CN113433514B - Parameter self-learning interference suppression method based on expanded deep network - Google Patents
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Abstract
The invention provides a parameter self-learning interference suppression method based on an expanded depth network, which comprises the steps of carrying out short-time Fourier transform on an original echo signal containing interference to obtain a time-frequency spectrum data matrix, carrying out sub-block segmentation processing on the time-frequency spectrum data matrix, establishing the expanded depth network, training by taking a training set as the input of the expanded depth network, and simultaneously substituting a verification set for model evaluation to obtain an optimal training model; and inputting the test set into an optimal training model to identify and analyze the interference echo matrix. The method effectively separates interference and reconstructs signals, converts the original unsupervised decomposition problem into a supervised neural network learning problem, greatly reduces the iteration times, can obtain algorithm hyper-parameters by self-adaptive solving, does not depend on a large number of data sets, and avoids the possibility of overfitting of a training network under a small data amount.
Description
Technical Field
The invention relates to the field of signal processing, in particular to an interference suppression method. On the basis of the model-based iterative optimization method, the invention introduces a deep expansion concept, realizes equivalent substitution of iterative steps by combining a cyclic neural network, completes optimized self-learning of the hyperparameter of the algorithm, reduces the complexity of the algorithm and can realize effective extraction and separation of radio frequency interference in signals.
Background
In recent years, the problem of radio frequency interference in radar echoes is becoming more serious, and the radio frequency interference has adverse effects on imaging processes, image interpretation, quantitative remote sensing applications and the like. The realization idea of the current interference separation and reconstruction method is mostly based on model driving, and iterative search is carried out by utilizing specific physical prior knowledge constraint and optimization criterion to solve the optimal solution. Generally, such iterative algorithms require artificial setting of some hyper-parameters (e.g., matrix rank, sparsity, etc. model parameters, regularization coefficients, etc.) so that the algorithms can reach optimal solutions in fewer iterations. However, the setting and optimization process of the hyper-parameters is a difficult and time-consuming manual work, heuristic search is performed by relying on manual experience, the difficulty is doubled with the increase of the number of the parameters, hundreds of iterations and even thousands of iterations are often required, and the requirement of high timeliness of radio frequency interference suppression cannot be met. Different parameters are required to be adjusted for different scene data, and the method does not have good generalization. Even with automatic (online) parameter selection methods (e.g., adaptive step size selection methods), the computational complexity is large, even beyond the complexity of the optimization problem itself.
The artificial intelligence method represented by deep learning can acquire deep intrinsic feature information of a target, forms more abstract high-level representation attribute categories or features by combining low-level features to find refined feature representation of data, is preliminarily applied to a radio frequency interference suppression method, achieves a good effect, and is one of important development trends of signal processing. However, such deep learning methods rely essentially on large data, and achieve interference suppression by learning from training samples to approximate a finite closed form expression, closer to the black-box mechanism, and lack interpretability. Meanwhile, the model parameters are very many, the requirements on the quantity and quality of training data are high, and otherwise, an overfitting phenomenon is easy to occur.
How to combine the traditional model driving method with the data driving method to improve the performance of the interference suppression method is a hot problem of research. The general approximation theorem states that a single hidden layer forward network of a finite number of neurons can approximate a continuous function over an immediate set. If each iteration of an iterative algorithm can be replaced with one layer in a deep neural network and then several such layers are connected, it is possible to achieve a significant improvement in convergence.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a parameter self-learning interference suppression method based on an expanded deep network. On the basis of an iterative optimization method based on a model, the original unsupervised decomposition problem can be converted into a learning problem based on a supervised neural network by utilizing a deep expansion technology. Through the transformation, the iteration times are greatly reduced, the hyper-parameters can be independently learned from the data, manual setting is not needed, and the efficiency and the accuracy of the algorithm can be improved.
The basic idea of the invention is as follows: the interference has characteristics different from each other in echoes in different directions due to rapid change along with time, and has sparsity; in the adjacent azimuth echoes, the scene echo data changes slowly, and has low rank. And decomposing the data matrix into a low-rank component and a sparse component by adopting robust principal component analysis and unsupervised iterative optimization to realize the separation of interference and useful signals. Each iteration in the iterative algorithm is equivalently replaced by each layer of the neural network, so that the solving algorithm based on the model can be converted into an end-to-end learning problem, the iteration times are greatly reduced, the hyper-parameters can be independently learned from data, manual setting is not needed, and the efficiency and the accuracy of the algorithm can be improved.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: sequentially carrying out short-time Fourier transform on the original echo signals containing the interference to obtain a time-frequency spectrum data matrix X epsilon P×Q×N Wherein P and Q are the time unit number and the frequency unit number of the frequency spectrum when the azimuth echo is single time respectively, and N is the azimuth echo number;
step 2: time setting frequency spectrum data matrix X is belonged to P×Q×N Performing sub-block segmentation to obtain K × N sub-block data matrices with the size of p × q, wherein K = PQ/PQ, vectorizing all K × N sub-block data matrices, and splicing to obtain a time-frequency spectrum sub-block data matrix with the size of PQ × 1, wherein D ∈ £ £ is pq×N Respectively constructing a training set, a verification set and a test set;
and step 3: establishing an expanded depth network;
time setting frequency spectrum sub-block data matrix D epsilon pq×N And (3) carrying out radar interference suppression, and solving the problem expressed as the following extreme value:
wherein | · | purple * Is the kernel norm, | ·| luminance 1,2 Is a 1,2 Norm, H 1 And H 2 Is a measurement matrix, L is epsilon pq×N Is a useful signal time-frequency spectrum sub-block data matrix meeting the low rank condition, and S e £ £ pq×N The interference time-frequency spectrum sub-block data matrix meeting the sparse condition.
The optimization problem is solved iteratively by adopting a soft threshold iterative algorithm, and the solving formula of the kth iteration is as follows:
among them, SVT (g) Is a singular value threshold operator, L f Lipschitz constant, T, which is a quadratic term (g) Is a soft threshold, the value of the soft threshold and a hyperparameter lambda 1 And λ 2 Correlation, L k Is the useful signal time-frequency spectrum sub-block data matrix, L, obtained after the kth iteration k Is an interference time-frequency spectrum sub-block data matrix obtained after the kth iteration;
the expanded depth network is adopted to equivalently replace the iteration step, and the improved iteration solving and updating formula is as follows:
wherein P is 1 ,P 2 ,P 3 ,P 4 ,P 5 ,P 6 Is a convolution kernel;
and 4, step 4: training a training set as the input of the expanded depth network in the step 3, substituting the training set into a verification set for model evaluation, and obtaining an optimal training model when the loss function parameters enable the convergence of the loss function minimum Mean Square Error (MSE) of the verification set not to change any more; and inputting the test set into an optimal training model to identify and analyze the interference echo matrix.
In the step 2, the K x N time-frequency spectrum sub-block data matrixes D are respectively constructed into a training set and a verification set, and a test set is additionally constructed, wherein the number of the test sets is the same as that of the verification sets.
The expanded depth network comprises K1 convolution layers of 5 multiplied by 5 and K2 convolution layers of 3 multiplied by 3, and the single-layer structure of the expanded depth network is shown in figure 2.
The invention has the beneficial effects that:
1. the invention utilizes the low rank characteristic of the echo and the sparse characteristic of the interference, and can effectively separate and reconstruct the signal of the interference.
2. Compared with the conventional method for solving the optimal solution based on model iteration, the method equivalently replaces the iterative process with the cyclic neural network, converts the original unsupervised decomposition problem into the supervised neural network learning problem, greatly reduces the iteration times, and can obtain the algorithm hyper-parameter through self-adaptive solution.
3. Compared with a conventional method (such as a neural network Resnet) for solving an optimal solution based on learning, the method is different from a black box model of the conventional neural network, and has strong theoretical interpretability, so that the network does not depend on a large number of data sets in theory, and the possibility of overfitting of a training network under a small data amount is avoided.
Drawings
FIG. 1 is a general flow diagram of the process of the present invention.
FIG. 2 is a flow diagram of a network monolayer;
FIG. 3 is a schematic diagram of data preprocessing of one embodiment of the method of the present invention;
FIG. 4 is a graph of the loss function for each round of the training phase in the method of the present invention;
FIG. 5 is a time-frequency diagram of the original echo, FIG. 5 (a) is a time-frequency diagram of RF interference, FIG. 5 (b) is a time-frequency diagram of an echo signal with interference pollution, FIG. 5 (c) is a time-frequency diagram of predicted interference estimated by an expanded depth network, FIG. 5 (d) is a time-frequency diagram of predicted echo estimated by an expanded depth network, and FIG. 5 (e) is a time-frequency diagram of predicted echo estimated by an expanded depth network.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the drawings.
The invention is described in further detail below with reference to the figures and the specific embodiments. The specific embodiment herein is only one case of the method, and not all embodiments may be included, and the content of this section will make the working principle, specific steps and implementation effect of the method more clearly understood by those skilled in the art through the specific embodiment;
step 1: FIG. 1 is a diagram illustrating an expanded deep network based parameter self-learning interference suppressor according to an embodiment of the present inventionThe general flow chart of the method is to sequentially carry out short-time Fourier transform on the original echo signals containing interference to obtain a time-frequency spectrum data matrix
4096 and 256 are respectively the time unit number and the frequency unit number of the single azimuth echo time spectrum, and 10 is the azimuth echo number;
step 2: preprocessing the time-frequency diagram of the echo signal added with interference, wherein the preprocessing process is as shown in figure 3, and the preprocessing process is a time-frequency spectrum data matrix
The subblock division processing was performed to obtain 2560 subblock data matrices of 64 × 64 sizes. And further vectorizing all the sub-block data matrixes, and splicing to obtain 2560 time-frequency spectrum sub-block data matrixes with the size of 4096 multiplied by 1. In the embodiment, the training set is 2000, the verification set is 560, and the test set is 560;
and 3, step 3: time-setting frequency-spectrum sub-block data matrix
Radar interference suppression is performed, and is expressed as the following extremum problem to solve:
wherein | · | charging * Is the kernel norm, | ·| luminance 1,2 Is a 1,2 Norm, H 1 And H 2 Is a matrix of measurements of the position of the object,
for the input matrix contaminated by the disturbance,
is a useful signal time-frequency spectrum sub-block data matrix satisfying the low rank condition,
the interference time-frequency spectrum sub-block data matrix meeting the sparse condition.
The optimization problem can be solved iteratively by using a soft threshold iterative algorithm. The solution formula for the kth iteration is as follows:
wherein H 1 And H 2 Is a measurement matrix, SVT (g) Is a singular value threshold operator, L f Lipschitz constant, T, which is a quadratic term (g) Is a soft threshold whose value is related to the hyperparameter lambda 1 And λ 2 And (6) correlating.
The invention adopts the equivalent substitution iteration step of the expanded depth network. The network comprises K1 convolution layers of 5 × 5 and K2 convolution layers of 3 × 3, and the single-layer structure of the network is shown in FIG. 2. The improved iterative solution update formula is as follows:
wherein P is 1 ,P 2 ,P 3 ,P 4 ,P 5 ,P 6 Is a convolution kernel. The present embodiment includes 3 convolution layers of 5 × 5 and 7 convolution layers of 3 × 3 from input to output, and the hyper-parameter λ 1 And λ 2 The initial values are set to 0.4 and 1.8, respectively. The network adopts an MSE loss function as iterative updating of the parameter of the convolutional layer, and adopts an Adam optimization algorithm to optimize the parameter of the convolutional layer, wherein the learning rate is set to be 0.002; the single-layer step of the network is shown in 2, namely the input matrix D polluted by interference replaces the soft threshold value iterative algorithm by the convolution operator PThe characteristic is extracted by multiplication operation, and the singular value threshold step of the soft threshold iterative algorithm is reserved to alternately solve the low-rank echo matrix L k+1 And sparse interference matrix S k+1 。
And 4, step 4: training and verifying by taking the training set and the verification set as the input of the expanded depth network in the step 3, so that the model is the optimal model for training when the minimum Mean Square Error (MSE) of the loss function of the verification set realizes convergence, namely no change exists, and the test set is substituted into the stored model for testing; the loss function curve of each round of the training set is shown in fig. 4, the test set verification result is shown in fig. 5 (d) and fig. 5 (e), and it can be seen from the graph that interference with different energy levels has obvious damage effect on the original data, and the original echo matrix can be effectively separated from the echo matrix polluted by the interference by selecting a model after training.
The expanded deep network architecture adopted by the invention can adjust the neuron, the optimization algorithm, the loss function, the learning rate and the attenuation rate or the convolution layer number according to the model of the verification set, so as to improve the precision of interference suppression.
Claims (3)
1. A parameter self-learning interference suppression method based on an expanded deep network is characterized by comprising the following steps:
step 1: sequentially carrying out short-time Fourier transform on original echo signals containing interference to obtain a time-frequency spectrum data matrix
P and Q are respectively the time unit number and the frequency unit number of the frequency spectrum when a single azimuth echo is carried out, and N is the azimuth echo number;
step 2: time-to-time spectrum data matrix
Performing sub-block segmentation to obtain K × N sub-block data matrices with size of p × q, wherein K = PQ/PQ, vectorizing all K × N sub-block data matrices, and splicing to obtain block data matrices with size of PQ × 1Time-frequency spectrum sub-block data matrix
Respectively constructing a training set, a verification set and a test set;
and step 3: establishing an expanded depth network;
time-setting frequency-spectrum sub-block data matrix
And (3) carrying out radar interference suppression, and solving the problem expressed as the following extreme value:
wherein | · | purple * Is kernel norm, | · | purple 1,2 Is a 1,2 Norm, H 1 And H 2 Is a matrix of measurements of the position of the object,
is a useful signal time-frequency spectrum sub-block data matrix meeting the low rank condition,
is an interference time-frequency spectrum sub-block data matrix which meets the sparse condition;
the optimization problem is iteratively solved by adopting a soft threshold iterative algorithm, and the solving formula of the kth iteration is as follows:
wherein, the first and the second end of the pipe are connected with each other,
is a singular value threshold operator, L f Is the Lipschitz constant of the quadratic term,
is a soft threshold, the value of which is associated with a hyper-parameter lambda 1 And λ 2 Correlation, L k Is a useful signal time-frequency spectrum sub-block data matrix obtained after the kth iteration, S k Is an interference time-frequency spectrum sub-block data matrix obtained after the kth iteration; l is a radical of an alcohol k+1 Is a useful signal time-frequency spectrum sub-block data matrix obtained after the (k + 1) th iteration, S k+1 Is an interference time-frequency spectrum sub-block data matrix obtained after the (k + 1) th iteration;
the expanded depth network is adopted to equivalently replace the iteration step, and the improved iteration solving and updating formula is as follows:
wherein P is 1 ,P 2 ,P 3 ,P 4 ,P 5 ,P 6 Is a convolution kernel;
and 4, step 4: training by taking the training set as the input of the expanded deep network in the step 3, and meanwhile substituting the training set into the verification set for model evaluation, wherein when the loss function parameters enable the minimum mean square error convergence of the loss function of the verification set not to change any more, the training set is an optimal model; and inputting the test set into an optimal training model to identify and analyze the interference echo matrix.
2. The parameter self-learning interference suppression method based on the expanded deep network is characterized by comprising the following steps of:
in the step 2, the K-N time-frequency spectrum sub-block data matrixes D are respectively constructed into a training set and a verification set, and a test set is additionally constructed, wherein the test set and the verification set are the same in number.
3. The parameter self-learning interference suppression method based on the expanded deep network as claimed in claim 1, wherein:
the expanded depth network includes K1 convolutional layers of 5 × 5 and K2 convolutional layers of 3 × 3.
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