A path adaptive downhole image reconstruction method

Abstract

This invention provides a path-adaptive downhole image reconstruction method. This method improves the accuracy and efficiency of atom selection by incorporating particle swarm optimization (PSO) and utilizes atom coherence to fill the support set. This selection method does not rely on atom coherence ranking but focuses only on the coherence relationships between atoms, effectively improving atom quality. Furthermore, regularization methods reduce support set redundancy, resulting in a more energy-concentrated support set. In addition, this invention adaptively increases the number of paths and expands the atom range by using adjacent residuals as a criterion, and uses a threshold parameter to reasonably control the number of iterations. When the number of paths reaches a certain level, the residual reconstruction coefficients are used to select the optimal path, thereby improving the algorithm's convergence efficiency.

Description

Technical Field

[0001] This invention relates to the field of image reconstruction, and in particular to a path-adaptive downhole image reconstruction method. Background Technology

[0002] Intelligent monitoring systems in coal mines are a crucial link in ensuring coal mine production. However, limited underground communication resources make it difficult to guarantee the quality of acquired video images. The compressed sensing transmission model based on sparse theory offers a novel transmission architecture that effectively changes this situation. Sparse reconstruction, as a vital component of the compressed sensing model, plays a crucial role in image quality. Therefore, it is necessary to design efficient and robust methods within the new transmission framework to ensure signal reconstruction accuracy, providing stronger support for subsequent early warning and linkage mechanisms.

[0003] In greedy matching pursuit methods, the earlier proposed methods all used the selection method based on the inner product of atoms and residuals. However, these two methods only select one atom to supplement the support set in each iteration, which to some extent limits the running speed of the method. To overcome this limitation, the regularized orthogonal matching pursuit method with a threshold setting selects multiple atoms in each iteration to improve the efficiency of the method, and uses a regularization method to reprocess the selected atoms, thereby ensuring reconstruction accuracy. Compressed sampling matching pursuit and subspace pursuit methods continue the selection method of multiple atoms. These two methods establish a backtracking mechanism to iteratively select atoms in the support set multiple times to seek the optimal combination of atoms to improve the signal reconstruction accuracy, achieving significant results. The multi-path matching pursuit method proposed by combining the tree structure search mode can find the true support set from multiple sub-support sets with a high probability, thereby ensuring accurate signal reconstruction.

[0004] The methods described above each have their advantages, but all require pre-defined sparsity, thus limiting their applicability. To address this shortcoming, the sparsity adaptive matching pursuit method adopts a segmented strategy. Within a segment, it continues the subspace pursuit method to obtain the optimal atomic combination, while between segments, it gradually approximates the true support set by increasing the step size. This overcomes the limitation of sparsity as an initial condition. However, since the step size and iteration stopping condition are relatively fixed, they cannot be adjusted according to the results, leaving significant room for improvement in the method's reconstruction performance. Summary of the Invention

[0005] Based on this, to address the problems existing in the prior art, this invention provides a path-adaptive downhole image reconstruction method. By combining particle swarm optimization and the concept of correlation sets, a new path update method is designed to adaptively increase the number of paths, thus optimizing the reconstruction process. Furthermore, a regularization method is used to achieve secondary selection of the support set. In addition, this invention sets a threshold parameter to reasonably control the number of iterations, effectively balancing reconstruction accuracy and efficiency. The technical solution of this invention is as follows:

[0006] The specific technical solution of this invention is as follows:

[0007] This invention provides a path-adaptive downhole image reconstruction method, which includes the following steps:

[0008] S1: Initialization, support set Λ0 = φ, iteration number t = 1, residual r0 = y, path base q = 1

[0009] S2: Particle initialization. The initial positions of the particles are the same as those of the atoms, and the total number of particles is N. The number of particle swarm iterations is n = 1.

[0010] S3: Update the particle velocity and position parameters, calculate the fitness function, and select the atoms corresponding to the top q optimal values ​​in the global state for output. The process is as follows:

[0011] (1) Update the particle velocity and position parameters using equations (1) and (2), calculate the fitness function, and select the atoms corresponding to the top q optimal values ​​in the global state.

[0012]

[0013]

[0014] In the formula, pbest i =(p i1 ,p i2, p i3 ,...,p id (gbest) represents the optimal position of an individual particle. j =(p j1 ,p j2, p j3 ,...,p jd ) represents the optimal position of the group. ω is a weighting factor; the particle's global search capability increases with its value. c1 and c2 are the particle's growth factors based on itself and the group, respectively. γ1 and γ2 are randomly generated real numbers within the interval [0,1]. n is the number of iterations. During the iteration process, v max It is set as the upper limit for the velocity of all particles.

[0015] (2) Calculate the fitness function

[0016] Where: a i To observe the atoms in the observation matrix Φ, r t-1 The residual obtained after the (t-1)th iteration

[0017] (3) Use the fitness function to determine if the condition is met. If the condition is met, output the first q atoms and proceed to step S4. Otherwise, update the particle swarm iteration count n = n + 1 and proceed to step S3.

[0018] S4: Using the concept of correlation sets, a coherence threshold is set to calculate the set that meets the correlation criteria, and the path set is further obtained. The specific steps are as follows:

[0019] (1) Calculate the relevant set Λ η1 (j)={i∈Ω|μ(i,j)>η1}

[0020] (2) Obtain the path set Λ η1 (Ω)=∪i ∈Ω Λ η1 (i)

[0021] S5: Regularize the path set obtained in S4 to obtain a more concentrated energy set. The specific steps are as follows:

[0022] (1) To Perform regularization, where |a i |≤2|a j |,(i,j∈J0), where J0 is the group with the highest energy.

[0023] (2) Obtain set Φ C The corresponding index set is C, and Λ = Λ t-1 ∪C

[0024] S6: Based on the obtained support set, calculate the residual between the estimate obtained in this iteration and the observed vector, and judge the obtained residual. The specific steps are as follows:

[0025] (1) Calculate the residual

[0026] (2) If f(r) = ||r t-1 ||2-||r new ||2<η2, or ||r new If ||≤opt×||y||2, then stop the iteration and proceed to step S4; otherwise, proceed to step S7.

[0027] Where, Φ Λ For the support set already obtained, r new This represents the residual generated in this iteration.

[0028] S7: Determine whether to increase the number of paths based on the magnitude of adjacent residuals. The specific steps are as follows:

[0029] (1) If ||r new ||2≥||r t-1 ||2, When the atoms in the current path are saturated and the reconstruction residual cannot be further reduced, update the number of paths q = q + 1, and q ≤ L, then proceed to step S2.

[0030] (2) If q > L transpose S8, then Λ t =Λ, r t =r new The iteration count is t = t + 1, and the transpose step is S2.

[0031] S8: When path q > L, in order to avoid redundant atoms affecting the reconstruction accuracy, the least squares method is used to select the atom with the largest reconstruction coefficient, and a set of atoms is established based on this. After merging it into the support set, the estimated value of the signal is obtained.

[0032] S9: Output.

[0033] The beneficial effects of this invention are as follows:

[0034] This invention proposes a path adaptive matching and tracking method. This method combines particle swarm optimization and sets an atomic coherence threshold to flexibly control the number of atoms selected. By adaptively increasing the number of paths to expand the range of atom selection, it combines regularization methods to accurately process atoms and eliminate erroneous atoms, thereby optimizing the atom selection accuracy. Finally, by using residual-based reconstruction coefficients and threshold parameters to reasonably set the path basis and iteration stopping conditions, the reconstruction accuracy can be effectively improved while ensuring a certain computational speed. Attached Figure Description

[0035] Figure 1 A flowchart of a path-adaptive downhole image reconstruction method;

[0036] Figure 2 This is a flowchart of step S4;

[0037] Figure 3 The flowcharts for steps S6 and S7 are shown below;

[0038] Figure 4 This image shows the reconstruction results of the Lena diagram using the present invention and seven other methods.

[0039] Figure 5 This is a reconstruction result of the underground tunnel map using the present invention and seven other methods. Detailed Implementation

[0040] The present invention will be further described in detail below with reference to the accompanying drawings and the following embodiments. Detailed Implementation

[0042] The following is in conjunction with the appendix Figure 1 The following embodiments further illustrate specific implementations of the present invention. These embodiments are used to explain the present invention but are not intended to limit its scope. One embodiment of the present invention discloses a path-adaptive downhole image reconstruction method, such as... Figure 1 As shown, the method includes the following steps:

[0043] S1: Initialization, support set Λ0 = φ, iteration number t = 1, residual r0 = y, path base q = 1

[0044] S2: Particle initialization. The initial positions of the particles are the same as those of the atoms, and the total number of particles is N. The number of particle swarm iterations is n = 1.

[0045] S3: Update the particle velocity and position parameters, calculate the fitness function, and select the atoms corresponding to the top q optimal values ​​in the global state for output. The process is as follows:

[0046] (1) Update the particle velocity and position parameters using equations (3) and (4), calculate the fitness function, and select the atoms corresponding to the top q optimal values ​​in the global state.

[0047]

[0048]

[0049] In the formula, pbest i =(p i1 ,p i2 ,p i3 ,...,p id (gbest) represents the optimal position of an individual particle. j =(p j1 ,p j2 ,p j3 ,...,p jd ) represents the optimal position of the group. ω is a weighting factor; the particle's global search capability increases with its value. c1 and c2 are the particle's growth factors based on itself and the group, respectively. γ1 and γ2 are randomly generated real numbers within the interval [0,1]. n is the number of iterations. During the iteration process, v max It is set as the upper limit for the velocity of all particles.

[0050] (2) Calculate the fitness function

[0051] Where: a iTo observe the atoms in the observation matrix Φ, r t-1 The residual obtained after the (t-1)th iteration

[0052] (3) Use the fitness function to determine if the condition is met. If the condition is met, output the first q atoms and proceed to step S4. Otherwise, update the particle swarm iteration count n = n + 1 and proceed to step S3.

[0053] S4: Using the concept of correlation sets, a coherence threshold is set to calculate the set that meets the correlation criteria, and the path set is further obtained. The specific steps are as follows:

[0054] (1) Calculate the relevant set Λ η1 (j)={i∈Ω|μ(i,j)>η1}

[0055] (2) Obtain the path set Λ η1 (Ω)=∪i ∈Ω Λ η1 (i)

[0056] S5: Regularize the path set obtained in S4 to obtain a more concentrated energy set. The specific steps are as follows:

[0057] (1) To Perform regularization, where |a i |≤2|a j |,(i,j∈J0), where J0 is the group with the highest energy.

[0058] (2) Obtain set Φ C The corresponding index set is C, and Λ = Λ t-1 ∪C

[0059] S6: Based on the obtained support set, calculate the residual between the estimate obtained in this iteration and the observed vector, and judge the obtained residual. The specific steps are as follows:

[0060] (1) Calculate the residual

[0061] (2) If f(r) = ||r t-1 ||2-||r new ||2<η2, or ||r new If ||≤opt×||y||2, then stop the iteration and proceed to step S4; otherwise, proceed to step S7.

[0062] Where, Φ Λ For the support set already obtained, r new This represents the residual generated in this iteration.

[0063] S7: Determine whether to increase the number of paths based on the magnitude of adjacent residuals. The specific steps are as follows:

[0064] (1) If ||r new ||2≥||r t-1 ||2, When the atoms in the current path are saturated and the reconstruction residual cannot be further reduced, update the number of paths q = q + 1, and q ≤ L, then proceed to step S2.

[0065] (2) If q > L transpose S8, then Λ t =Λ, r t =r new The iteration count is t = t + 1, and the transpose step is S2.

[0066] S8: When path q > L, in order to avoid redundant atoms affecting the reconstruction accuracy, the least squares method is used to select the atom with the largest reconstruction coefficient, and a set of atoms is established based on this. After merging it into the support set, the estimated value of the signal is obtained.

[0067] S9: Output.

[0068] The present invention will be further described below.

[0069] This invention provides a path-adaptive downhole image reconstruction method. Under the premise of unknown sparsity, this method combines particle swarm optimization to expand the atomic selection range by gradually increasing the number of atoms in the path set. Then, a regularization method is used to perform a secondary evaluation of the support set to improve the probability of obtaining the true support set. Based on the residual convergence, a more reasonable iteration stopping condition is set. In addition, to prevent the number of atoms in the path set from increasing too much, the residual reconstruction coefficient is used to select the best path set to improve reconstruction efficiency.

[0070] In step S2, the selection of the initial base atoms requires screening all atoms in the observation matrix, which increases complexity. Therefore, this invention uses particle swarm optimization to improve the accuracy and efficiency of atom selection. At this point, the fitness function is...

[0071]

[0072] The particle velocity and position parameters are updated using equations (6) and (7), and the fitness function is calculated. The atoms corresponding to the top q optimal values ​​in the global state are selected for output.

[0073]

[0074]

[0075] In the formula, pbest i =(p i1 ,p i2, p i3,...,p id (gbest) represents the optimal position of an individual particle. j =(p j1 ,p j2, p j3 ,...,p jd ) represents the optimal position of the group. ω is a weighting factor; the particle's global search capability increases with its value. c1 and c2 are the particle's growth factors based on itself and the group, respectively. γ1 and γ2 are randomly generated real numbers within the interval [0,1]. n is the number of iterations. During the iteration process, v max It is set as the upper limit for the velocity of all particles.

[0076] After obtaining the path-based atoms using step S3, in step S4, this invention utilizes the concept of correlation sets and takes into account the actual computational requirements of this invention. Atoms that meet the conditions are selected using formulas (8) and (9).

[0077] μ(i,j)=| i ,a j >|,(a i ,a j ∈Φ) (8)

[0078] Λ η (j)={i|μ(i,j)>η} (9)

[0079] Because no fixed step size is set, and only a coherence threshold is configured, the selection of atoms is more flexible and adjustable. That is, after the path is adaptively increased, if an atom in the matrix has a high correlation with the q path basis atoms under that path, more atoms will be selected. If the correlation is low, only a few atoms will be used to fill the matrix. This selection method does not depend on the atomic coherence ordering, but only focuses on the coherence relationship between atoms, effectively improving the atomic quality.

[0080] In step S5, to further improve the precision of the support set atoms and avoid excessive atomic redundancy, the selected atoms are regularized and then evaluated a second time.

[0081] |a i |≤2|a j |,(i,j∈J0) (10)

[0082] The specific regularization method involves grouping the atoms in the support set into different subsets, ensuring that the correlation between atoms in these subsets satisfies the condition that the maximum value is no greater than twice the minimum value. Then, the total energy of each subset is calculated, and the set with the highest energy is selected. This results in a more concentrated set of atoms, enhancing the precision of atom selection while improving processing speed. ​

[0083] In steps S6 and S7, the present invention judges based on the size of adjacent residuals. If the atoms in the current path are saturated and the reconstruction residual cannot be further reduced, the number of paths is adaptively increased to obtain a better atom combination. The specific method is as follows: set the initial number of paths to 1, that is, select the atom with the largest inner product as the basis, construct a set of atoms using formula (9), and then perform regularization processing on it to complete the reconstruction and obtain the residual r. new If the residual does not meet the condition, the path is updated to q = q + 1; if the condition is met, q remains unchanged and the next iteration continues. When the path q = d, the d-path atom set is formed by using the optimal d atoms selected by the particle swarm optimization method as the basis, which can be expressed as Equation (11). Then, in the same way, it is determined whether to update the number of paths and the support set, and the next iteration continues until the stopping condition is met.

[0084]

[0085] In step S6, the residual threshold setting directly affects the stability of the reconstruction. If the value is too small, it affects the convergence speed; if the value is too large, the reconstruction accuracy cannot be guaranteed. Due to the convergence condition of the SAMP method ||r new The parameter opt in ||≤opt×||y||2 is very small, which increases the probability of excessive iterations. Therefore, after obtaining the residual using equation (12), this invention combines the difference between adjacent residuals f(r)=||r t-1 ||2-||r new 2. Make a comprehensive judgment on the convergence status.

[0086]

[0087] This invention adaptively selects stopping conditions based on different convergence scenarios, enabling it to complete iterations within a reasonable numerical range while maintaining reconstruction accuracy. When the stopping condition is met, the estimated signal value is output using equation (13).

[0088]

[0089] While increasing the number of paths expands the range of atom selection, it also leads to a rapid increase in computational complexity. As the number of iterations increases, the residual decreases slowly, and the projection coefficients of some correct atoms approach zero, making them easily confused with invalid atoms. To avoid redundant atoms affecting reconstruction accuracy, the least squares method is used when path q > L.

[0090]

[0091] Select the atom with the largest reconstruction coefficient and use Equation (15) to establish a set of atoms and incorporate it into the support set.

[0092]

[0093] Finally, the signal estimate is calculated using the obtained support set.

[0094] This invention is not limited to the preferred embodiments described above. Anyone can derive other products in various forms under the guidance of this invention. However, regardless of any changes in shape or structure, any technical solution that is the same as or similar to this application falls within the protection scope of this invention.

Claims

1. A path-adaptive downhole image reconstruction method, characterized in that, The method includes the following steps: S1: Initialization, support set Λ0 = φ, iteration number t = 1, residual r0 = y, path base q = 1 S2: Particle initialization. The initial positions of the particles are the same as those of the atoms, and the total number of particles is N. The number of particle swarm iterations is n = 1. S3: Update the particle velocity and position parameters, calculate the fitness function, and select the atoms corresponding to the top q optimal values ​​in the global state for output. The process is as follows: (1) Update the particle velocity and position parameters using equations (1) and (2), calculate the fitness function, and select the atoms corresponding to the top q optimal values ​​in the global state. In the formula, pbest i =(p i1 ,p i2, p i3 ,...,p id (gbest) represents the optimal position of an individual particle. j =(p j1 ,p j2, p j3 ,...,p jd ) represents the optimal position of the group. ω is a weighting factor; the particle's global search capability increases with its value. c1 and c2 are the particle's growth factors based on itself and the group, respectively. γ1 and γ2 are randomly generated real numbers within the interval [0,1]. n is the number of iterations. During the iteration process, v max It is set as the upper limit for the velocity of all particles. (2) Calculate the fitness function Where: a i To observe the atoms in the observation matrix Φ, r t-1 The residual obtained after the (t-1)th iteration (3) Use the fitness function to determine if the condition is met. If the condition is met, output the first q atoms and proceed to step S4. Otherwise, update the particle swarm iteration count n = n + 1 and proceed to step S3. S4: Using the concept of correlation sets, a coherence threshold is set to calculate the set that meets the correlation criteria, and the path set is further obtained. The specific steps are as follows: (1) Calculate the relevant set (2) Obtain the path set S5: Regularize the path set obtained from S4 to obtain a more concentrated energy set. The specific steps are as follows: (1) To Perform regularization, where |a i |≤2|a j |,(i,j∈J0), where J0 is the group with the highest energy. (2) Obtain set Φ C The corresponding index set is C, and Λ = Λ t-1 ∪C S6: Based on the obtained support set, calculate the residual between the estimate obtained in this iteration and the observed vector, and judge the obtained residual. The specific steps are as follows: (1) Calculate the residual (2) If f(r) = ||r t-1 ||2-||r new ||2<η2, or ||r new If ||≤opt×||y||2, then stop the iteration and proceed to step S4; otherwise, proceed to step S7. Where, Φ Λ For the support set already obtained, r new This represents the residual generated in this iteration. S7: Determine whether to increase the number of paths based on the magnitude of adjacent residuals. The specific steps are as follows: (1) If ||r new ||2≥||r t-1 ||2, When the atoms in the current path are saturated and the reconstruction residual cannot be further reduced, update the number of paths q = q + 1, and q ≤ L, then proceed to step S2. (2) If q > L transpose S8, then Λ t =Λ, r t =r new The iteration count is t = t + 1, and the transpose step is S2. S8: When path q > L, in order to avoid redundant atoms affecting the reconstruction accuracy, the least squares method is used to select the atom with the largest reconstruction coefficient, and a set of atoms is established based on this. After merging it into the support set, the estimated value of the signal is obtained. S9: Output.

2. The path-adaptive downhole image reconstruction method as described in claim 1, characterized in that, Atom filling is performed using the particle swarm optimization algorithm combined with the concept of correlation sets to improve the quality of atom selection in the support set.

3. The path-adaptive downhole image reconstruction method as described in claim 1, characterized in that... The system judges the value of adjacent residuals. If the atoms in the current path are saturated, it adaptively increases the number of paths to obtain a better combination of atoms.

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