LU102399B1 - Gpr image denoising method and system based on bayesian inference - Google Patents
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Abstract
The present invention discloses a GPR image denoising method and system based on Bayesian inference. The method comprises: selecting several set denoising models, and constructing a Bayesian network according to the denoising models, and the relationship between signals and noises; wherein the denoising models, the signals and the noises are respectively used as random variable nodes in the Bayesian network; calculating a joint probability density of each random variable node in the Bayesian network; and inferring, by the Bayesian network, an input GPR image to be predicted by means of a junction tree algorithm, calculating a posterior probability that each pixel belongs to a valid signal or noise, and selecting a maximum posterior probability to achieve signal and noise separation of the GPR image. The method and system fuse multiple denoising models by means of the Bayesian network, and calculate the maximum posterior probability of each pixel in the Bayesian network by means of the junction tree algorithm, thereby achieving signal and noise separation.
Description
GPR IMAGE DENOISING METHOD AND SYSTEM BASED ON 102399
BAYESIAN INFERENCE Field of the Invention The present invention relates to the field of denoising technology for ground penetrating radar images, and particularly to a GPR image denoising method and system based on Bayesian inference. Background of the Invention The statement of this section mercly provides background art information related to the present invention. and does not necessarily constitute the prior art. Ground Penetrating Radar (GPR) effectively detects an underground target by means of the reflection principle of high-frequency electromagnetic beams. and is often used in many ficlds such as archeology. mineral exploration, disaster geological survey, geotechnical investigation. engineering quality inspection, inspection of building structures and detection of military targets. However. during the actual application process, due to the complex outdoor environment. billboards, buildings, plants, ete. all produce clectromagnetic interference. to form various interference waves, which affects the data quality of the ground penetrating radar. Many methods have been proposed to remove interference noise. A method based on filtering and denoising has been widely used, and it has a good effect on some noises with certain distribution, but has a poor effect on unknown interference wave noise in a GPR image. A method of denoising in a wavelet domain is also very common. In addition, there are some methods that combine wavelet transtorm and filtering methods, for example, combine median filtering and wavelet threshold denoising. Median filtering is performed on an image alter wavelet threshold denoising to effectively remove Gaussian noise from the image. When denoising based on a wavelet threshold, the selection of the threshold and a threshold function is very important to the denoising LU102399 result. but the optimal threshold and threshold function are difficult to determine from different noise characteristics.
Under a Bayesian framework. the prior art assumes the prior value of a wavelet coefficient as a generalized Gaussian distribution (GGD), and estimates the threshold by means of a BayesShrink method, which has a better effect on relatively high noise power.
The effect on some low-frequency noises or clutters similar to signals is not obvious.
Summary of the Invention In order to solve the above problems. the present invention proposes a GPR image denoising method and system based on Bayesian inference.
The method and system fuse multiple denoising models by means of a Bayesian network, and calculate a maximum posterior probability of cach pixel in the Bayesian network by using a junction tree algorithm. thereby achieving signal and noise separation.
In some embodiments, the following technical solution is adopted: A GPR image denoising method based on Bayesian inference includes: selecting several set denoising models, and constructing a Bayesian network according to the denoising models, and the relationship between signals and noises. wherein the denoising models, the signals and the noises are respectively used as random variable nodes in the Bayesian network: calculating a joint probability density of each random variable node in the Bayesian network: and inferring. by the Bayesian network, an input GPR image to be predicted by means of a junction tree algorithm. calculating a posterior probability that cach pixel belongs to a valid signal or noise, and selecting a maximum posterior probability to achieve signal and noise separation of the GPR image.
Further, in selecting several set denoising models. the denoising models include: Haar wavelet translorm.
Kuwahara filter, three-dimensional block matching filter, sym6 LU102399 wavelet transform. and Wiener filter models.
Further, calculating a joint probability density of each random variable node in the Bayesian network specifically includes: quantifying a coefficient of each random variable node by using a threshold; directed edges in the network representing the relations between different random variable nodes. setting a conditional probability value of cach node by means of experience, and obtaining a conditional probability table of the nodes; and obtaining the joint probability density according to the conditional probability table.
Further, obtaining the joint probability density according to the conditional probability table is specifically: P(U)= PU.K.H.BW.Y.S, N) = P(T)P(K | NP(H|NP(B|K.H) P(Y | B)P(W | BYP(S |W.Y)P(N|W,Y) (3) where.
P(I) represents the probability of I.
P(K|I) represents the probability of K based on the occurrence of I.
P(H|D) represents the probability of occurrence of H based on the occurrence of 1. P(B| K.
H) represents the probability of occurrence of B based on the occurrence of K and I, P(Y|B) represents the probability of occurrence of Y based on the occurrence of B.
P(W|B) represents the probability of occurrence of W based on the occurrence of B.
P(S|W.Y) represents the probability of occurrence of S based on the occurrence of W and Y, and P(N|W,Y) represents the probability of occurrence of N bascd on the occurrence of Wand Y.
Further, inferring, by the Bayesian network, an input GPR image to be predicted by means of a junction tree algorithm is specifically: connecting all parent nodes with the same child nodes. and transforming all the directed edges into undirected edges, to construct a Moral graph: triangulating the Moral graph, and when a ring in the Moral graph has more than a set number of nodes, adding an undirected edge to the ring to connect two non-adjacent nodes:
identifying cliques in the triangulated graph; and LU102399 establishing a junction tree, wherein the junction tree must contain all the cliques. and each intersection is used as a separation node connecting two cliques.
Further, the conditional probability table in the Bayesian network is transformed into the junction tree, the junction tree that satisfies global consistency is obtained by means of message passing, a probability distribution of any random variable in the original Bayesian network is solved, any clique containing the random variable is selected, and the clique is marginalized to solve the probability distribution.
In some other embodiments, the following technical solution is adopted: A GPR image denoising system based on Bayesian inference includes: an apparatus for sclecting several set denoising models, and constructing a Bayesian network according to the denoising models, and the relationship between signals and noises; whercin the denoising models, the signals and the noises are respectively used as random variable nodes in the Bayesian network: an apparatus for calculating a joint probability density of each random variable node in the Bayesian network: and an apparatus for inferring, by the Bayesian network, an input GPR image to be predicted by means of a junction tree algorithm, calculating a posterior probability that each pixel belongs to a valid signal or noise, and sclecting a maximum posterior probability to achieve signal and noise separation ol the GPR image.
In some other embodiments, the following technical solution is adopted: A terminal device includes a processor for implementing instructions and a computer-readable storage medium for storing multiple instructions that are adapted to be loaded by the processor to perform the above-mentioned GPR image denoising method based on Bayesian inference.
In some other embodiments, the following technical solution is adopted: A computer-readable storage medium stores multiple instructions that are adapted to be loaded by a processor of a terminal device to perform the above-mentioned GPR image denoising method based on Bayesian inference.
LU102399 Compared with the prior art. the beneficial effects of the present invention are: In the present invention, the coefficients ol the denoising models or the coeflicient characteristics thercof are fused together in the form of a Bayesian network, the 5 mutual relationships thereof are described by the conditional probability table, and inferring is performed by means of the junction tree algorithm.
The junction tree is first constructed, then message passing is performed, the posterior probability that cach pixel belongs to a valid signal or noise is calculated, and the maximum posterior probability is selected to achieve signal and noise separation. thereby achieving a desired denoising result.
Experimental results show that the denoising effect displayed by the method of the present invention not only eliminates clutters. but also well retains valid signals.
Brief Description of the Drawings
FIG. 1 is a schematic diagram of a Bayesian network: FIG. 2 is a schematic diagram of a GPR image denoising method based on Bayesian inference according to Embodiment 1 of the present invention: FIG. 3 is a denoising integrated model of a Bayesian network according to Embodiment 1 of the present invention:
FIG. 4 is a schematic diagram of Moral according to Embodiment | of the present invention: FIG. 5 is a schematic diagram of triangulation according to Embodiment 1 of the present invention, FIG. 6 is a schematic diagram of a junction tree:
FIG. 7 is a schematic diagram of three 50*50 areas: FIGS. 8(a)-(f) are comparison diagrams of denoising results using different algorithms.
Detailed Description of Embodiments LU102399 It should be noted that the following detailed descriptions are exemplary and are intended to provide further descriptions of the present application. All technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical filed to which the present application belongs, unless otherwise indicated. It should be noted that terms uscd herein are merely intended to describe specific implementation modes, rather than to limit the exemplary implementation modes according to the present application. As used herein, the singular form is also intended to comprise the plural form unless otherwise indicated in the context. In addition, it should be understood that when the terms “contain” and/or “include” are used in the description, they are intended to indicate the presence of features, steps. operations, devices, components and/or combinations thereof.
The embodiments in the present invention and the features in the embodiments can be combined with each other without conflicts.
[Embodiment i One or more implementation modes disclose a GPR image denoising method based on Bayesian inference, including the following steps: Several set denoising models arc sclected, and a Bayesian network is constructed according to the denoising models, and the relationship between signals and noises; wherein the denoising models, the signals and the noises are respectively used as random variable nodes in the Bayesian network: A joint probability density of each random variable node in the Bayesian network is calculated: The Bayesian network infers an input GPR image to be predicted by means of a junction tree algorithm, calculates a posterior probability that each pixel belongs to a valid signal or noise, and selects a maximum posterior probability to achieve signal and noise separation of the GPR image.
The method proposed in this embodiment fuses multiple denoising models by means LU102399 of the Bayesian network, and calculates the maximum posterior probability of each pixel in the Bayesian network by means of the junction tree algorithm, thereby achieving signal and noise separation. The following briefly introduces the theoretical basis of the Bayesian networks and two denoising model backgrounds.
A. Wiener filter denoising (Wiener filter) Wiener filter is to remove noise from a noisy signal based on adaptive minimum mean square error (MSE). When the input signal is a generalized stationary process.
the input signal is filtered according to second-order statistical characteristics thereof through the following formula: MON 2 MSE=S SW, x) :=l - WI (1) G + x, =, vi The parameters # and © ’ represent the mean and variance of an image, and the noise characteristic of a noise variance von the ground penetrating radar image 1s unknown. Here, a mean of all local estimated variances is used as the noise variance. The Wiener filter can well protect valid signals while denoising. On this basis, eight neighborhood features of the filter coefficient are selected later for further processing.
B. Wavelet threshold denoising Wavelet threshold denoising is a relatively classic image denoising method. Here, symé is selected as a wavelet basis. Three-layer decomposition is performed to obtain a group of wavclet cocfficients Wu; which are then processed by mcans of a hard threshold function. When the wavelet threshold method is used for denoising, factors such as the selection of the wavelet basis, the number of decomposition layers, and the threshold function all have different denoising effects. In the following sections.
gradient values of wavelet cocfficients after denoising are selected as features for further processing.
LU102399 C.
Bayesian network The Bayesian network is a probability graph model, which mainly expresses and infers uncertain factors through probability knowledge.
The Bayesian network is composed of a set of vertices and a set of directed edges.
The set of vertices includes related factors as random variables, while the directed edges describe the causal relationship between various factors, for example, parent nodes are often causes of child nodes, and child nodes are often results of parent nodes.
FIG. 1 shows a simple Bayesian network.
The joint probability distribution of the network is: PUY = P(MYPW)YP(N | Y W)P(S|Y.
IW) (2) In practical applications, a Bayesian network model is often established for multiple random variables.
Based on the expression of joint probability density distribution, a posterior probability of each random variable is calculated by means of an inference algorithm.
Each denoising method has its own characteristics and effects, but for a ground penetrating radar image, because the characteristics of signals and noises are unknown, and interference waves arc relatively complicated, a single method cannot achieve the desired denoising effect.
Fusing various denoising methods with a Bayesian network is proposed herein to construct an integrated model, and obtain posterior probabilities of noises and valid signals by means of a junction tree inference algorithm, to achieve signal and noise separation.
An algorithm framework is as shown in FIG. 2. In this embodiment, several common denoising models arc sclected to construct a Bayesian network, as shown in FIG. 3. Random variable nodes in the network represent various denoising models, signals and noises.
In order to simplify the calculation in subsequent inference. a threshold is used to quantity the coefficient of each vertex.
See Table 1 for node details.
Table 1 Sct of vertices
Node Meaning ype Value HU102999 I Original Image numeric {0,1} H Haar wavelet numeric {0,1} K Kuwahara filter numeric {0,1} B BM3D numeric {0,1} Y Symé wavelet numeric 40, 1,2} Ww Wiener filter numeric 10, 1, 2} N Noise boolean {1.1} S Signal boolean {T, F} The directed edges in the network represent the relations between different random variable nodes, and a conditional probability table of the nodes is obtained through statistical histograms of model coefficients.
Sce Table 2 for details.
Table 2 Conditional probability table of denoising model nodes i 1 P(T) P(H=0|T) P(K=0/D) H K P(B=0H.K) | 0 0.25 0.99 0.99 0 0.9 1 0.75 0.01 0.01 ) 1 0.5 B P(Y=0B) P(Y=1B) P(W=0IB) P(W=I1|B) 0 0.5 0 0.8 0.15 0.8 0.15 ! ] 0.1 1 0.15 0.8 0.15 0.8 it can be seen from the network that the Wiener filter and sym6 wavelet threshold denoising methods arc directly related to the valid signal and noise.
Therefore, corresponding eight neighborhoods and gradient features are selected as vertex information, and quantification of a discrete value {0, 1, 2} is performed (see the experiment part). The corresponding conditional probability table is shown in Table 3. Table 3 Conditional probability table of signal and noise
HH LU102399 Y W P(N=T|Y,W) P(S=T|Y,W) 0 ‘ 0. - 0.3 0 1 0,65 0.3 The 2 0.6 0.35 Joint 0 0.6 0.4 1 1 0.55 0.45 2 0.4 0.6 0 0.6 0.4 2 1 0.4 0.6 2 0.3 0.7 probability density of the Bayesian network is as follows: P(U)= PU.KH.BW.Y.S.N) = P(I)P(K | NP(H\N)P(B|K.H) PY | B)P(W | B)P(S|W.Y)P(N |W.Y) (3) After the Bayesian network and the conditional probability distribution table are determined. a joint probability distribution of all variables in the network is obtained. message passing is performed in combination with given evidences, and finally, a probability distribution of a certain node variable is calculated by marginalization.
This query process is called Bayesian inference.
Common Bayesian inference methods are divided into exact inference and approximate inference, and junction tree inference in the exact inference is used here.
The Junction Tree algorithm is an exact inference algorithm of the Bayesian network that currently has the fastest calculation speed and the widest application.
It returns exact 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.
The undirected graph is transformed into a tree structure by fully using the conditional independence in the Bayesian network. which greatly reduces the computational complexity. Then, the idea of message passing is used. When a new evidence is LU102399 added, a message is passed on the junction trec by means of separation nodes and cliques according to the conditional probability distribution tablet. After the message is passed, a joint distribution of all the variables is solved. The probability distribution of a certain random variable can be obtained from a potential of any clique containing the variable, which can be implemented by a marginalization formula: P(X)= wl)
FAX Where, U is the clique containing the variable X, and YU) is the potential of the clique U. First, a junction tree is constructed. In this process, a directed acyclic graph is finally transformed into a tree structure, It should be noted that the nodes in the junction tree are no longer single variables, but cliques consisting of multiple variables. The specific steps are as follows: 1) Constructing a Moral graph: All parent nodes with the same child nodes are connected. and all directed edges are transformed into undirected edges, as shown in FIG. 4. 2) Triangulating the graph: when a ring in the Moral graph has more than 4 nodes, an undirected edge is added to the ring to connect two non-adjacent nodes. The ring YSWN in FIG. 4 conforms to this characteristic, and needs to be triangulated, as shown in FIG. 5. 3) Identifying Cliques: cliques are identified in the triangulated graph. Each clique is a subgraph of the undirected graph. A set of cliques C identified here is: HK, BHK BYW and YSWN A set of separation nodes S, that is, cross nodes between the cliques are: HK B,and YW. 4) Establishing a junction tree: The established junction tree must contain all the cliques, and each intersection is used as a separation node connecting two cliques, as shown in FIG. 6.
It can be scen from FIG. 6 that there are two types of nodes in the junction tree, the 0102399 elliptic nodes are cliques and cach clique has its own potential and a corresponding probability distribution.
The square nodes are separation nodes.
When a new evidence is added. a message is passed and received between the cliques through the separation nodes.
After the junction tree is constructed. the conditional probability table in the Bayesian network is transformed into the junction tree, a junction tree that satisfies global consistency is obtained by means of message passing, a probability distribution of any random variable in the original Bayesian network can be solved. any clique containing the random variable is selected, and the clique is marginalized to solve the probability distribution.
It should be noted that. in the junction tree, the potential product of the cliques divided by the potential product of the separation nodes is equivalent to the joint probability distribution of the Bayesian network.
The specific expression is as follows: | [Twix PU) = — z [Jr 0 - W(IHK Ww (BHK yy (BYW yy (YSWN) y (HK (Bw (YSW) = P(DPK | NP(HINP(B|KA)PO | B) PW | B)P(SIW.Y)P(N(W,Y) (4) By formula (4), a corresponding distribution function is assigned to cach clique to initialize the potential of each clique: w(IHK) = PO)PH\DP(K|N w(BHK)Y=P(B|H,K) w(BYW)=P0|B)PW | B) W(YSWN)= P(S|W.Y)P(N | W.Y) w(HK)=w(B)=w(YIW)=1 (5) In the junction tree. when any two cliques V and W and a cross node S thereof SYW)= P(S)=S y) satisfy x Us . the junction tree is referred to have global consistency. and the entire network system reaches a steady state at this time.
If a
; oo LU102399 new evidence is added to cause wi) yd ). in order to maintain the global consistency in the junction tree. message passing is required on the junction tree (the arrows in FIG. 6 indicate the direction of message passing). The potential of cach clique is updated by the following formula: w (HK) =D y(IK) ! = X P(NP(HINP(K}1)
I "(HK wrk = UN i w(K) = > PPK | DPI HPBI KH) ! vw (B) = S'w'(BHK)
AH = X PUP(KIDPUTT)P(B/K,H)
KH wr BYW)= Ey py y(B) = > PINPH I DP(K| DPB KIDPY | B)PUW | B)
FR w (YW) = S'w'(BYW) ñ = > PODP(KÆ|NPOI|NP(B| K, HY PY I BYP(W | B) IN ñ * W wasn = LO) ray WOW) = > PUHPK|DP(H | DP(B| KH)
INH SPY BIP | BYP(S|Y WIPIN|Y I) (6) 3 i So far. the potential of each clique has been updated, and the probability distribution of any random variable can be obtained. If the probability distribution of a signal S is intended to be obtained, the potential y (YSWN) in formula (6) can be marginalized in combination with the evidence information given: P(S)= Dw (YSWN) (7)
FHA For example. an evidence Y=0W=1 i given to calculate the posterior probability of P(SST\Y=0W 1 Here, the posterior probability is obtained by LU102399 means of the potential WYSWN) of the clique FSWN : P(S=T)= Sy‘ (YSWN)
FHON = > ( SPODPIK INPUT DPB KAP)
YN LAH SPY = 0) BPW = BPS =TY =0W =DP(N|Y =0W =D) (8) i In formula (8). S does not depend on nodes 1, K. H. and B. so formula (8) can be simplified into the following form: P(S=T7T)= > PIS=T|Y=0W=0O)P(N|Y=0W =1) (9) = The result of formula (9) is calculated to be 0.4 in combination with the conditional probability table. Similarly, the probability value under the cvidence N=T is calculated to be 0.6. Based on the selection of a maximum posterior probability, this node is considered as a noise node. By analogy, the probability that each pixel in the image belongs to a valid signal or noise can be calculated through this inference process, and the maximum posterior probability is selected to determine whether the node is noise. This Bayesian exact inference method that integrates multiple denoising models shows good performance.
The experimental data selects real ground penetrating radar images interfered by billboards. During the experiment, cight neighborhoods D(W) of node W and gradient values G(Y) of node Y are selected to replace the coefficient values of W and Y as an evidence for Bayesian inference. When the coelficient C of each node in the Bayesian network is quantified, the parameters are set as follows:
wale) = ie < 200 , value = 0 IH KB C, > 200, value = 1 Cy <100, value = 0 value( D(W))=4100 < Cp) < 200, value = 1 Cyr) 2200 ‚value =2 Com (0 value =0 value(G(YY=40C 7, < 40, value =1 Cour > 40, value =2 (10) Some evaluations are made to the experimental results as follows: 1) Method Noise In the absence of an original noise-free image as a reference, method noise is used to test the denoising effect, which is calculated by the Euclidean difference between the denoised image and the noisy image.
The method noise helps to understand the performance and limitations of denoising algorithms, because removing details or textures would produce larger method noise.
By observing the Method noise results, which geometric features or details arc preserved and which clutter noises are eliminated can be clearly seen.
Therefore, the method of this embodiment well removes noises while retaining valid signals. 2) Signal to Noise Ratio (SNR) Since the experimental image comes from real data and there is no pure reference image, three small areas of 50*50 arc randomly selected, as shown in FIG. 7. The signal to noise ratio is calculated by the ratio of the mean to variance of the three small areas, so as to compare with each denoising algorithm.
See Table 4 for specific values.
Table 4 SNR comparison BM3D denoise Symö6 wavelet Kuwahara Our denoise Area SNR SNR filter SNR SNR
1 3.2516 4.5638 3.0517 4.5638 102399 2 4.2987 5.3487 3.9681 5.3505 3 4.9967 5.3139 4.0700 5.3139 Comparing the algorithm proposed in this embodiment with the common BM3D denoising model, wavelet threshold denoising model and Kuwahara filter denoising model, the results show that the method of this embodiment has a higher signal to noise ratio. 3) Visual quality evaluation Another important criterion for judging the performance of denoising algorithms is visual quality evaluation, which is also the most direct evaluation method reflecting the denoising cffeet.
Several classic denoising algorithms are selected for comparison. as shown in FIGS. 8(a)-(1). In this embodiment, several classic denoising algorithms are selected for comparison.
FIG. 8(a) is a noisy image used in the experiment: FIG. 8(b) shows a BM3D algorithm, which has good local smoothing effect, but obvious artifacts: the bilateral filter denoising of FIG. 8(c) and the haar wavelet denoising of FIG. 8(d) have certain suppression effect on clutters. but weaken valid signals: and the wiener algorithm in FIG. 8(e) better retains valid signals. but has poor effect of removing clutters.
It can be seen that the denoising effect shown in FIG. 8(f) by the method of this embodiment not only eliminates clutters, but also retains valid signals.
Embodiment 2 In onc or more implementation modes, disclosed is a GPR image denoising method based on Bayesian inference, including: an apparatus for selecting several set denoising models, and constructing a Bayesian network according to the denoising models, and the relationship between signals and LU102399 noises: wherein the denoising models, the signals and the noises are respectively used as random variable nodes in the Bayesian network: an apparatus for calculating a joint probability density of cach random variable node in the Bayesian network; and an apparatus for inferring. by the Bayesian network. an input GPR image to be predicted by means of a junction tree algorithm, calculating a posterior probability that cach pixel belongs to a valid signal or noise, and selecting a maximum posterior probability to achieve signal and noise separation of the GPR image.
Embodiment 3 In one or more implementation modes. disclosed is a terminal device, including a server. wherein the server includes a memory, a processor, and a computer program stored on the memory and executable on the processor, and when the processor executes the program, the GPR image denoising method based on Bayesian 13 inference in Embodiment | is implemented.
For the sake of brevity, details are not described herein again. ft should be understood that, in this embodiment, the processor may be a central processing unit (CPU). and the processor may also be other general-purpose processor. digital signal processor (DSP), application-specific integrated circuits (ASIC). field programmable gate array (FPGA) or other programmable logie device, discrete gate or transistor logic device, discrete hardware component, ete.
The general-purpose processor may be a microprocessor or any conventional processor, etc.
The memory may be a read-only memory or a random access memory, and provides instructions and data to the processor.
À part of the memory may also include a non-volatile random access memory.
For example, the memory may also store information of device types.
In the implementation process. the steps of the above-mentioned method may be completed by an integrated logic circuit of hardwarc in the processor or by LU102399 instructions in the form of software. The GPR image denoising method based on Bayesian inference in Embodiment 1 may be directly implemented by a hardware processor. or by a combination of hardware and software modules in the processor. The software modules may be located in a storage medium that is mature in the art, such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory, an electrically crasable programmable memory, or a register. The storage medium is located in the memory, and the processor reads the information in the memory and combines the hardware to complete the steps of the above method. To avoid repetition, details arc not described herein again.
Those of ordinary skill in the art may realize that the units and algorithmic steps of each example described in combination with the embodiments may be implemented by electronic hardware or a combination of computer software and electronic hardware. Whether these functions are executed by hardware or software depends on a specific application and design constraint conditions of the technical solution. Professionals may implement the described functions for each specific application by using different methods, but such implementation should not be considered beyond the scope of the present application.
The specific embodiments of the present invention are described above with reference to the accompanying drawings, but are not intended to limit a protection scope of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort arc still within the protection scope of the present invention on the basis of the technical solution of the present invention.
Claims (9)
1. A GPR image denoising method based on Bayesian inference. comprising: selecting several set denoising models. and constructing a Bayesian network according to the denoising models, and the relationship between signals and noises; wherein the denoising models. the signals and the noises are respectively used as random variable nodes in the Bayesian network: calculating a joint probability density of each random variable node in the Bayesian network: and inferring, by the Bayesian network, an input GPR image to be predicted by means of a junction tree algorithm, calculating a posterior probability that each pixel belongs to a valid signal or noise. and selecting a maximum posterior probability to achieve signal and noisc separation of the GPR image.
2. The GPR image denoising method based on Bayesian inference according to claim 1, wherein in selecting several set denoising models. the denoising models comprise: Haar wavelet transform. Kuwahara filter, three-dimensional block matching filter, sym6 wavelet transform, and Wiener filter models.
3. The GPR image denoising method based on Bayesian inference according to claim
1. wherein calculating a joint probability density of cach random variable node in the Bayesian network specifically comprises: quantifying a coefficient of each random variable node by using a threshold; directed edges in the network representing the relations between different random variable nodes. setting a conditional probability value of each node by means of experience, and obtaining a conditional probability table of the nodes: and obtaining the joint probability density according to the conditional probability table.
4. The GPR image denoising method based on Bayesian inference according to claim
3. wherein obtaining the joint probability density according to the conditional probability table is specifically:
PU) = P(I.K.H,B,W.Y.S.N) LU102399 =P(NHPIK|NYPH| DP(B|K.H) PY | B)P(W | B)P(S|W.Y)P(N|W,F) (3) where, P(I) represents the probability of I, P(K|I) represents the probability of K based on the occurrence of I, P(H]I) represents the probability of occurrence of H based on the occurrence of 1. P(B| K. IT) represents the probability of occurrence of B based on the occurrence of K and H. P(Y|B) represents the probability of occurrence of Y based on the occurrence of B, P(WIB) represents the probability of occurrence of W based on the occurrence of B. P(S|W.Y) represents the probability of occurrence of S based on the occurrence of W and Y, and P(N|W.Y) represents the probability of occurrence of N based on the occurrence of W and Y.
5. The GPR image denoising method based on Bayesian inference according to claim 1, wherein inferring. by the Bayesian network, an input GPR image to be predicted by means of a junction trec algorithm is specifically: connecting all parent nodes with the same child nodes, and transforming all the directed edges into undirected edges, to construct a Moral graph: triangulating the Moral graph, and when a ring in the Moral graph has more than a set number of nodes. adding an undirected edge to the ring to connect two non-adjacent nodes: identifying cliques in the triangulated graph; and establishing a junction tree, wherein the junction tree must contain all the cliques. and each intersection is used as a separation node connecting two cliques.
6. The GPR image denoising method based on Bayesian inference according to claim
5. wherein the conditional probability table in the Bayesian network is transformed into the junction tree, the junction tree that satisties global consistency is obtained by means of message passing, a probability distribution of any random variable in the original Bayesian network is solved, any clique containing the random variable is selected. and the clique is marginalized to solve the probability distribution.
7. A GPR image denoising system based on Bayesian inference. comprising:
an apparatus for selecting several set denoising models, and constructing a Bayesian LU102399 network according to the denoising models. and the relationship between signals and noises; wherein the denoising models. the signals and the noises arc respectively used as random variable nodes in the Bayesian network: an apparatus for calculating a joint probability density of each random variable node in the Bayesian network: and an apparatus for inferring. by the Bayesian network, an input GPR image to be predicted by means of a junction tree algorithm, calculating a posterior probability that each pixel belongs to a valid signal or noise. and selecting a maximum posterior probability to achieve signal and noise separation of the GPR image.
8. A terminal device, comprising a processor for implementing instructions and a computer-readable storage medium for storing multiple instructions. whercin the instructions are adapted to be loaded by the processor to perform the GPR image denoising method based on Bayesian inference according to any one of claims 1-6.
9. A computer-readable storage medium, storing multiple instructions therein. wherein the instructions are adapted to be loaded by a processor of a terminal device to perform the GPR image denoising method based on Bayesian inference according to any one of claims 1-6.
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| CN114494819A (en) * | 2021-10-14 | 2022-05-13 | 西北工业大学 | Anti-interference infrared target identification method based on dynamic Bayesian network |
| CN114494819B (en) * | 2021-10-14 | 2024-03-08 | 西北工业大学 | Anti-interference infrared target identification method based on dynamic Bayesian network |
| CN117892118A (en) * | 2024-03-08 | 2024-04-16 | 华侨大学 | Underdetermined working mode parameter identification method, device, equipment and storage medium |
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