy The filtering can be performed by the following formula:

[0125]

[0126] Among them, D Wiener-Hopf , R Wiener-Hopf They are the depth map and reflectivity map after adaptive filtering, H D , H R represents the convolution kernel of the Wiener-Hopf filter, k, l represent the neighboring pixels of pixel x, y, denote the noise power of the depth map and reflectivity map respectively, Represent the local variance of the depth map and reflection intensity map at pixel x and y respectively.

[0127] Furthermore, the depth map D noisy and reflectivity map R noisy Calculate the cross power spectral density between the estimated signal and the expected response, the power spectral density of the signal, and the power spectral density of the noise to obtain H D , H R .

[0128] Although Wiener-Hopf adaptive filtering can effectively suppress noise, the signal photon counts obtained by single-photon lidar for underwater target detection are small. In some cases where light attenuation is severe, the average number of photons per pixel in the reconstructed image of the underwater target scene is even ≯1. Therefore, the variance of the inferred filter value is too large, which will lead to greater uncertainty in image reconstruction. This uncertainty may cause significant reconstruction errors.

[0129] In order to reduce this uncertainty, in an embodiment of the present application, after the Wiener-Hopf filtering operation, an improved deconvTV processing is required. The idea is to first perform smoothing constraints on the depth map and the reflectivity map through deconvTV (Total Variation deconvolution) processing, and maintain the edge information by minimizing the sum of the absolute values ​​of the image gradients while suppressing noise. Then, a morphological reconstruction operation that combines global features with local features is used to enhance the details by highlighting the edges and textures in the image, so as to improve the accuracy of image reconstruction and enhance the visual effect.

[0130] 5-2) Total variation deconvolution processing:

[0131] deconvTV (Total Variation deconvolution) is an image deconvolution algorithm based on total variation regularization, mainly used in the field of image processing and restoration. It combines deconvolution and total variation regularization processing, uses TV regularization terms to maintain image edges while suppressing noise, and solves the optimal solution by minimizing the objective function.

[0132] Specifically, in an embodiment of the present application, the total variation deconvolution process performed on the depth map or reflectivity map after Wiener-Hopf adaptive filtering can be expressed as follows:

[0133] deconvTV(I Wiener-Hopf ,PSF,Opts)(4),

[0134] Among them, I Wiener-Hopf Represents the D that needs to be deconvTV operated Wiener-Hopf or R Wiener-Hopf , PSF represents the point spread function, Opts represents the parameters needed to perform deconvTV processing, including the regularization parameter μ, the initial penalty parameter rho_r, the maximum number of iterations max_itr, the regularization parameter beta of the weight TV norm, the update constant gamma, the tolerance tol, etc.

[0135] When the underwater single-photon lidar uses a Gaussian beam, the value of the point spread function at x, y can be expressed as follows:

[0136]

[0137] where σ is the standard deviation of the Gaussian beam.

[0138] The specific calculation of deconvTV processing can be performed by the following formula:

[0139]

[0140] Among them, I deconvTV is the depth map or reflectivity map after total variation deconvolution, I is the image variable to be optimized in the iterative optimization process, λ is the regularization parameter of the data fidelity term, τ is the regularization parameter of the total variation term, is the image gradient operator, ||·||2 is the L2 norm, and ||·||1 is the L1 norm.

[0141] 5-3) Morphological reconstruction operation of global feature fusion and local feature fusion:

[0142] The purpose of the morphological reconstruction operation is to further improve the image quality by using operations such as corrosion, dilation, opening and closing to assist deconvTV processing. Specifically, in some preferred embodiments, the morphological reconstruction operation includes sequentially performing edge detection and morphological closing operations, distance transformation and morphological reconstruction, connected region processing and image enhancement.

[0143] Specifically, edge detection and morphological closing operations are performed by the following formula:

[0144] E closed =close(C(I deconvTV ),S(N)) (7),

[0145] Among them, C(I deconvTV ) represents the image I deconvTV Extract edges, close represents the morphological closing operation, S(N) is the neighborhood of pixels in the image, Eclosed It is the edge map obtained by edge detection and morphological closing operation.

[0146] Specifically, distance transformation and morphological reconstruction are performed by the following formula:

[0147]

[0148] Where W(~Eclosed) is E closed The distance transform of the complement of , max(·) is the normalization operation, Reconstruct() is the morphological reconstruction function, I Reconstructed is the image after morphological reconstruction.

[0149] Connected region processing and image enhancement are used to process connected regions in an image to enhance visual contrast. Specifically, the following formula is used:

[0150]

[0151] Among them, LabelImg==p represents the connected area marked as p, mode(·) represents all pixel values ​​in the statistical area, ∪ represents all connected areas, and num represents the number of connected areas. Indicates image sharpening processing, I final Depth map or reflectivity map generated for final optimization.

[0152] In some preferred embodiments, The operation can be performed using the pre-trained Real-ESRGAN model to further improve the resolution and visual quality of the image.

[0153] <VI. Signal-to-noise separation operation based on the statistical characteristics of photon number distribution>

[0154] As underwater single-photon lidar is increasingly used in many fields such as marine exploration, underwater archaeology, environmental monitoring and underwater navigation, it faces various more stringent imaging conditions and imaging indicators, which put forward higher requirements on the technical solutions for target reconstruction. For example, although the statistical characteristics of echo signal photons can be enhanced by increasing the number of laser pulses emitted at the same position, thereby shortening the sliding window length and improving the estimation accuracy, for targets moving slowly underwater (such as underwater targets moving at a speed not exceeding 2m / s), too many laser pulses will inevitably increase the measurement and data processing time, resulting in the inability to track the slow-moving targets in a timely manner, while fewer laser pulses will inevitably cause the problem of suppressing noise photons inside the system; for example, in an environment with high light attenuation or high ambient light intensity, the difficulty of separating the statistical characteristics of noise photons and signal photons in the echo signal will increase, and it is impossible to simultaneously meet the requirements of processing speed and processing accuracy by simply increasing the sliding window length or increasing the number of laser pulses.

[0155] It can be seen that in order to simultaneously improve the reconstruction accuracy and reconstruction speed of underwater slow-moving targets, it is necessary to further utilize the spatiotemporal distribution characteristics of noise photons and signal photons to perform signal-noise separation operations on the basis of comprehensively considering the number of pulses and window length, so as to meet the increasingly challenging underwater detection and imaging needs.

[0156] 6-1) Optimization of laser pulse times and sliding window length:

[0157] When high-resolution imaging of underwater targets is required, the number of pixels will increase in a quadratic relationship with the image size. If high-resolution reconstruction of slow-moving targets is required, the number of laser pulse scans M for each pixel location must be reduced as much as possible while ensuring the imaging effect. It can be seen from the test method provided in the present application that for each pixel, at least 5 sets of laser pulse measurement data are required to make the statistical characteristics of the echo signal and the noise signal in the superimposed photon number sequence significantly different. That is, preferably, the lower limit of the number M of laser pulses for superimposing the photon number at each pixel location is 5 times.

[0158] At the same time, as the number of laser pulses M decreases, the selection of the sliding window length W needs to take into account both the estimation accuracy and the processing speed. If W is too small, it may lead to the misidentification of certain noise maximum positions under low pulse numbers. If W is too large, too much noise will be introduced near the effective signal in the reflectivity calculation. In some preferred embodiments, in order to take into account both the speed of target reconstruction and the imaging accuracy, when the depth-reflectivity estimation based on modal fusion is performed on the superimposed photon number sequence of each pixel point, the preset sliding window length ranges from 5 time bins to 9 time bins, that is, 5≤W≤9.

[0159] 6-2) Filtering of system noise:

[0160] When the underwater target is in a high-attenuation underwater environment, the signal in the echo data will be extremely weak. At this time, the noise inside the system will significantly interfere with the extraction of target information. For this reason, in some preferred embodiments, a mask operation is used to filter the system noise photons accumulated in the front of the echo signal.

[0161] In some specific embodiments, for the superimposed photon number sequence of each pixel point x, y that has been reconstructed into an X×Y×Z three-dimensional data structure, the following formula can be used to perform mask operation to filter system noise:

[0162]

[0163] Among them, B, B masked are the superimposed photon number sequences of each pixel before and after the mask operation, j is the index in the time axis direction, BlindBin is the length of the mask, and the above formula means that the first BlindBin elements in the superimposed photon number sequence of each pixel are set to zero to filter out the system noise before the signal arrives.

[0164] The length of BlindBin will have a significant impact on signal extraction and recognition. If it is set arbitrarily and too large, the system will have a large blind area. If it is set too small, the mask operation will lose its meaning because the noise generated by the system will still affect the determination of the time index and the number of photons.

[0165] In order to reasonably set the length of BlindBin, in some preferred embodiments, Figure 7 As shown, a pre-estimation step 101' and a step 102' can be further added before step 100, wherein, in step 101', a photon number superposition operation based on N laser pulses is preliminarily performed on the original echo data (wherein the value of N is not greater than M), and then the depth of each pixel point is pre-estimated using the aforementioned depth-reflectivity estimation process based on modal fusion (that is, the same steps as step 200 are adopted, but only the depth is estimated); after obtaining the above-mentioned pre-estimation result, the depth of each pixel can be roughly obtained in step 102' and the length of BlindBin can be set on this basis, and then step 100 is re-executed to perform a photon number superposition operation on M laser pulses, and a mask operation is performed on the superimposed photon number sequence through step 103'.

[0166] In addition, it should be noted that the mask operation shown in formula (10) can be used to perform system noise filtering on the superimposed photon number sequence, and can also be performed on the photon number sequence corresponding to each laser pulse before the photon number is superimposed. The only difference is the order of the photon number superposition operation, which will not affect the noise filtering effect.

[0167] 6-3) Filtering of various noise photons aliased with signal photons:

[0168] Although the mask operation can filter out the system noise photons at the front of the time axis, it cannot be applied to filter out various noise photons that are mixed with the echo signal photons after the BlindBin. These noise photons include both system noise photons and noise photons generated by ambient light. In some preferred embodiments of the present application, these noise photons are filtered by matched filtering.

[0169] Assume that the input signal is the superposition of the expected signal (target signal) and noise, where s expect (t) is the expected signal, s noise (t) is noise, then the received echo signal s input (t) can be expressed by the following formula.

[0170] s input (t) = s expect (t)+s noise (t) (11),

[0171] Obviously, the waveform of the echo signal reflected by the target has a strong correlation with the waveform of the laser pulse emitted by the lidar. Therefore, the form of the pulse response h(t) can be determined based on the pulse width and waveform of the laser pulse, and then it can be convolved with the input signal to obtain the output signal y(t) as shown in the following formula:

[0172] y(t)=s input (t)*h(t)=(s input (t)+s noise (t))*h(t) (12)

[0173] Since the expected signal s in the input signal expect The (t) part completely matches the impulse response of the filter, so the amplitude of the output signal after convolution is the largest, while the noise s noise The convolution of part (t) with h(t) will not produce the desired signal s expect (t) The same correlation peak value, so the influence of noise in the output signal is suppressed. It can be seen that the use of the above matched filtering can effectively filter out various types of noise generation from the original signal, which is more conducive to the detection of the target signal.

[0174] Considering that the superimposed photon number sequence of each pixel point is a discrete signal, it can be expressed as follows, which can be further expressed in a unified form with (10):

[0175] B MF (x,y,j)=B(x,y,j)*h(j) (13),

[0176] Where h(j) is the discrete pulse response determined by the pulse width and waveform of the laser pulse emitted by the single-photon laser radar, B MF is the superposition photon number sequence after matched filtering.

[0177] Optionally, the mask operation of formula (10) and the matched filtering of formula (13) can be performed separately in real time or jointly to better achieve signal-to-noise separation.

[0178] In addition, in some preferred embodiments, considering that in the depth-reflectivity estimation based on modal fusion, a sliding window with a width of W is used to retrieve the target signal, therefore, h(j) can also be intercepted using a window with a length of W to improve the processing speed while ensuring the matched filtering effect.

[0179] <Specific Example 1>

[0180] according to Figure 1 The single-photon laser radar with scanning imaging is shown and the method provided in the present application is used to reconstruct the target set in the experimental pool, wherein the laser is a solid-state laser with a wavelength of 532nm, a laser pulse emission frequency of 1-5kHz, an average power of 175mW, a single pulse energy of 35μJ, and a pulse width of 600ps. The scanning imaging module uses a two-axis galvanometer to perform two-dimensional beam scanning, with an optical deflection angle of ±22.5° and an optical resolution of 12μrad.

[0181] Figure 8 Shown is a schematic diagram of the experimental pool layout. The available size of the experimental pool is about 12m*13m*6m. The single-photon laser radar and the underwater target are placed at both ends of the pool respectively.

[0182] The front view and three-dimensional structure of the underwater target are shown in Fig. 9 and Fig.10 , taking the highest square plane as the reference plane, the underwater target information includes 12 planes with depths of 0 / 25 / 50 / 75 / 100 / 150 / 200 cm and three different reflectivities.

[0183] By increasing the light attenuation in the experimental pool to simulate the harsh underwater environment, Fig.11 shows the propagation of laser pulses underwater. Fig.11As shown, the visibility in the experimental pool is extremely poor, and the underwater visible light camera is still completely unable to capture underwater targets at a relatively close distance.

[0184] Fig. 12A In order to use the method provided by this application, 50 pulses are used for each pixel to reconstruct the underwater target, and the obtained depth map (left side) and reflectivity map (right side) are Fig. 12B This is the reconstruction result using 500 pulses. For comparison, FIG. 13A to FIG. 13D The depth map (left side) and reflectivity map (right side) obtained when the pulse number is 50 using the peak, cross-correlation, first photon, and first photon group algorithms are shown respectively.

[0185] It can be seen from the above figures that compared with various existing algorithms, the target reconstruction method provided by the present application has a good ability to repair abnormal points based on strong information extraction capabilities, and the depth resolution reaches 2.5 cm.

[0186] <Specific Example 2>

[0187] This embodiment adopts the same experimental environment and experimental equipment as the specific embodiment 1, using Fig.14 The underwater target with a hollow structure shown is used to test the lateral resolution of the method provided in the present application. The lateral resolution of the underwater target at its minimum point is 5 mm.

[0188] Fig.15A , Fig. 15B and Fig. 15C The reconstructed depth map (left) and reflectivity map (right) corresponding to 32 pixels / 10 laser pulses, 64 pixels / 10 laser pulses, and 128 pixels / 20 laser pulses respectively. It can be seen from the figure that in the imaging result of 32 pixels / 10 pulses, the overall shape of the underwater target can be clearly seen and can be distinguished. In the imaging result of 128 pixels / 20 pulses, the detailed information of the hollow underwater target has been fully displayed, and the minimum resolution has reached about 5mm. This effectively proves that the method used in this application can achieve rapid and accurate reconstruction of underwater targets in relatively harsh underwater environments.

[0189] The above is a detailed introduction to the specific implementation methods of the present application. For those skilled in the art, several improvements and modifications may be made to the present application without departing from the principles of the present application. These improvements and modifications also fall within the scope of protection of the claims of the present application.

Claims

1. An underwater single-photon lidar target reconstruction method based on modal fusion and collaborative variational imaging optimization, characterized in that: The following steps are involved: The original echo data of the underwater single-photon laser radar is reconstructed into a superimposed photon number sequence corresponding to X×Y pixel points, wherein the superimposed photon number sequence corresponding to each pixel point is generated by superimposing the photon number of multiple laser pulse echo signals received at its location based on the time bin grid, and the number of laser pulses M for superimposing the photon number of each pixel point is the same; The depth-reflectivity estimation based on modal fusion is performed on the superimposed photon number sequence of each pixel point to obtain the depth map and reflectivity map of the underwater target; The depth map and reflectivity map of underwater targets are optimized based on the collaborative variational imaging optimization strategy.

2. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 1 is characterized in that: For the superimposed photon number sequence of any pixel point, depth-reflectivity estimation based on modal fusion is performed, including the following steps: Use a sliding window of preset length to slide stepwise on the superimposed photon number sequence of the pixel point with a time bin as a step length to intercept multiple candidate groups; Select the candidate group with the largest number of photons as the group where the target signal is located; Determine the underwater target depth corresponding to the pixel point based on the time bin number corresponding to the maximum value element in the group where the target signal is located, and The reflectivity of the underwater target corresponding to the pixel is determined based on the sum of the number of photons in the group where the target signal belongs.

3. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 2 is characterized in that: The underwater target is a slow-moving target, and, The lower limit of M is 5 times and / or the length of the sliding window is between 5 time bins and 9 time bins.

4. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 1 is characterized in that: It also includes performing a signal-noise separation operation on the superimposed photon number sequence of each pixel point based on the statistical characteristics of the photon number distribution, and the signal-noise separation operation includes at least one of a mask operation and a matched filter.

5. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 4 is characterized in that: The mask operation is specifically: Where x and y are the horizontal and vertical coordinates of the pixel point, B and B masked are the superimposed photon number sequences before and after the mask operation, j is the index in the time axis direction, and BlindBin is the length of the mask.

6. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 5 is characterized in that: The following steps are also performed before performing the mask operation: Performing a photon number superposition operation based on N laser pulses and a depth estimation on the original echo data, where N is less than or equal to M; The length of the BlindBin is determined based on the result of the pre-estimation of the depth.

7. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 5 is characterized in that: The matched filtering is specifically: B MF (x,y,j)=B(x,y,j)*h(j), Wherein, h(j) is the pulse response determined based on the pulse width and waveform of the laser pulse, B MF is the superposition photon number sequence after matched filtering.

8. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 1 is characterized in that: The collaborative variational imaging optimization strategy includes performing a Wiener-Hopf adaptive filtering operation, a total variational deconvolution operation, and a morphological reconstruction operation of fusing global features with local features on the depth map and / or reflectivity map.

9. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 8 is characterized in that: The Wiener-Hopf adaptive filtering operation is performed by the following formula: Among them, D noisy , R noisy are the depth map and reflectivity map before adaptive filtering, D Wiener-Hopf , R Wiener-Hopf They are the depth map and reflectivity map after adaptive filtering, H D , H R are the impulse response functions of the Wiener-Hopf filter corresponding to the depth map and reflectivity map, respectively. k and l are the neighboring pixels of pixel x and y. are the noise powers of the depth map and reflectivity map, respectively, are the local variances of the depth map and reflection intensity map at pixel x and y respectively.

10. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 8, characterized in that: The total variation deconvolution operation is performed as follows: Among them, I Wiener-Hopf is the depth map D before the total variation deconvolution operation Wiener-Hopf Or reflectivity map R Wiener-Hopf , I deconvTV is the depth map or reflectivity map after the total variation deconvolution operation, I is the image variable to be optimized in the iterative optimization process, λ is the regularization parameter of the data fidelity term, τ is the regularization parameter of the total variation term, ▽ is the image gradient operator, ||·||2 is the L2 norm, ||·||1 is the L1 norm, PSF is the point spread function, and σ is the standard deviation of the Gaussian beam.

11. The underwater single-photon laser radar target reconstruction method based on modal fusion and collaborative variational imaging optimization according to claim 8, characterized in that: The morphological reconstruction operation includes edge detection and morphological closing operation, distance transformation and morphological reconstruction, and connected region processing and image enhancement performed sequentially; The edge detection and morphological closing operation are performed by the following formula: E closed =close(C(I deconvTV ),S(N)), Among them, C(I deconvTV ) is the image I deconvTV Extract edges, close represents the morphological closing operation, S(N) is the neighborhood of pixels in the image, E closed The edge map is obtained by edge detection and morphological closing operation; The distance transformation and morphological reconstruction are performed by the following formula: Where W(~Eclosed) is E closed The distance transform of the complement of , max(·) is the normalization operation, Reconstruct() is the morphological reconstruction function, I Reconstructed It is the image after morphological reconstruction; The connected region processing and image enhancement are performed by the following formula: Among them, LabelImg==p represents the connected area marked as p, mode(·) is the value of all pixels in the statistical area, ∪ is all connected areas, num is the number of connected areas, For image clarity processing, I final Depth map or reflectivity map generated for final optimization.

Images