A noise-robust high-resolution range profile feature selection method

Abstract

The present invention relates to a noise-robust high-resolution range image feature selection method, comprising: obtaining a high-resolution range image sample set of a target, and performing feature extraction on the high-resolution range image of each target to obtain an original feature set; respectively calculating the ReliefF evaluation value, mRMR evaluation value and noise robustness parameter of each feature in the original feature set; performing multi-evaluation value fusion processing on the ReliefF evaluation value, mRMR evaluation value and noise robustness parameter of each feature to obtain a fusion evaluation value of each feature; according to the fusion evaluation value, using a sequence floating forward search method, performing feature search on the original feature set to obtain an optimal feature subset under a preset dimension, so as to use the optimal feature subset for subsequent target recognition operations. The method of the present invention takes noise factors into consideration, and uses a sequence floating forward search algorithm to search for feature subsets. The selected feature subset has small dimensions, low redundancy, good noise robustness, and greatly improves the probability of target recognition.

Description

Technical Field

[0001] The invention belongs to the field of radar technology, and in particular relates to a noise-robust high-resolution range profile feature selection method. Background Art

[0002] When the radar system detects ground targets, the scene includes the target to be attacked and the interference of false targets (such as civilian vehicles, simple houses, etc.). The scattering characteristics of such false targets are similar to those of the target to be attacked, and target recognition technology is needed to identify and eliminate them. Target recognition is a multi-classification problem. By learning the characteristics of known data, a description of known data is formed, and then the similarity between new samples and known data is calculated to classify new samples. In the target recognition process, it is first necessary to extract features from the high-resolution range profile (HRRP) of various types of targets. Different features have different effects on recognition performance. If feature selection is not performed, the original high-dimensional feature combination will not only lead to poor generalization performance of the model and slow calculation speed, but also the high redundancy between features will lead to subsequent recognition performance degradation. Therefore, it is very necessary to study more effective feature selection algorithms.

[0003] At present, the most studied methods are filtering feature selection algorithms, encapsulation feature selection algorithms and hybrid feature selection methods. Among them, the filtering feature selection algorithm calculates the contribution of each feature to the classification based on the intrinsic relationship of the data, which is independent of the subsequent classification algorithm, has low computational complexity and fast speed. Wang Xu et al. proposed in "K-anonymous feature selection based on extreme gradient enhancement of feature importance" to sort individual features according to feature importance, and select the top-ranked features from the feature sorting to form the optimal feature subset. However, this method involves the problem of how to set the threshold, and it is easy to ignore the combination effect between features, and the selected feature combination is prone to redundant features. The encapsulation feature selection algorithm uses the training accuracy of the subsequent learning algorithm to evaluate the quality of the feature subset, with small deviation, but it is prone to overfitting and large computational complexity. The hybrid feature selection method uses both filtering and encapsulation methods. First, the filtering method is used to eliminate most irrelevant or noise-sensitive features, thereby reducing the scale of feature search, and then the encapsulation feature selection method is used to select the optimal feature subset. The hybrid feature selection method achieves a compromise between performance and computational complexity. Its computational complexity is lower than that of the encapsulation method, its performance is better than that of the filtering method, and it is not prone to overfitting.

[0004] The actual working scene of the radar seeker is very complex, and the signal-to-noise ratio of the collected echo data is relatively low. When selecting features, features that are robust to noise should be selected so that the recognition system of the radar seeker has high noise robustness. In addition, most of the targets that need to be identified in practical applications are non-cooperative targets and the storage capacity of the radar seeker is limited, so it is very meaningful to find a set of optimal feature subsets with small feature dimensions, less redundant information between features, and high noise robustness. Summary of the invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a noise-robust high-resolution range image feature selection method. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The present invention provides a noise-robust high-resolution range profile feature selection method, comprising the following steps:

[0007] Step 1: Obtain a sample set of high-resolution range images of the target, and perform feature extraction on the high-resolution range image of each target to obtain an original feature set;

[0008] Step 2: Calculate the ReliefF evaluation value, mRMR evaluation value and noise robustness parameter of each feature in the original feature set respectively;

[0009] Step 3: performing multi-evaluation value fusion processing on the ReliefF evaluation value, the mRMR evaluation value and the noise robustness parameter of each feature to obtain a fusion evaluation value of each feature;

[0010] Step 4: According to the fusion evaluation value, the original feature set is searched using a sequence floating forward search method to obtain an optimal feature subset under a preset dimension, so as to use the optimal feature subset for subsequent target recognition operations.

[0011] In one embodiment of the present invention, step 1 comprises:

[0012] Acquire a sample set of high-resolution range images of dual-polarization targets collected by a radar, and preprocess the high-resolution range image of each target to overcome the sensitivity of the high-resolution range image;

[0013] Feature extraction is performed on the pre-processed high-resolution range image to obtain frequency domain features and time domain features of the high-resolution range image, and the original feature set is obtained by combining them.

[0014] In one embodiment of the present invention, step 2 comprises:

[0015] Calculate the ReliefF evaluation value of each feature according to the ReliefF evaluation criteria;

[0016] The mRMR evaluation value of each feature was calculated according to the mRMR evaluation criteria;

[0017] Noise is added to the high-resolution range image sample set of the target, and corresponding features are extracted from the noise-contaminated high-resolution range image sample set to obtain a noise feature set, and noise robustness parameters of each feature are calculated based on the noise feature set and the original feature set.

[0018] In one embodiment of the present invention, the ReliefF evaluation value of each feature is calculated according to the ReliefF evaluation criterion, including:

[0019] The original feature set is recorded as X, where X is an M×N matrix, each sample contains M features, and there are N samples in total;

[0020] Take sample R from X, select K neighboring points from samples of the same type as sample R in X, denoted as H, and select K neighboring points from samples of different types from sample R, denoted as M;

[0021] The weight matrix W is calculated as follows:

[0022]

[0023] In the above formula, q represents the number of iterations, H j represents the jth nearest neighbor sample of the same type as sample R, M j (C) indicates class The jth nearest neighbor sample in the , p(C) is the probability of category C appearing, class(R) is the category to which sample R belongs, p(class(R)) is the probability of the category to which sample R belongs, diff(x i ,R,H j ) represents samples R and H j In feature x i The difference on is as follows:

[0024]

[0025] In the selected feature S m-1 Based on this, an incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:

[0026] ΔW(x i )=W([S m-1 ,x i ])-W(S m-1 );

[0027] In the formula, ΔW(x i ) represents the feature x i ReliefF evaluation value.

[0028] In one embodiment of the present invention, the mRMR evaluation value of each feature is calculated according to the mRMR evaluation criteria, including:

[0029] According to the definition of mutual information, the mutual information between a single feature and a category is calculated as follows:

[0030]

[0031] In the formula, x i and C represent the i-th feature in the original feature set X and the category to which the feature belongs, respectively. i ) represents the feature x i The marginal probability distribution of , p(C) represents the marginal probability distribution of category C, and p(x i ,C) represents the feature x i and the joint probability distribution of category C;

[0032] The maximum correlation between the original feature set X and the category is defined as:

[0033]

[0034] In the formula, M represents the number of features contained in the original feature set X;

[0035] The mutual information between features is calculated as follows:

[0036]

[0037] The minimum correlation between features is defined as:

[0038]

[0039] mRMR combines both measures and defines the following criteria:

[0040] maxΦ(D,Q)=DQ;

[0041] In the selected feature S m-1 Based on this, an incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:

[0042]

[0043] In the formula, ΔI(x j ) represents the feature x j The mRMR evaluation value of , m represents the number of selected feature subsets, C represents the feature x i Category.

[0044] In one embodiment of the present invention, noise is added to the high-resolution range image sample set of the target, and corresponding features are extracted from the noise-contaminated high-resolution range image sample set to obtain a noise feature set. According to the noise feature set and the original feature set, a noise robustness parameter of each feature is calculated, including:

[0045] Add noise to the high-resolution range image of each target;

[0046] The time domain and frequency domain features are extracted from the noise-contaminated high-resolution range image to obtain a noise feature set, denoted as R(x i ,n), where x i is the i-th feature, i=1,2,…,M, n is the index of the signal-to-noise ratio, n=1,2,…,I;

[0047] Calculate the deviation between the features at different signal-to-noise ratios and the corresponding features without noise:

[0048] R c (x i ,n)=|R(x i ,n)-R X (x i )|;

[0049] Based on the deviation, the noise robustness parameter of the feature is calculated:

[0050]

[0051] Where P snr (x i ) represents the feature x i The noise robustness parameter of .

[0052] In one embodiment of the present invention, step 3 comprises:

[0053] The Z-score standardization method is used to normalize the ReliefF evaluation value and the mRMR evaluation value of each feature, and the separability increment value of the feature is obtained as follows:

[0054]

[0055] In the formula, ΔH(x i ) represents the feature x i The incremental value of divisibility, ΔW(x i ) represents the feature x i ReliefF evaluation value, ΔI(x i ) represents the feature x i The mRMR evaluation value, mean and std represent the calculation process of mean and standard deviation respectively;

[0056] According to the separability increment value and the noise robustness parameter of the feature, the fusion evaluation value of the feature is calculated according to the following formula:

[0057] J(x i )=ΔH(x i )-βP snr (x i );

[0058] In the formula, J(x i ) represents the feature x i The fusion evaluation value, P snr (x i ) represents the feature x i The noise robustness parameter of β represents the proportion of noise robustness factors in the feature selection process.

[0059] In one embodiment of the present invention, step 4 comprises:

[0060] The fusion evaluation values ​​of the features are sorted, and the two features with the highest fusion evaluation values ​​are selected as the initial feature subset. The feature search is performed using the sequence forward search method to obtain the optimal feature subset under the preset dimension, where:

[0061] Suppose that when the k-th step search is completed, the feature subset obtained is A k , then, the k+1th step searches for the following operations:

[0062] Forward selection of new features: Select a feature x from the set of features to be selected i Add feature subset A k , forming a new feature subset A k+1 =A k +x i , where x i is to make A k+1 The fusion evaluation value J(A k+1 ) Increase the maximum feature;

[0063] Backward elimination of old features: k+1 Select a feature x from j , so that the fusion evaluation value of the feature subset after removing the feature is reduced to the minimum, for x j and x i Make a judgment,

[0064] If x j and x i If they are the same feature, feature x will not be removed. j , and set k=k+1, and continue to the next step of searching;

[0065] If x jand x i If they are not the same features, then x j From A k+1 Eliminate from the feature set and generate a new feature subset A k ′=A k+1 -x j , continue from feature subset A k Select a feature x from t , so that the fusion evaluation value of the feature subset after removing the feature is reduced to the minimum, and the fusion evaluation value J(A k ′-x t ) and the feature subset A obtained when the k-1 step search is completed k-1 The fusion evaluation value J(A k-1 ) to make a judgment,

[0066] If J(A k ′-x t )≤J(A k-1 ), then feature x is not removed t , and let A k =A k ′, continue the forward selection of new features;

[0067] If J(A k ′-x t )>J(A k-1 ), then x t From A k ′, and generate a new subset A k-1 ′=A k -x t , and let k = k-1, and continue the operation of removing old features backward;

[0068] Among them, when k=2, the backward elimination of old features is stopped, and when k is greater than the preset dimension, the forward selection of new features is stopped.

[0069] Compared with the prior art, the present invention has the following beneficial effects:

[0070] 1. The noise-robust high-resolution range profile feature selection method of the present invention effectively combines the feature ReliefF evaluation value and the mRMR evaluation value noise robustness parameter to make a more comprehensive and correct evaluation of the separability of the feature.

[0071] 2. The noise-robust high-resolution range image feature selection method of the present invention uses a sequence floating forward feature search algorithm to search for feature subsets, which not only ensures that the results are close to the global optimum, but also avoids global search. In the search process, new features are continuously selected forward and old features are eliminated backward, so that the dimension of the final feature subset is smaller. A small feature dimension means good generalization performance, and the noise robustness factor is taken into account when calculating the feature evaluation value, so the noise robustness of the feature subset finally selected is better.

[0072] 3. The noise-robust high-resolution range profile feature selection method of the present invention analyzes each feature more comprehensively and takes noise factors into consideration, and uses a sequence floating forward search algorithm to search for feature subsets. The selected feature subsets have small dimensions, low redundancy, and good noise robustness, which greatly improves the probability of target recognition.

[0073] The above description is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present invention more obvious and easy to understand, the following specifically cites a preferred embodiment and describes it in detail with the accompanying drawings as follows. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 is a schematic diagram of a noise-robust high-resolution range profile feature selection method provided by an embodiment of the present invention;

[0075] Figure 2 is a flow chart of a noise-robust high-resolution range profile feature selection method provided by an embodiment of the present invention;

[0076] Figure 3 is a comparison diagram of the recognition results of the method of the present invention provided by an embodiment of the present invention and the existing method;

[0077] Figure 4 It is a comparison diagram of the search with and without features based on the method proposed by the present invention provided by an embodiment of the present invention;

[0078] Figure 5 is a noise robustness parameter diagram of each feature provided by an embodiment of the present invention;

[0079] Figure 6 It is a comparison diagram of the influence of the presence or absence of noise robustness on the recognition performance provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0080] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, a noise-robust high-resolution range image feature selection method proposed in the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0081] The above and other technical contents, features and effects of the present invention are clearly presented in the following detailed description of the specific implementation modes in conjunction with the accompanying drawings. Through the description of the specific implementation modes, the technical means and effects adopted by the present invention to achieve the predetermined purpose can be more deeply and specifically understood. However, the attached drawings are only for reference and explanation purposes and are not used to limit the technical solutions of the present invention.

[0082] Embodiment 1

[0083] HRRP is the vector sum of the target scattering point sub-echoes obtained based on the radar broadband signal projected in the radar line of sight direction. It contains characteristic information such as target structure and scattering point distribution, and has the advantages of easy acquisition, small amount of calculation, relaxed error estimation, and fast calculation speed. Therefore, HRRP has become a research hotspot in the field of radar target recognition and classification.

[0084] HRRP-based target recognition is generally divided into training stage and recognition stage. Each stage has three links: preprocessing, feature extraction and selection, and classifier design or testing. Among them, preprocessing is mainly to overcome the three major sensitivities of HRRP, including: posture sensitivity, translation sensitivity, and amplitude sensitivity. Feature extraction includes both various mathematical and physical features extracted from HRRP that characterize the essence of the target, and the operation of projecting the original high-dimensional feature matrix or the original HRRP transform into a space with good separability. The feature selection algorithm screens the extracted features, selects a set of optimal feature subsets with good separability, uses the optimal feature subset of the training sample as the input of the classifier, tunes the parameters of the classifier, and uses the test recognition sample to verify the performance of the classifier. From the above three links, it can be found that the optimal feature subset of the training sample will directly affect the performance of the classifier, so it is particularly important to select a feature subset with good separability, low information redundancy, and small dimension.

[0085] In HRRP radar target recognition, recognition performance, noise robustness and storage requirements are all key factors in measuring the performance of a classifier. Taking the above factors into consideration, this embodiment provides a noise robust high resolution range profile feature selection method.

[0086] Please refer to Figure 1 and Figure 2 , Figure 1 is a schematic diagram of a noise-robust high-resolution range profile feature selection method provided by an embodiment of the present invention; Figure 2 1 is a flow chart of a noise-robust high-resolution range profile feature selection method provided by an embodiment of the present invention. As shown in the figure, the method includes:

[0087] Step 1: Obtain a sample set of high-resolution range images of the target, and perform feature extraction on the high-resolution range image of each target to obtain an original feature set;

[0088] Specifically, step 1 includes:

[0089] Step 1.1: Obtain a sample set of dual-polarization target high-resolution range images collected by the radar, and pre-process the high-resolution range image of each target to overcome the sensitivity of the high-resolution range image;

[0090] In this embodiment, the high-resolution range image sample set includes N groups of high-resolution range images of the dual-polarization radar for the target, and the high-resolution range image includes co-polarization high-resolution range images S LL and cross-polarization high-resolution range image S RL .

[0091] Overcoming the sensitivity of high-resolution range images mainly involves overcoming the three major sensitivities of HRRP, including attitude sensitivity, translation sensitivity, and amplitude sensitivity. Specifically, the centroid alignment method is used to avoid translation sensitivity, the amplitude is normalized to overcome amplitude sensitivity, and the minimum interval without moving across the range unit is selected as a training sample to overcome attitude sensitivity.

[0092] Step 1.2: Extract features from the preprocessed high-resolution range image to obtain frequency domain features and time domain features of the high-resolution range image, and combine them to obtain the original feature set.

[0093] Specifically, the preprocessed co-polarization high-resolution range image S LL and cross-polarization high-resolution range image S RL The two channels of data are Fourier transformed to obtain the corresponding two channels of frequency domain data S L ' L and S′ RL , feature extraction is performed on the above four data, and 50 features including entropy feature, polarization angle feature, amplitude feature, moment feature, mean, standard deviation, average fluctuation feature and differential fluctuation feature are obtained. The specific features and labels are shown in Table 1. These features constitute the original feature set X: X = {X m,n}, where m∈[1,M], n∈[1,N], M is the number of features contained in each sample, and N is the number of samples in the high-resolution range image sample set.

[0094] Table 1. Characteristics and numbers

[0095]

[0096] In this embodiment, features are extracted from the time domain and frequency domain respectively. The four-way data reflects target characteristics at different levels, making the target characteristics more thoroughly displayed. The extracted features can better reflect the target's own characteristics and improve the subsequent target recognition rate.

[0097] Step 2: Calculate the ReliefF evaluation value, mRMR evaluation value and noise robustness parameter of each feature in the original feature set respectively;

[0098] Specifically, step 2 includes:

[0099] Step 2.1: Calculate the ReliefF evaluation value of each feature according to the ReliefF evaluation criteria;

[0100] The ReliefF algorithm iteratively updates the weight of each feature by comparing the inter-class distance and intra-class distance within the range of Euclidean distance k, and obtains the evaluation value of each feature. The ReliefF algorithm comprehensively considers the local inter-class distance and intra-class distance of the feature, and evaluates the classification ability of the feature through the "hypothesis interval": if the inter-class distance is greater than the intra-class distance, its weight is increased; if the inter-class distance is less than the intra-class distance, its weight is reduced. The weight is continuously updated by comparing the inter-class distance with the intra-class distance, and the final weight calculated is used as the evaluation value of each feature.

[0101] Specifically, step 2.1 includes:

[0102] (1) The original feature set is recorded as X, where X is an M×N matrix, that is, each sample contains M features and there are N samples in total;

[0103] (2) Take sample R from X, select K neighboring points from samples of the same type as sample R in X, denoted as H, and select K neighboring points from samples of different types from sample R, denoted as M;

[0104] (3) Calculate the weight matrix W according to the following formula:

[0105]

[0106] In the above formula, q represents the number of iterations, H j represents the jth nearest neighbor sample of the same type as sample R, M j (C) indicates class The jth nearest neighbor sample in the , p(C) is the probability of category C appearing, class(R) is the category to which sample R belongs, p(class(R)) is the probability of the category to which sample R belongs, diff(x i ,R,H j ) represents samples R and H j In feature x iThe difference on is as follows:

[0107]

[0108] (4) After the selected feature S m-1 Based on this, an incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:

[0109] ΔW(x i )=W([S m-1 ,x i ])-W(S m-1 ) (3);

[0110] In the formula, ΔW(x i ) represents the feature x i ReliefF evaluation value.

[0111] In this embodiment, ΔW(x i ) value is larger, indicating that the feature x i The greater the separability and the smaller the redundancy between the selected features. The ReliefF algorithm will make the feature x with the largest ΔW i as selected features.

[0112] Step 2.2: Calculate the mRMR evaluation value of each feature according to the mRMR evaluation criteria;

[0113] The mRMR algorithm uses mutual information theory to calculate the correlation coefficient between each feature and the category and between features, and uses the difference between the two as the evaluation value of each feature. Mutual information represents the amount of information shared between two variables, and can be used to measure the strength of mutual dependence between two variables. It is not limited to linear correlation, and can also evaluate nonlinear relationships between variables. Given two random variables X and Y, their respective marginal probability distributions and joint probability distributions are p(x), p(y), and p(x,y), respectively, then the mutual information between them is defined as:

[0114]

[0115] If variables X and Y are completely unrelated or independent of each other, the mutual information is minimum and the result is 0, that is, there is no overlapping information between the two variables; conversely, the higher the degree of mutual dependence between variables X and Y, the larger the mutual information value, and the more identical information is contained.

[0116] Specifically, step 2.2 includes:

[0117] (1) According to the definition of mutual information, the mutual information between a single feature and a category is calculated as follows:

[0118]

[0119] In the formula, x i and C represent the i-th feature in the original feature set X and the category to which the feature belongs, respectively. i ) represents the feature x i The marginal probability distribution of , p(C) represents the marginal probability distribution of category C, and p(x i ,C) represents the feature x i and the joint probability distribution of category C.

[0120] Among them, I(x i ; The larger the value of I(x), the more category information the feature contains and the greater its contribution to classification; conversely, i ; C) The smaller the value, the less category information the feature contains and the lower its contribution to classification.

[0121] (2) The maximum correlation between the original feature set X and the category is defined as:

[0122]

[0123] In the formula, M represents the number of features contained in the original feature set X;

[0124] (3) The mutual information between features is calculated as follows:

[0125]

[0126] Among them, I(x i ;x j ) value is larger, indicating that the feature x i and feature x j The greater the correlation, the greater the redundancy.

[0127] (4) The minimum correlation between features is defined as:

[0128]

[0129] (5) In order to select a feature set with high separability and low redundancy, mRMR combines two measures and defines the following criteria:

[0130] maxΦ(D,Q)=DQ (9);

[0131] (6) After the selected feature S m-1 Based on this, an incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula:

[0132]

[0133] In the formula, ΔI(xi ) represents the feature x i The mRMR evaluation value of , m represents the number of selected feature subsets, C represents the feature x i Category.

[0134] Among them, ΔI(x i ) value is larger, indicating that the feature x i The greater the separability and the smaller the redundancy with the selected features. The mRMR algorithm will make the feature x with the largest ΔI i as the selected feature.

[0135] Step 2.3: Add noise to the high-resolution range image sample set of the target, and perform corresponding feature extraction on the noise-contaminated high-resolution range image sample set to obtain a noise feature set. Based on the noise feature set and the original feature set, calculate the noise robustness parameter of each feature.

[0136] Specifically, step 2.3 includes:

[0137] (1) Add noise to the high-resolution range image sample of each target;

[0138] In this embodiment, the signal-to-noise ratio of the dual-polarization HRRP is set to [5:5:30] dB.

[0139] (2) The noise-contaminated high-resolution range image is subjected to feature extraction in the time domain and frequency domain respectively to obtain the noise feature set, denoted as R(x i ,n), where x i is the i-th feature, i = 1, 2, ..., M, n is the index of the signal-to-noise ratio, n = 1, 2, ..., I;

[0140] (3) Calculate the deviation between the features at different signal-to-noise ratios and the corresponding features without noise:

[0141] R c (x i ,n)=|R(x i ,n)-R X (x i )| (11);

[0142] (4) Based on the deviation, calculate the noise robustness parameter of the feature:

[0143]

[0144] Where P snr (x i ) represents the feature x i The noise robustness parameter of .

[0145] From the definition of noise robustness parameter, we can see that the more sensitive the feature is to noise, the higher the noise Psnr The larger the value, the more robust the feature is to noise. snr The smaller the value.

[0146] Since the signal-to-noise ratio of the echo signal collected by the radar seeker may be low, the noise robustness factor should be fully considered when selecting features, and features that are robust to noise should be selected so that the recognition system of the radar seeker has high noise robustness.

[0147] Step 3: Perform multi-evaluation value fusion processing on the ReliefF evaluation value, mRMR evaluation value and noise robustness parameter of each feature to obtain the fusion evaluation value of each feature;

[0148] Since the dimensions of the evaluation values ​​calculated by different evaluation criteria are different and have different value ranges, the evaluation values ​​(separability values) of the features calculated by the ReliefF and mRMR criteria need to be normalized before being fused.

[0149] Specifically, step 3 includes:

[0150] Step 3.1: Use the Z-score standardization method to normalize the ReliefF evaluation value and mRMR evaluation value of each feature, and obtain the incremental value of the separability of the feature as follows:

[0151]

[0152] ΔH(x i ) represents the feature x i The incremental value of divisibility, ΔW(x i ) represents the feature x i ReliefF evaluation value, ΔI(x i ) represents the feature x i The mRMR evaluation value, mean and std represent the calculation process of the mean and standard deviation respectively.

[0153] Step 3.2: According to the feature's separability increment value and noise robustness parameter, the fusion evaluation value of the feature is calculated according to the following formula:

[0154] J(x i )=ΔH(x i )-βP snr (x i ) (14);

[0155] In the formula, J(x i ) represents the feature x i The fusion evaluation value, P snr (x i ) represents the feature x iThe noise robustness parameter of β represents the proportion of noise robustness factors in the feature selection process.

[0156] Since the importance of a feature is jointly determined by the separability and noise robustness of the feature, in this embodiment, J is used as an important basis for feature search, and a feature subset with high separability and strong noise robustness can be selected.

[0157] Step 4: According to the fusion evaluation value, the original feature set is searched using the sequence floating forward search method to obtain the optimal feature subset under the preset dimension, so as to use the optimal feature subset for subsequent target recognition operations.

[0158] Specifically, step 4 includes:

[0159] The fusion evaluation values ​​of the features are sorted, and the two features with the highest fusion evaluation values ​​are selected as the initial feature subset. The feature search is performed using the sequence forward search method to obtain the optimal feature subset under the preset dimension, where:

[0160] Suppose that when the k-th step search is completed, the feature subset obtained is A k , then, the k+1th step searches for the following operations:

[0161] (1) Forward selection of new features: Select a feature x from the set of features to be selected i Add feature subset A k , forming a new feature subset A k+1 =A k +x i , where x i is to make A k+1 The fusion evaluation value J(A k+1 ) increases the maximum feature;

[0162] (2) Backward elimination of old features: k+1 Select a feature x from j , so that the fusion evaluation value of the feature subset after removing the feature is reduced to the minimum, for x j and x i Make a judgment,

[0163] If x j and x i If they are the same feature, feature x will not be removed. j , and set k=k+1, and continue to the next step of searching;

[0164] If x j and x i If they are not the same features, then x j From A k+1 Eliminate from the feature set and generate a new feature subset Ak ′=A k+1 -x j , continue from feature subset A k Select a feature x from t , so that the fusion evaluation value of the feature subset after removing the feature is reduced to the minimum, and the fusion evaluation value J(A k ′-x t ) and the feature subset A obtained when the k-1 step search is completed k-1 The fusion evaluation value J(A k-1 ) to make a judgment,

[0165] If J(A k ′-x t )≤J(A k-1 ), then feature x is not removed t , and let A k =A k ′, continue the forward selection of new features;

[0166] If J(A k ′-x t )>J(A k-1 ), then x t From A k ′, and generate a new subset A k-1 ′=A k -x t , and let k = k-1, and continue the operation of removing old features backward;

[0167] Among them, when k=2, the backward elimination of old features is stopped, and when k is greater than the preset dimension, the forward selection of new features is stopped.

[0168] It should be noted that the optimal feature subset is used for subsequent target recognition operations, and the optimal feature subset is subsequently input into the SVM classifier to train the classifier model, and the performance of the classifier is tested using test data to obtain recognition results for various types of targets.

[0169] It is worth noting that step 4 can also be repeated to obtain the recognition results of the optimal feature subsets under different dimensions, and the set of feature subsets with the best recognition results can be used as the optimal feature subset of the entire system.

[0170] The noise-robust high-resolution range image feature selection method of this embodiment effectively combines the ReliefF evaluation value and the mRMR evaluation value noise robustness parameter of the feature to make a more comprehensive and correct evaluation of the separability of the feature. The sequential floating forward feature search algorithm is used to search for feature subsets, which not only ensures that the results are close to the global optimum, but also avoids global search. In the search process, new features are continuously selected forward and old features are eliminated backward, so that the dimension of the final feature subset is small. Small feature dimension means good generalization performance, and the noise robustness factor is considered when calculating the feature evaluation value, so the noise robustness of the feature subset finally selected is better. Each feature can be analyzed more comprehensively, and the noise factor is considered. The sequential floating forward search algorithm is used to search for feature subsets. The selected feature subset has a small dimension, low redundancy, and good noise robustness, which greatly improves the probability of target recognition.

[0171] Embodiment 2

[0172] This embodiment verifies and illustrates the effect of the noise-robust high-resolution range profile feature selection method of Embodiment 1 through specific experiments.

[0173] Test conditions:

[0174] The radar transmit signal adopts a linear frequency modulation-step frequency system. The signal frequency is in the W band, the number of pulses is 128, and the pulse step frequency Δf=10MHz. From these parameters, the radar transmit signal synthesis bandwidth can be obtained as B=1.2GHz.

[0175] Simulation content and result analysis:

[0176] This embodiment uses the actual measurement data of six types of targets, such as radar vehicles, trucks, corner reflectors, houses, hangars, and shelter vehicles, as sample template library data. The measured data is preprocessed by center of gravity alignment and amplitude normalization, and the co-polarization data and cross-polarization data are Fourier transformed to obtain two frequency domain data. 50 features, such as entropy features, polarization angle features, amplitude features, moment features, mean, standard deviation, average fluctuation features, and differential fluctuation features, are extracted from the above four data. The specific feature names and corresponding numbers are shown in Table 1.

[0177] In order to verify the performance advantage of the feature selection method of the present invention, two traditional filtering feature selection algorithms are compared. The comparison results are shown in Table 2 and Figure 3 , Figure 3It is a comparison chart of the recognition results of the method of the present invention provided by the embodiment of the present invention and the existing method. As can be seen from Table 2, the average correct recognition probability of the method of the present invention is higher than that of the other two feature selection algorithms with a single evaluation criterion, the average correct recognition rate is improved by nearly 1.15 percentage points, and the number of optimal feature subsets is the smallest. In actual engineering applications, it can better improve the calculation speed and reduce memory pressure. Due to the small feature dimension, it has better generalization performance. Figure 3 It can be seen that when the feature dimensions are the same, the average correct recognition rate of the feature selection method of the present invention is higher than that of the feature selection algorithms of the other two single evaluation criteria, but when the dimensions increase to a certain number, the average correct recognition results of the three feature selection algorithms are not much different; in addition, the recognition results of the feature selection method of the present invention show a relatively stable trend after the number of feature dimensions reaches 5, while the other two single evaluation criteria still have a small range of fluctuations.

[0178] Table 2. Comparison of recognition results

[0179]

[0180] In order to study the impact of feature search on the performance of the recognition system, a comparative experiment with and without feature search was conducted based on the comprehensive evaluation criteria. The results are as follows: Figure 4 As shown, Figure 4 It is a comparison diagram of the method proposed by the present invention with and without feature search provided by the embodiment of the present invention. It can be seen from the figure that after feature search, better recognition results can be obtained at lower feature dimensions. When feature search is not performed, the recognition results are improved with the increase of feature dimensions. When the feature dimensions increase to a certain number, the recognition results of the two methods are relatively close. It can be seen that after feature search, the number of feature dimensions can be further reduced while maintaining good recognition results for the entire recognition algorithm.

[0181] In order to verify the noise robustness performance of the present invention, a comparative experiment with and without considering the noise robustness factor was conducted based on the comprehensive evaluation criteria. The results are shown in Table 3 and Figure 5-6 As shown in Table 3, it can be seen that the features selected by considering the noise robustness factor are less affected by noise, have small feature dimensions, and have good recognition performance. Figure 5 is a noise robustness parameter diagram of each feature provided by an embodiment of the present invention. A higher parameter value indicates that the noise robustness of the feature is poor. Figure 5 It can be seen that features numbered 16, 28, 45, 47, and 50 are more sensitive to noise. Figure 6 is a comparison chart of the influence of noise robustness on recognition performance provided by the embodiment of the present invention. Figure 6It can be seen that the features selected by considering the noise robustness factor are less sensitive to noise. As the signal-to-noise ratio continues to decrease, the recognition results gradually decrease, but the rate of decrease is relatively slow. Without considering the noise robustness factor, the optimal feature subset selected contains features that are more sensitive to noise, such as features numbered 16 and 28. As the signal-to-noise ratio decreases, the recognition results drop sharply. When the signal-to-noise ratio is 5dB, the ability to correctly recognize is almost lost.

[0182] Table 3. Effect of noise robustness on recognition rate

[0183] Whether to consider noise robustness Optimal feature subset Average correct recognition rate no 13、16、39、29、43、44、28、7 95.21％ yes 13、39、29、44、43 96.97％

[0184] The noise-robust high-resolution range image feature selection method of the present invention analyzes features from multiple different angles. The ReliefF criterion uses the distance between features to measure the contribution of a feature to classification. mRMR uses the mutual information theory to calculate the correlation between features and the correlation between features and categories, and measures the noise robustness of the feature by calculating the deviation between the feature value after being contaminated by noise and the original feature value. Based on the feature evaluation value, the sequence floating forward search algorithm is used to perform feature search, and the combination effect between features is fully considered to optimize the feature subset obtained by the search. Finally, the encapsulated feature selection idea is used, and the recognition result of the SVM classifier is used as the evaluation criterion to select the feature subset with the best recognition result as the optimal feature subset for the entire system.

[0185] Compared with the feature selection algorithm of a single evaluation criterion, the feature selection method of the present invention can have better recognition performance when the feature dimension is low, and the recognition performance is relatively stable with the increase of the feature dimension. When selecting the optimal feature subset, a sequential forward floating search algorithm is adopted, which can make the result reach the global optimum while avoiding global search. In addition, the noise robustness factor is considered when calculating the feature evaluation value. Therefore, it also has a certain recognition function when the signal-to-noise ratio is low.

[0186] The feature selection method of the present invention can quickly remove redundant features to achieve effective recognition, has a small feature dimension, and has good robustness. It is a good method for performing feature separability analysis on high-resolution range images and has certain engineering application significance.

[0187] It should be noted that, in this article, the term "comprises", "comprising" or any other variant is intended to cover non-exclusive inclusion, so that an article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed. In the absence of more restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the article or device comprising the element.

[0188] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. A noise-robust high-resolution range profile feature selection method, It is characterized in that The following steps are involved: Step 1: Obtain a sample set of high-resolution range images of the target, and perform feature extraction on the high-resolution range image of each target to obtain an original feature set; Step 2: respectively calculating the ReliefF evaluation value, mRMR evaluation value and noise robustness parameter of each feature in the original feature set; Step 2 includes: Calculate the ReliefF evaluation value of each feature according to the ReliefF evaluation criteria; The mRMR evaluation value of each feature was calculated according to the mRMR evaluation criteria; Noise is added to the high-resolution range image sample set of the target, and corresponding features are extracted from the noise-contaminated high-resolution range image sample set to obtain a noise feature set. According to the noise feature set and the original feature set, a noise robustness parameter of each feature is calculated, including: Add noise to the high-resolution range image of each target; The time domain and frequency domain features are extracted from the noise-contaminated high-resolution range image to obtain a noise feature set, denoted as R(x i ,n), where x i is the i-th feature, i = 1, 2, ..., M, n is the index of the signal-to-noise ratio, n = 1, 2, ..., I; Calculate the deviation between the features at different signal-to-noise ratios and the corresponding features without noise: R c (x i ,n)=|R(x i ,n)-R X (x i )|; Based on the deviation, the noise robustness parameter of the feature is calculated: Where P snr (x i ) represents the feature x i Noise robustness parameter of ; Step 3: performing multi-evaluation value fusion processing on the ReliefF evaluation value, the mRMR evaluation value and the noise robustness parameter of each feature to obtain a fusion evaluation value of each feature; Step 4: According to the fusion evaluation value, the original feature set is searched using a sequence floating forward search method to obtain an optimal feature subset under a preset dimension, so as to use the optimal feature subset for subsequent target recognition operations.

2. The noise-robust high-resolution range profile feature selection method according to claim 1, It is characterized in that The step 1 comprises: Acquire a sample set of high-resolution range images of dual-polarization targets collected by a radar, and preprocess the high-resolution range image of each target to overcome the sensitivity of the high-resolution range image; Feature extraction is performed on the pre-processed high-resolution range image to obtain frequency domain features and time domain features of the high-resolution range image, and the original feature set is obtained by combining them.

3. The noise-robust high-resolution range profile feature selection method according to claim 1, It is characterized in that The ReliefF evaluation value of each feature is calculated according to the ReliefF evaluation criteria, including: The original feature set is recorded as X, where X is an M×N matrix, each sample contains M features, and there are N samples in total; Take sample R from X, select K neighboring points from samples of the same type as sample R in X, denoted as H, and select K neighboring points from samples of different types from sample R, denoted as M; The weight matrix W is calculated as follows: In the above formula, q represents the number of iterations, H j represents the jth nearest neighbor sample of the same type as sample R, M j (C) indicates class The jth nearest neighbor sample in the , p(C) is the probability of category C appearing, class(R) is the category to which sample R belongs, p(class(R)) is the probability of the category to which sample R belongs, diff(x i ,R,H j ) represents samples R and H j In feature x i The difference on is as follows: In the selected feature S m-1 Based on this, an incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula: ΔW(x i )=W([S m-1 ,x i ])-W(S m-1 ); In the formula, ΔW(x i ) represents the feature x i ReliefF evaluation value.

4. The noise-robust high-resolution range profile feature selection method according to claim 1, It is characterized in that The mRMR evaluation value of each feature is calculated according to the mRMR evaluation criteria, including: According to the definition of mutual information, the mutual information between a single feature and a category is calculated as follows: In the formula, x i and C represent the i-th feature in the original feature set X and the category to which the feature belongs, respectively. i ) represents the feature x i The marginal probability distribution of , p(C) represents the marginal probability distribution of category C, and p(x i ,C) represents the feature x i and the joint probability distribution of category C; The maximum correlation between the original feature set X and the category is defined as: In the formula, M represents the number of features contained in the original feature set X; The mutual information between features is calculated as follows: The minimum correlation between features is defined as: mRMR combines both measures and defines the following criteria: maxΦ(D,Q)=DQ; In the selected feature S m-1 Based on this, an incremental search is performed, and the importance of the features in the remaining feature space is calculated according to the following formula: In the formula, ΔI(x j ) represents the feature x j The mRMR evaluation value of , m represents the number of selected feature subsets, C represents the feature x i Category.

5. The noise-robust high-resolution range profile feature selection method according to claim 1, It is characterized in that The step 3 comprises: The Z-score standardization method is used to normalize the ReliefF evaluation value and the mRMR evaluation value of each feature, and the separability increment value of the feature is obtained as follows: In the formula, ΔH(x i ) represents the feature x i The incremental value of divisibility, ΔW(x i ) represents the feature x i ReliefF evaluation value, ΔI(x i ) represents the feature x i The mRMR evaluation value, mean and std represent the calculation process of mean and standard deviation respectively; According to the separability increment value and the noise robustness parameter of the feature, the fusion evaluation value of the feature is calculated according to the following formula: J(x i )=ΔH(x i )-βP snr (x i ); In the formula, J(x i ) represents the feature x i The fusion evaluation value, P snr (x i ) represents the feature x i The noise robustness parameter of β represents the proportion of noise robustness factors in the feature selection process.

6. The noise-robust high-resolution range profile feature selection method according to claim 1, It is characterized in that The step 4 comprises: The fusion evaluation values ​​of the features are sorted, and the two features with the highest fusion evaluation values ​​are selected as the initial feature subset. The feature search is performed using the sequence forward search method to obtain the optimal feature subset under the preset dimension, where: Suppose that when the k-th step search is completed, the feature subset obtained is A k , then, the k+1th step searches for the following operations: Forward selection of new features: Select a feature x from the set of features to be selected i Add feature subset A k , forming a new feature subset A k+1 =A k +x i , where x i is to make A k+1 The fusion evaluation value J(A k+1 ) increases the maximum feature; Backward elimination of old features: k+1 Select a feature x from j , so that the fusion evaluation value of the feature subset after removing the feature is reduced to the minimum, for x j and x i Make a judgment, If x j and x i If they are the same feature, feature x will not be removed. j , and set k=k+1, and continue to the next step of searching; If x j and x i If they are not the same features, then x j From A k+1 Eliminate from the feature set and generate a new feature subset A k ′=A k+1 -x j , continue from feature subset A k Select a feature x from t , so that the fusion evaluation value of the feature subset after removing the feature is reduced to the minimum, and the fusion evaluation value J(A k ′-x t ) and the feature subset A obtained when the k-1 step search is completed k-1 The fusion evaluation value J(A k-1 ) to make a judgment, If J(A k ′-x t )≤J(A k-1 ), then feature x is not removed t , and let A k =A k ′, continue the forward selection of new features; If J(A k ′-x t )>J(A k-1 ), then x t From A k ′, and generate a new subset A k-1 ′=A k -x t , and let k = k-1, and continue the operation of removing old features backward; Among them, when k=2, the backward elimination of old features is stopped, and when k is greater than the preset dimension, the forward selection of new features is stopped.

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