WO2021120520A1 - 一种基于贝叶斯推理的gpr图像去噪方法及系统 - Google Patents

一种基于贝叶斯推理的gpr图像去噪方法及系统 Download PDF

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WO2021120520A1
WO2021120520A1 PCT/CN2020/091874 CN2020091874W WO2021120520A1 WO 2021120520 A1 WO2021120520 A1 WO 2021120520A1 CN 2020091874 W CN2020091874 W CN 2020091874W WO 2021120520 A1 WO2021120520 A1 WO 2021120520A1
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probability
denoising
noise
bayesian network
bayesian
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原达
苗翠
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山东工商学院
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00—Image enhancement or restoration
    • G06T5/70—Denoising; Smoothing
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N5/00—Computing arrangements using knowledge-based models
    • G06N5/04—Inference or reasoning models
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00—Indexing scheme for image analysis or image enhancement
    • G06T2207/20—Special algorithmic details
    • G06T2207/20076—Probabilistic image processing

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  • the invention relates to the technical field of denoising for ground penetrating radar images, in particular to a GPR image denoising method and system based on Bayesian inference.
  • Ground Penetrating Radar uses the reflection principle of high-frequency electromagnetic beams to effectively detect underground targets. It is often used in archaeology, mineral exploration, disaster geological surveys, geotechnical engineering surveys, engineering quality inspections, and building structures. Many fields such as detection and military target detection. However, in the actual application process, due to the relatively complex outdoor environment, billboards, buildings, plants, etc. will produce electromagnetic interference, forming various interference waves, affecting the quality of ground penetrating radar data. Many methods have been proposed to remove interfering noise.
  • the method based on filtering and denoising is widely used, and it has a good effect on some noises with a certain distribution, but the effect is not ideal for the unknown interference wave noise in our GPR image.
  • the method of denoising in the wavelet domain is also very common.
  • wavelet transform and filtering methods such as combining median filtering and wavelet threshold denoising, after wavelet threshold denoising Median filtering is performed on the image to effectively remove the Gaussian noise in the image.
  • the selection of threshold and threshold function is very important to the denoising result, but it is difficult to determine the optimal threshold and threshold function for different noise characteristics.
  • the prior art assumes that the prior value of wavelet coefficients is a generalized Gaussian distribution (GGD), and uses the BayesShrink method to estimate the threshold, which has a better effect on larger noise power. The effect of some low-frequency noise or clutter similar to the signal is not obvious.
  • GMD generalized Gaussian distribution
  • the present invention proposes a GPR image denoising method and system based on Bayesian inference.
  • the method and system use Bayesian network to fuse multiple denoising models, and use the joint tree algorithm to calculate the Bayesian The maximum posterior probability of each pixel in the Yess network, so as to achieve signal-to-noise separation.
  • a GPR image denoising method based on Bayesian inference including:
  • the Bayesian network uses the joint tree algorithm to reason, calculates the posterior probability of each pixel belonging to the effective signal and noise, and realizes the signal-to-noise separation of the GPR image by selecting the maximum posterior probability .
  • the denoising models include: Haar wavelet transform, Kuwahara filter, three-dimensional block matched filter, sym6 wavelet transform, and Wiener filter.
  • calculating the joint probability density of each random variable node in the Bayesian network includes:
  • the directed edges in the network represent the connections between nodes of different random variables.
  • the conditional probability value of each node is set through experience, and the conditional probability table of each node is obtained;
  • the joint probability density is obtained according to the conditional probability table.
  • the joint probability density is obtained according to the conditional probability table, specifically:
  • P(U) P(I,K,H,B,W,Y,S,N)
  • P(I) represents the probability of I
  • I) represents the probability of K based on the occurrence of I
  • I) represents the probability of H occurring based on the occurrence of I
  • K, H) represents the probability that B occurs based on the occurrence of K and H
  • B) represents the probability that Y occurs based on the occurrence of B
  • B) represents the probability that W occurs based on the occurrence of B
  • W,Y) represents the probability of S occurring based on the occurrence of W and Y
  • W,Y) represents the probability of N occurring based on the occurrence of W, Y.
  • the Bayesian network uses the joint tree algorithm to perform inference, specifically:
  • the ring in the Moral graph has more than the set number of nodes, add an undirected edge to the ring to connect two non-adjacent nodes;
  • the joint tree must include all clique nodes, and the intersection is used as a separation node connecting the two clique nodes.
  • conditional probability table in the Bayesian network is transformed into the joint tree, and the joint tree that satisfies the global consistency is obtained through message passing, and the probability distribution of any random variable in the original Bayesian network is obtained, and the random For any clique node of a variable, the probability distribution can be obtained by marginalizing it.
  • a GPR image denoising system based on Bayesian inference including:
  • the Bayesian network uses the joint tree algorithm to reason, calculates the posterior probability of each pixel belonging to the effective signal and noise, and selects the maximum posterior probability to realize the GPR image's confidence. Noise separation device.
  • a terminal device which includes a processor and a computer-readable storage medium, the processor is used to implement each instruction; the computer-readable storage medium is used to store a plurality of instructions, the instructions are suitable for being loaded by the processor and executing the above-mentioned shell-based The GPR image denoising method based on Yees' inference.
  • a computer-readable storage medium in which a plurality of instructions are stored, and the instructions are suitable for being loaded by a processor of a terminal device and executing the aforementioned Bayesian inference-based GPR image denoising method.
  • the coefficients of the denoising models or their coefficient characteristics are merged together in the form of Bayesian network, the mutual relationship is described by the conditional probability table, and the joint tree algorithm is used for reasoning.
  • the joint tree is constructed first, and then the message is transmitted.
  • the posterior probability of each pixel belonging to the effective signal and noise is calculated, and the signal-to-noise separation is achieved by selecting the maximum posterior probability, so as to achieve the ideal denoising result.
  • Figure 1 is a schematic diagram of Bayesian network
  • FIG. 2 is a schematic diagram of a GPR image denoising method based on Bayesian inference in Embodiment 1 of the present invention
  • Figure 3 is a Bayesian network denoising integrated model in the first embodiment of the present invention.
  • Figure 5 is a schematic diagram of triangulation in the first embodiment of the present invention.
  • Figure 6 is a schematic diagram of a joint tree
  • Figure 7 is a schematic diagram of three 50*50 areas
  • Figure 8(a)-(f) are comparison diagrams of denoising results using different algorithms.
  • a GPR image denoising method based on Bayesian inference which includes the following steps:
  • the Bayesian network uses the joint tree algorithm to reason, calculates the posterior probability of each pixel belonging to the effective signal and noise, and realizes the signal-to-noise separation of the GPR image by selecting the maximum posterior probability .
  • the method proposed in this embodiment uses the Bayesian network to fuse multiple denoising models, and uses the joint tree algorithm to calculate the maximum posterior probability of each pixel in the Bayesian network, so as to realize signal-to-noise separation.
  • Wiener filtering is based on adaptive minimum mean square error MSE to remove noise from noisy signals.
  • MSE adaptive minimum mean square error
  • the parameter ⁇ and ⁇ 2 represents the mean and variance of the image.
  • the noise characteristic of the noise variance v 2 on the ground penetrating radar image is unknown.
  • the average of all local estimated variances is used as the noise variance.
  • Wiener filtering can better protect the effective signal while denoising, and then select the eight-neighborhood feature of the filter coefficient for further processing on this basis.
  • Wavelet threshold denoising wavelet threshold denoising
  • Wavelet threshold denoising is a more classic image denoising method.
  • sym6 is selected as the wavelet base and three-layer decomposition is performed to obtain a set of wavelet coefficients. Then through the hard threshold function for processing.
  • factors such as the choice of wavelet base, the number of decomposition layers, and the threshold function will all have different denoising effects.
  • the gradient values of wavelet coefficients after denoising are selected as features for further processing.
  • Bayesian network (Bayesian network)
  • Bayesian network is a kind of probabilistic graph model, which mainly expresses and infers uncertain factors through probabilistic knowledge.
  • the Bayesian network is composed of a set of vertices and a set of directed edges.
  • the set of vertices are related factors to make random variables, and directed edges describe the causal relationship between various factors. For example, the reason why the parent node is often the child node, the child The node is often the result of the parent node. As shown in Figure 1, it is a simple Bayesian network.
  • the joint probability distribution of the network is:
  • a Bayesian network model is often established for multiple random variables, based on the joint probability density distribution expression, and the posterior probability of each random variable is calculated through an inference algorithm.
  • Each denoising method has its own characteristics and effects, but for ground penetrating radar images, because the characteristics of the signal and noise are unknown, and the interference wave is more complicated, using one method alone cannot achieve the ideal denoising effect.
  • This paper proposes to use Bayesian network to fuse various denoising methods to construct an integrated model, and obtain the posterior probability of noise and effective signal through a joint tree inference algorithm to achieve signal-to-noise separation.
  • the algorithm framework is shown in Figure 2.
  • each random variable node in the network represents various denoising models, signals and noise.
  • thresholds are used to quantize the coefficients of each vertex. The node details are shown in Table 1.
  • the directed edges in the network represent the connections between different random variable nodes, and the conditional probability table of each node is obtained through the statistical histogram of each model coefficient. See Table 2 for details.
  • the Wiener filtering and sym6 wavelet threshold denoising method have a direct causal relationship with the effective signal and noise. Therefore, the corresponding eight-neighborhood and gradient features are selected as the vertex information.
  • the corresponding conditional probability table is shown in Table 3.
  • the joint probability density of the Bayesian network is as follows:
  • P(U) P(I,K,H,B,W,Y,S,N)
  • Bayesian inference A query process is called Bayesian inference. Common Bayesian reasoning methods are divided into precise reasoning and approximate reasoning, and the joint tree reasoning in precise reasoning is used here.
  • the Junction Tree algorithm is currently the fastest and most widely used Bayesian network precise reasoning algorithm. It returns accurate query results according to the joint probability distribution of the Bayesian network.
  • the algorithm first converts the computationally complex directed graph into an undirected graph, which has greater connectivity than the directed graph, and makes full use of the conditional independence in the Bayesian network to transform it into a tree structure, which greatly reduces the computational complexity the complexity. Then adopt the idea of message transmission.
  • the conditional probability distribution table separate nodes and clique nodes are used to pass on the joint tree. After the message is passed, the joint distribution of all variables is obtained.
  • the probability distribution of a random variable can be obtained from the potential of any clique node that contains the variable, and it can be realized by the marginalization formula:
  • U is the clique node containing the variable X
  • ⁇ (U) is the potential of the clique node U.
  • each clique node is a subgraph of an undirected graph.
  • the group node set C identified here are: IHK, BHK, BYW, YSWN.
  • Separate node set S that is, the cross nodes between clique nodes are: HK, B, YW.
  • the established joint tree must contain all clique nodes, and the intersection is used as the separation node connecting the two clique nodes. As shown in Figure 6.
  • the ellipse is a clique node and each clique node has its own potential and corresponding probability distribution.
  • the squares are separated nodes. When new evidence is added, the group nodes use the separated nodes to transmit and receive messages.
  • the conditional probability table in the Bayesian network is transformed into the joint tree, and the joint tree that meets the global consistency is obtained through message passing, that is, the probability distribution of any random variable in the original Bayesian network can be obtained. , Select any clique node that contains the random variable and marginalize it to get the probability distribution.
  • the result of equation (9) is calculated to be 0.4.
  • the point is considered to be a noise point.
  • the probability that each pixel in the image belongs to the effective signal and noise can be calculated through this inference process, and the largest posterior probability is selected to determine whether the point is noise.
  • the experimental data selects real ground penetrating radar images interfered by billboards.
  • the eight-neighborhood D(W) and Y gradient values G(Y) of node W are selected to replace the coefficient values of W and Y as evidence.
  • Bayesian inference When the coefficients C i of each node in the Bayesian network are quantized, the parameters are set as follows:
  • the method noise method is used to test the denoising effect, which is calculated by the Euclidean difference between the denoising processed image and the noisy image.
  • Method noise helps to understand the performance and limitations of denoising algorithms, because removing details or textures will produce larger method noise.
  • the method of this embodiment can well remove the noise on the basis of retaining the effective signal.
  • Figure 8(a) is the noisy image used in the experiment
  • Figure 8(b) is the BM3D algorithm.
  • the local smoothing effect is better, but there are more obvious artifacts.
  • the bilateral filter denoising in Figure 8(c) Compared with the haar wavelet denoising in Figure 8(d), it has a certain suppression effect on clutter, but the effective signal part is also weakened.
  • the wiener algorithm in Figure 8(e) retains the effective signal better. But the effect of removing clutter is not very good. It can be seen that the denoising effect shown in Fig. 8(f) of the method of this embodiment not only eliminates the clutter, but also retains the effective signal well.
  • a GPR image denoising system based on Bayesian inference including:
  • the Bayesian network uses the joint tree algorithm to reason, calculates the posterior probability of each pixel belonging to the effective signal and noise, and selects the maximum posterior probability to realize the GPR image's confidence. Noise separation device.
  • a terminal device including a server, the server including a memory, a processor, and a computer program stored in the memory and running on the processor, and the processor executes the The program implements the GPR image denoising method based on Bayesian inference in the first embodiment. For the sake of brevity, I will not repeat them here.
  • the processor may be the central processing unit CPU, the processor may also be other general-purpose processors, digital signal processors DSP, application-specific integrated circuits ASIC, ready-made programmable gate array FPGAs or other programmable logic devices. , Discrete gates or transistor logic devices, discrete hardware components, etc.
  • the general-purpose processor may be a microprocessor or the processor may also be any conventional processor or the like.
  • the memory may include a read-only memory and a random access memory, and provides instructions and data to the processor, and a part of the memory may also include a non-volatile random access memory.
  • the memory can also store device type information.
  • each step of the above method can be completed by an integrated logic circuit of hardware in the processor or instructions in the form of software.
  • the GPR image denoising method based on Bayesian inference in the first embodiment may be directly implemented by a hardware processor, or executed by a combination of hardware and software modules in the processor.
  • the software module may be located in a mature storage medium in the field, such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers.
  • the storage medium is located in the memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware. To avoid repetition, it will not be described in detail here.

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Abstract

一种基于贝叶斯推理的GPR图像去噪方法及系统，包括：选取设定的若干去噪模型，根据去噪模型、信号与噪声之间的关系构造贝叶斯网络；所述去噪模型、信号与噪声分别作为贝叶斯网络中的随机变量节点；计算贝叶斯网络中各随机变量节点的联合概率密度；对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现GPR图像的信噪分离。本方法及系统借助了贝叶斯网络融合多种去噪模型，并使用联合树算法计算出贝叶斯网络中每个像素点的最大后验概率，从而实现信噪分离。

Description

一种基于贝叶斯推理的GPR图像去噪方法及系统 技术领域
本发明涉及针对探地雷达图像的去噪技术领域，尤其涉及一种基于贝叶斯推理的GPR图像去噪方法及系统。
背景技术
本部分的陈述仅仅是提供了与本发明相关的背景技术信息，不必然构成在先技术。
探地雷达(Ground Penetrating Radar,GPR)利用高频电磁波束的反射原理来对地下目标进行有效探测，常被用于考古、矿产勘查、灾害地质调查、岩土工程勘察、工程质量检测、建筑结构检测以及军事目标探测等众多领域。但在实际应用过程中，由于室外环境较为复杂，广告牌、建筑、植物等都会产生电磁干扰，形成各种各样的干扰波，影响探地雷达数据质量。许多方法被提出来去除干扰噪声。
基于滤波去噪的方法被广泛应用，对一些分布确定的噪声具有很好的效果，而对于我们GPR图像中的未知干扰波噪声，效果不是太理想。
在小波域中进行去噪的方法也是很常见的，另外，还有一些方法将小波变换和滤波方法相结合的方法，比如将中值滤波和小波阈值去噪相结合，将小波阈值去噪后的图像再进行中值滤波，有效去除图像中的高斯噪声。基于小波阈值去噪时，阈值及阈值函数的选取对去噪结果至关重要，但不同的噪声特性很难确定最优的阈值和阈值函数。
在贝叶斯框架下，现有技术将小波系数的先验值假设为广义高斯分布(GGD)，使用BayesShrink方法来估计阈值，对较大的噪声功率具有较好的效果。对一些低频噪声或与信号相近的杂波效果不明显。
发明内容
为了解决上述问题，本发明提出了一种基于贝叶斯推理的GPR图像去噪方法及系统，该方法及系统借助了贝叶斯网络融合多种去噪模型，并使用联合树算法计算出贝叶斯网络中每个像素点的最大后验概率，从而实现信噪分离。
在一些实施方式中，采用如下技术方案：
一种基于贝叶斯推理的GPR图像去噪方法，包括：
选取设定的若干去噪模型，根据去噪模型、信号与噪声之间的关系构造贝叶斯网络；所述去噪模型、信号与噪声分别作为贝叶斯网络中的随机变量节点；
计算贝叶斯网络中各随机变量节点的联合概率密度；
对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现GPR图像的信噪分离。
进一步地，选取设定的若干去噪模型，所述去噪模型包括：哈尔小波变换、Kuwahara滤波、三维块匹配滤波、sym6小波变换和维纳滤波。
进一步地，计算贝叶斯网络中各随机变量节点的联合概率密度，具体包括：
使用阈值将各随机变量节点系数进行量化处理；
网络中的有向边代表了不同随机变量节点之间的联系，通过经验设置各节点的条件概率值，得到各节点的条件概率表；
根据条件概率表得到联合概率密度。
进一步地，根据条件概率表得到联合概率密度，具体为：
P(U)＝P(I,K,H,B,W,Y,S,N)
＝P(I)P(K|I)P(H|I)P(B|K,H)
P(Y|B)P(W|B)P(S|W,Y)P(N|W,Y)     (3)
其中，P(I)表示I的概率，P(K|I)表示在I发生的基础上K的概率，P(H|I)表示在I发生的基础上H发生的概率，P(B|K,H)表示在K、H发生的基础上B发生的概率，P(Y|B)表示在B发生的基础上Y发生的概率，P(W|B)表示在B发生的基础上W发生的概率，P(S|W,Y)表示在W,Y发生的基础上S发生的概率，P(N|W,Y)表示在W,Y发生的基础上N发生的概率。
进一步地，对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，具体为：
将所有的具有相同子节点的父节点相连，同时将所有的有向边变成无向边，构造Moral图；
对Moral图进行三角化处理，当Moral图中的环有超过设定个数的节点数时，对该环增加一条无向边连接两个非相邻接点；
在三角化图中，确定团节点；
建立联合树，所述联合树必须包含所有团节点,交集作为连接两个团节点的分隔节点。
进一步地，将贝叶斯网络中的条件概率表转化到联合树中,通过消息传递得到满足全局一致性的联合树,求出原贝叶斯网络中任意随机变量的概率分布,选取包含该随机变量的任意团节点,对其进行边际化即求出概率分布。
在另一些实施方式中，采用如下技术方案：
一种基于贝叶斯推理的GPR图像去噪系统，包括：
用于选取设定的若干去噪模型，根据去噪模型、信号与噪声之间的关系构造贝叶斯网络；所述去噪模型、信号与噪声分别作为贝叶斯网络中的随机变量节点的装置；
用于计算贝叶斯网络中各随机变量节点的联合概率密度的装置；
用于对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现GPR图像的信噪分离的装置。
在另一些实施方式中，采用如下技术方案：
一种终端设备，其包括处理器和计算机可读存储介质，处理器用于实现各指令；计算机可读存储介质用于存储多条指令，所述指令适于由处理器加载并执行上述的基于贝叶斯推理的GPR图像去噪方法。
在另一些实施方式中，采用如下技术方案：
一种计算机可读存储介质，其中存储有多条指令，所述指令适于由终端设备的处理器加载并执行上述的基于贝叶斯推理的GPR图像去噪方法。
与现有技术相比，本发明的有益效果是：
本发明将各去噪模型的系数或者其系数特征以贝叶斯网络的形式融合到一起，通过条件概率表描述出其相互关系，并通过联合树算法进行推理。先构建出联合树再进行消息传递，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现信噪分离，从而达到理想的去噪结果。
实验结果表明，本发明方法所展示的去噪效果不仅消除了杂波，也很好的保留了有效信号。
附图说明
图1是贝叶斯网络示意图；
图2是本发明实施例一中基于贝叶斯推理的GPR图像去噪方法示意图；
图3是本发明实施例一中贝叶斯网络去噪集成模型；
图4是本发明实施例一中Moral化示意图；
图5是本发明实施例一中三角化示意图；
图6是联合树示意图；
图7是三块50*50区域示意图；
图8(a)-(f)是分别采用不同算法的去噪结果对比图。
具体实施方式
应该指出，以下详细说明都是例示性的，旨在对本申请提供进一步的说明。除非另有指明，本发明使用的所有技术和科学术语具有与本申请所属技术领域的普通技术人员通常理解 的相同含义。
需要注意的是，这里所使用的术语仅是为了描述具体实施方式，而非意图限制根据本申请的示例性实施方式。如在这里所使用的，除非上下文另外明确指出，否则单数形式也意图包括复数形式，此外，还应当理解的是，当在本说明书中使用术语“包含”和/或“包括”时，其指明存在特征、步骤、操作、器件、组件和/或它们的组合。
在不冲突的情况下，本发明中的实施例及实施例中的特征可以相互组合。
实施例一
在一个或多个实施方式中，公开了一种基于贝叶斯推理的GPR图像去噪方法，包括以下步骤：
选取设定的若干去噪模型，根据去噪模型、信号与噪声之间的关系构造贝叶斯网络；所述去噪模型、信号与噪声分别作为贝叶斯网络中的随机变量节点；
计算贝叶斯网络中各随机变量节点的联合概率密度；
对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现GPR图像的信噪分离。
本实施例提出的方法中借助了贝叶斯网络来融合多种去噪模型，并使用联合树算法计算出贝叶斯网络中每个像素点的最大后验概率，从而实现信噪分离。下面简要介绍贝叶斯网络的理论基础和两种去噪模型背景。
A.Wiener filter denoising(维纳滤波)
维纳滤波是基于自适应最小均方差MSE来从含噪信号中去除噪声的，当输入的信号为广义平稳过程时，根据其二阶统计特性，通过以下公式来进行滤波:
Figure PCTCN2020091874-appb-000001
Figure PCTCN2020091874-appb-000002
x i,j＝y i,j-v 2
参数μandσ 2表示图像的均值和方差，噪声方差v 2在探地雷达图像上的噪声特性未知，这里使用所有局部估计方差的平均值来作为噪声方差。
维纳滤波在去噪的同时能较好的保护有效信号，后面在此基础上选取该滤波系数的八邻域特征来进一步处理。
B.Wavelet threshold denoising(小波阈值去噪)
小波阈值去噪是比较经典的图像去噪方法，这里选用sym6作为小波基，进行三层分解，得到一组小波系数
Figure PCTCN2020091874-appb-000003
然后通过硬阈值函数来进行处理。使用小波阈值方法进行去噪时，小波基的选择、分解层数、阈值函数等因素都会有不同的去噪效果。后面章节中选取了去噪后小波系数的梯度值作为特征来进行进一步处理。
C.Bayesian network(贝叶斯网络)
贝叶斯网络是一种概率图模型，主要是通过概率知识对不确定性因素进行表示和推理。贝叶斯网络由顶点集和有向边集构成，顶点集是相关因素来做随机变量，有向边则描述了各因素之间的因果影响关系，如父节点往往是子节点的原因,子节点往往是父节点的结果。如图1所示，就是一个简单的贝叶斯网络。
其中，该网络的联合概率分布为：
P(U)＝P(Y)P(W)P(N|Y,W)P(S|Y,W)     (2)
在实际应用中，往往对多个随机变量建立贝叶斯网络模型，基于联合概率密度分布表达，通过推理算法来计算各随机变量的后验概率。
每种去噪方法都有各自的特点和效果，但针对探地雷达图像，由于信号与噪声的特性未知，且干扰波比较复杂，因此单纯使用一种方法并不能达到理想的去噪效果。本文提出用贝叶斯网络来融合各种去噪方法构造集成模型，并通过联合树推理算法得到噪声和有效信号的后验概率，来达到信噪分离。算法框架如图2所示。
本实施例选取了几种常用的去噪模型来进行构造贝叶斯网络，如图3所示。
其中，网络中的各随机变量节点代表了各种去噪模型、信号与噪声。为了简化后续推理中的计算，使用阈值将各顶点系数进行量化处理。节点详情见表1。
表1顶点集
Figure PCTCN2020091874-appb-000004
Figure PCTCN2020091874-appb-000005
网络中的有向边代表了不同随机变量节点之间的联系，通过各模型系数的统计直方图得到各节点的条件概率表。详情见表2。
表2各去噪模型节点的条件概率表
Figure PCTCN2020091874-appb-000006
其中，从网络中可以看到其中与有效信号和噪声有直接因果关系的是维纳滤波和sym6小波阈值去噪方法，因此选择了对应的八邻域和梯度特征来作为顶点信息，并进行了离散值为{0,1,2}的量化(见实验部分)，其对应的条件概率表见表3。
表3信号和噪声的条件概率表
Figure PCTCN2020091874-appb-000007
该贝叶斯网络的联合概率密度如下：
P(U)＝P(I,K,H,B,W,Y,S,N)
＝P(I)P(K|I)P(H|I)P(B|K,H)
P(Y|B)P(W|B)P(S|W,Y)P(N|W,Y)   (3)
在确定了贝叶斯网络和条件概率分布表之后，得到网络中所有变量的的联合概率分布，结合给出的证据进行消息传递，最后通过边缘化处理来计算某个节点变量的概率分布，这一查询过程称为贝叶斯推理。常见的贝叶斯推理方法分为精确推理和近似推理，这里使用的是精确推理中的联合树推理。
联合树(Junction Tree)算法,是目前计算速度最快,应用最广的贝叶斯网络精确推理算法。其根据贝叶斯网络的联合概率分布，返回精确的查询结果。该算法首先将计算复杂的有向图转化为无向图，具有比有向图更大的连通性，并充分利用贝叶斯网络中的条件独立性进而转化成树结构，大大减少了计算的复杂度。然后采用消息传递的思想,在加入新证据时，根据条件概率分布表借助分离节点和团节点在联合树上进行传递，在消息传递之后，求得所有变量的联合分布。某个随机变量的概率分布可以由任一包含该变量的团节点的势中获取，具体通过边际化公式来实现：
Figure PCTCN2020091874-appb-000008
其中，U是包含变量X的团节点，ψ(U)是团节点U的势。
首先，来进行联合树的构造，在这个过程中，有向无环图最终转变为树结构，需要注意的是，联合树中的节点不再是单个变量，而是多个变量组成的团。具体的步骤如下：
1)构造Moral图:将所有的具有相同child节点的父节点相连，同时将所有的有向边变成无向边。如图4所示。
2)三角化图(Triangulating):当Moral图中的环有超过4个及以上节点数时，对该环增加一条无向边连接两个非相邻接点，图4中的环YSWN符合该特点，需要进行三角化处理。如图5所示。
3)区分团节点(Identifying Cliques):在三角化图中,确定团节点。其中，每个团节点都是无向图的子图。
这里确定的团节点集C有：IHK、BHK、BYW、YSWN。分离节点集S，即团节点之间的交叉节点有：HK、B、YW。
4)建立联合树:建立的联合树必须包含所有团节点,交集作为连接两个团节点的分隔节点。如图6所示。
通过图6可以看到，联合树中有两种类型的节点，椭圆形的为团节点且每个团节点处有自己的势和对应的概率分布。方形的为分隔节点，加入新的证据时，团节点之间通过分隔节点来进行消息的传送和接收。
联合树构建之后,要将贝叶斯网络中的条件概率表转化到联合树中,通过消息传递得到满足全局一致性的联合树,即可以求出原贝叶斯网络中任意随机变量的概率分布,选取包含该随机变量的任意团节点,对其进行边际化即可求出概率分布。
需要注意的是，在联合树中，各团节点的势乘积除以分隔节点的势乘积等同于贝叶斯网络的联合概率分布。具体表达如下：
Figure PCTCN2020091874-appb-000009
由式(4)为每个团节点分配对应的分布函数来初始化各团节点的势：
ψ(IHK)＝P(I)P(H|I)P(K|I)
ψ(BHK)＝P(B|H,K)
ψ(BYW)＝P(Y|B)P(W|B)
ψ(YSWN)＝P(S|W,Y)P(N|W,Y)
ψ(HK)＝ψ(B)＝ψ(YW)＝1        (5)
在联合树中，当任意两个团节点V和W及其交叉节点S满足
Figure PCTCN2020091874-appb-000010
时，称该联合树具有全局一致性，此时整个网络系统达到稳态。如果加入新的证据使ψ(V)→ψ *(V)时，为了保持联合树中的全局一致性，需要在联合树上进行消息传递(图6中的箭头为消息传递的方向)。通过以下公式来更新各团节点势：
Figure PCTCN2020091874-appb-000011
Figure PCTCN2020091874-appb-000012
Figure PCTCN2020091874-appb-000013
Figure PCTCN2020091874-appb-000014
Figure PCTCN2020091874-appb-000015
Figure PCTCN2020091874-appb-000016
至此，各团节点的势都已更新完毕，可以借此得到任何随机变量的概率分布，如想要获得信号S的概率分布情况，可利用公式(6)中的势ψ *(YSWN)，结合给出的证据信息，对其进行边缘化操作即可：
Figure PCTCN2020091874-appb-000017
例如给出证据Y＝0,W＝1，来计算P(S＝T|Y＝0,W＝1)的后验概率。这里借助团节点YSWN的势ψ *(YSWN)来获得：
Figure PCTCN2020091874-appb-000018
式(8)中，S并不依赖于I,K,H,B节点，所以可将公式(8)化简为如下形式：
Figure PCTCN2020091874-appb-000019
结合条件概率表，计算出(9)式结果为0.4，同理计算出该证据下N＝T的概率值为0.6，基于最大后验概率选择，认为该点属于噪声点。以此类推，可通过此推理过程计算出图像中每个像素点属于有效信号和噪声的概率，选取最大的后验概率来判定该点是否为噪声。这种集成了多种去噪模型的贝叶斯精确推理方法表现出较好的性能。
实验数据选取真实的受到广告牌干扰的探地雷达图像，实验过程中，选取节点W的八邻域D(W)和Y的梯度值G(Y)来代替W和Y系数值作为证据来进行贝叶斯推理。贝叶斯网络中的各节点系数C i进行量化时，参数设置如下：
Figure PCTCN2020091874-appb-000020
Figure PCTCN2020091874-appb-000021
Figure PCTCN2020091874-appb-000022
下面对实验结果进行一些评价：
1)Method Noise
在没有原无噪图做参考的情况下，采用method noise方法来检验去噪效果，该方法是通过去噪处理后的图像与含噪图像之间的欧氏差来计算的。方法噪声有助于了解去噪算法的性能和局限性，因为去除细节或纹理会产生较大的方法噪声。
通过观察Method noise结果，可以清楚的看到哪些几何特征或细节被保留了下来，哪些杂波噪声被消除了。因此，本实施例方法在保留有效信号的基础上很好的去除了噪声。
2)信噪比SNR
由于该实验图像来自于真实数据，无纯净参考图像，因此随机选取三个50*50的小块区域，如图7所示。通过其均值和方差的比值来计算信噪比，从而与各去噪算法进行比较。具体数值见表4。
表4信噪比对比
Figure PCTCN2020091874-appb-000023
将本实施例提出的算法与常用的BM3D去噪模型、小波阈值去噪模型和Kuwahara滤波去噪模型进行比对，结果表明本实施例方法具有较高的信噪比。
3)视觉质量评价
判断去噪算法性能的另一个重要标准是视觉质量评价，也是反映去噪效果最直接的评价方法。选取了几种经典的去噪算法进行对比，如图8(a)-(f)所示。
本实施例选取了几种比较经典的去噪算法来进行比较。其中，图8(a)是实验所用到的含噪图像，图8(b)为BM3D算法，局部平滑效果较好，但有较为明显的伪影现象，图8(c)的双边滤波去噪和图8(d)的haar小波去噪对杂波具有一定的抑制作用，但有效信号部分也被减弱了，图8(e)中的wiener算法相比之下较好的保留了有效信号，但对杂波的去除效果不是很好。可以看出，本实施例方法所展示的去噪效果图8(f)不仅消除了杂波，也很好的保留了有效信号。
实施例二
在一个或多个实施方式中，公开了一种基于贝叶斯推理的GPR图像去噪系统，包括：
用于选取设定的若干去噪模型，根据去噪模型、信号与噪声之间的关系构造贝叶斯网络；所述去噪模型、信号与噪声分别作为贝叶斯网络中的随机变量节点的装置；
用于计算贝叶斯网络中各随机变量节点的联合概率密度的装置；
用于对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现GPR图像的信噪分离的装置。
实施例三
在一个或多个实施方式中，公开了一种终端设备，包括服务器，所述服务器包括存储器、处理器及存储在存储器上并可在处理器上运行的计算机程序，所述处理器执行所述程序时实现实施例一中的基于贝叶斯推理的GPR图像去噪方法。为了简洁，在此不再赘述。
应理解，本实施例中，处理器可以是中央处理单元CPU，处理器还可以是其他通用处理器、数字信号处理器DSP、专用集成电路ASIC，现成可编程门阵列FPGA或者其他可编程逻辑器件、分立门或者晶体管逻辑器件、分立硬件组件等。通用处理器可以是微处理器或者该处理器也可以是任何常规的处理器等。
存储器可以包括只读存储器和随机存取存储器，并向处理器提供指令和数据、存储器的一部分还可以包括非易失性随机存储器。例如，存储器还可以存储设备类型的信息。
在实现过程中，上述方法的各步骤可以通过处理器中的硬件的集成逻辑电路或者软件形式的指令完成。
实施例一中的基于贝叶斯推理的GPR图像去噪方法可以直接体现为硬件处理器执行完成，或者用处理器中的硬件及软件模块组合执行完成。软件模块可以位于随机存储器、闪存、只读存储器、可编程只读存储器或者电可擦写可编程存储器、寄存器等本领域成熟的存储介质中。该存储介质位于存储器，处理器读取存储器中的信息，结合其硬件完成上述方法的步骤。为避免重复，这里不再详细描述。
本领域普通技术人员可以意识到，结合本实施例描述的各示例的单元即算法步骤，能够以电子硬件或者计算机软件和电子硬件的结合来实现。这些功能究竟以硬件还是软件方式来执行，取决于技术方案的特定应用和设计约束条件。专业技术人员可以对每个特定的应用来使用不同方法来实现所描述的功能，但是这种实现不应认为超出本申请的范围。
上述虽然结合附图对本发明的具体实施方式进行了描述，但并非对本发明保护范围的限制，所属领域技术人员应该明白，在本发明的技术方案的基础上，本领域技术人员不需要付出创造性劳动即可做出的各种修改或变形仍在本发明的保护范围以内。

Claims (9)

  1. 一种基于贝叶斯推理的GPR图像去噪方法，其特征在于，包括：
    选取设定的若干去噪模型，根据去噪模型、信号与噪声之间的关系构造贝叶斯网络；所述去噪模型、信号与噪声分别作为贝叶斯网络中的随机变量节点；
    计算贝叶斯网络中各随机变量节点的联合概率密度；
    对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现GPR图像的信噪分离。
  2. 如权利要求1所述的一种基于贝叶斯推理的GPR图像去噪方法，其特征在于，选取设定的若干去噪模型，所述去噪模型包括：哈尔小波变换、Kuwahara滤波、三维块匹配滤波、sym6小波变换和维纳滤波。
  3. 如权利要求1所述的一种基于贝叶斯推理的GPR图像去噪方法，其特征在于，计算贝叶斯网络中各随机变量节点的联合概率密度，具体包括：
    使用阈值将各随机变量节点系数进行量化处理；
    网络中的有向边代表了不同随机变量节点之间的联系，通过经验设置各节点的条件概率值，得到各节点的条件概率表；
    根据条件概率表得到联合概率密度。
  4. 如权利要求3所述的一种基于贝叶斯推理的GPR图像去噪方法，其特征在于，根据条件概率表得到联合概率密度，具体为：
    P(U)＝P(I,K,H,B,W,Y,S,N)
    ＝P(I)P(K|I)P(H|I)P(B|K,H)
    P(Y|B)P(W|B)P(S|W,Y)P(N|W,Y)  (3)
    其中，P(I)表示I的概率，P(K|I)表示在I发生的基础上K的概率，P(H|I)表示在I发生的基础上H发生的概率，P(B|K,H)表示在K、H发生的基础上B发生的概率，P(Y|B)表示在B发生的基础上Y发生的概率，P(W|B)表示在B发生的基础上W发生的概率，P(S|W,Y)表示在W,Y发生的基础上S发生的概率，P(N|W,Y)表示在W,Y发生的基础上N发生的概率。
  5. 如权利要求1所述的一种基于贝叶斯推理的GPR图像去噪方法，其特征在于，对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，具体为：
    将所有的具有相同子节点的父节点相连，同时将所有的有向边变成无向边，构造Moral图；
    对Moral图进行三角化处理，当Moral图中的环有超过设定个数的节点数时，对该环增加一条无向边连接两个非相邻接点；
    在三角化图中，确定团节点；
    建立联合树，所述联合树必须包含所有团节点,交集作为连接两个团节点的分隔节点。
  6. 如权利要求5所述的一种基于贝叶斯推理的GPR图像去噪方法，其特征在于，将贝叶斯网络中的条件概率表转化到联合树中,通过消息传递得到满足全局一致性的联合树,求出原贝叶斯网络中任意随机变量的概率分布,选取包含该随机变量的任意团节点,对其进行边际化即求出概率分布。
  7. 一种基于贝叶斯推理的GPR图像去噪系统，其特征在于，包括：
    用于选取设定的若干去噪模型，根据去噪模型、信号与噪声之间的关系构造贝叶斯网络；所述去噪模型、信号与噪声分别作为贝叶斯网络中的随机变量节点的装置；
    用于计算贝叶斯网络中各随机变量节点的联合概率密度的装置；
    用于对输入的待预测的GPR图像，贝叶斯网络通过联合树算法进行推理，计算出每一个像素点属于有效信号和噪声的后验概率，通过选择最大后验概率来实现GPR图像的信噪分离的装置。
  8. 一种终端设备，其包括处理器和计算机可读存储介质，处理器用于实现各指令；计算机可读存储介质用于存储多条指令，其特征在于，所述指令适于由处理器加载并执行权利要求1-6任一项所述的基于贝叶斯推理的GPR图像去噪方法。
  9. 一种计算机可读存储介质，其中存储有多条指令，其特征在于，所述指令适于由终端设备的处理器加载并执行权利要求1-6任一项所述的基于贝叶斯推理的GPR图像去噪方法。
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