CN116405100B - Distortion signal restoration method based on priori knowledge - Google Patents
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Abstract
The invention relates to the technical field of satellite communication, in particular to a distortion signal restoration method based on priori knowledge, which comprises the following steps: constructing a deep convolutional neural network model; determining an objective function of the deep convolutional neural network model; training the deep convolutional neural network model by taking the objective function as a target; extracting parameters of each layer after training is completed to form an optimal dictionary; obtaining a distortion signal in a satellite signal; transforming the distortion signal to obtain a time-frequency image of the distortion signal; inputting a time-frequency image of the distortion signal, and obtaining a time-frequency image of the restored signal through an optimal dictionary; and transforming the time-frequency image of the restored signal to obtain the restored signal. According to the invention, the optimal dictionary is obtained through training the deep convolutional neural network model, so that the parameters of the whole model are in the optimal parameters, and then various distortion signals can be restored in a universal way by utilizing the optimal dictionary, so that the model has the advantages of small constraint, strong generalization and wide application range of signal restoration.
Description
Technical Field
The invention relates to the technical field of satellite communication, in particular to a distortion signal restoration method based on priori knowledge.
Background
In the satellite communication field, distortion may occur during satellite signal transmission. The distorted signal may affect the quality and reliability of satellite communications, such as accuracy and stability of systems for satellite navigation positioning, earth observation control, and the like.
Therefore, research and application of a restoration technique for satellite distortion signals have become very important. The significance of recovering satellite distortion signals is to improve the reliability and efficiency of satellite communications. The satellite distortion signal recovery technology can improve the quality and stability of signal transmission, thereby improving the receiving quality and transmission rate of signals and ensuring the reliability and safety of satellite communication.
The background of recovering satellite distorted signals can be traced back to the development of digital signal processing techniques. With the continuous improvement of digital signal processing technology, attempts have been made to recover and process distorted signals by using digital signal processing technology, so as to improve reliability and performance of satellite communication, navigation, remote sensing and other applications.
At present, the satellite signal restoration method based on the digital signal processing technology mainly comprises methods based on a filter, a signal processing algorithm, machine learning and the like. Among them, in the signal restoring method based on machine learning, dictionary learning and deep learning are two directions which are developed more rapidly in recent years.
In dictionary learning, a distorted signal is represented as a linear combination of a set of basis vectors by learning the set of basis vectors, enabling restoration or reconstruction of the signal. In deep learning, the mapping relation between input and output is learned through a deep neural network, so that the reduction and noise reduction of signals are realized. However, the prior art still has many problems, such as strong constraint of the signal model and weak generalization, which limits the application range of signal restoration, and for example, the difficulty of parameter adjustment is large, and the model parameters are difficult to be in optimal parameters, so that the effect of restoring the distorted signal is poor, and the popularization of the technology is not facilitated.
In summary, the satellite distortion signal recovery technology has wide application and important significance in various fields such as satellite communication, satellite navigation and earth observation equipment control, but the current technology for signal recovery still needs improvement.
Disclosure of Invention
In order to solve the above-mentioned prior art problems, the present invention provides a distortion signal restoration method based on priori knowledge, including:
s101: constructing a deep convolutional neural network model, wherein the deep convolutional neural network model is of a multi-layer structure, and each layer is provided with a dictionary to be learned;
s102: determining an objective function of the deep convolutional neural network model, wherein the objective function is used for searching an optimal dictionary;
s103: training the deep convolutional neural network model by taking the objective function as a target;
s104: extracting parameters of each layer after training is completed to form an optimal dictionary;
s105: obtaining a distortion signal in a satellite signal;
s106: time-frequency image Z of distortion signal obtained by transforming distortion signal 0 ；
S107: time-frequency image Z of input distortion signal 0 Obtaining a time-frequency image Y of the restored signal through the optimal dictionary:
wherein L represents the number of layers of the deep convolutional neural network model, L represents the number of each layer,，Z l-1 represents the output of layer 1, < >>Representing an optimal dictionary of the first layer;
s108: and transforming the time-frequency image of the restored signal to obtain the restored signal.
The method has the advantages that the optimal dictionary is obtained through training of the deep convolutional neural network model, the deep convolutional neural network model can be automatically fitted, parameters of the whole model are in optimal parameters, the problem that parameters are difficult to adjust in traditional dictionary learning is avoided, the recovery effect on distorted signals is good, various distorted signals can be recovered universally by using the optimal dictionary, the constraint of the model is small, the generalization is strong, the application range of signal recovery is wide, and the popularization of technology is facilitated.
Drawings
Fig. 1 is a schematic flow chart of a distortion signal restoring method based on priori knowledge.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, a flow diagram of a distortion signal restoration method based on a priori knowledge is shown.
The distortion signal restoration method based on priori knowledge provided by the embodiment of the invention comprises the following steps:
s101: and constructing a deep convolutional neural network model, wherein the deep convolutional neural network model is of a multi-layer structure, and each layer is provided with a dictionary to be learned.
The deep convolutional neural network model comprises an input layer, a convolutional layer, an activation function, a pooling layer, a full connection layer and an output layer. The convolution layer is provided with a convolution kernel. The basic principle of the deep convolutional neural network model is the prior art, and the invention is not repeated.
The objective of dictionary learning is, among other things, to find an optimal set of bases and to represent the raw data in as sparse a manner as possible.
Further, for dictionary learning, there are currently two mainstream dictionary construction strategies: analysis dictionary method and learning dictionary method. The analysis dictionary method is a predetermined dictionary method including an ultra-complete discrete cosine transform dictionary, a fourier dictionary, and the like. These methods are easy to implement, but the representation of the data is simple and cannot be adapted, resulting in analysis dictionaries that cannot be widely used for different types and sources of data. Learning dictionary methods, which are often referred to as learning dictionary methods that obtain a specific dictionary from given data through a machine learning strategy, have a strong adaptive capacity, and can learn to obtain a dictionary with excellent performance even in the face of different data sets, such as an optimal direction method, a generalized principal component analysis algorithm, K-SVD, and the like. But when the actual model of the signal does not agree with the hypothetical model, deviations and distortions in the recovery result. For this reason, in the present invention, the classical dictionary learning is improved by using the deep learning model.
In one possible implementation, the dictionary D for each layer in the deep convolutional neural network model l Can be expressed as:
wherein ,Dl A dictionary representing a first layer, L representing the number of layers, k, of the deep convolutional neural network model l Representing the sample dimension of the first layer.
Classifying signals according to different signal sources, and outputting Z of each category in the deep convolutional neural network model at a first layer l Expressed as:
wherein C represents the total number of categories, C represents the number of sample categories, n represents the number of samples for each category,indicating the output of the class c signal at layer I, -/->Representing the output of the jth sample of class c at the first layer.
For example, signals may be classified into GPS signals, beidou signals, etc. according to the source.
It should be noted that, the signals sent by different satellites have specificity, and when the distorted signals are restored, if the differences between different categories cannot be considered, the effect of distortion restoration will be greatly affected. The invention aims to find an optimal dictionary, and has good distortion recovery effect on signals from different satellites without training a respective dictionary for each type of signals. Therefore, classifying the signals according to different signal sources can provide a basis for searching an optimal dictionary later, and meanwhile, the universality of the model can be improved.
S102: and determining an objective function of the deep convolutional neural network model, wherein the objective function is used for searching an optimal dictionary.
The objective function can calculate the error between the predicted result and the real result, and the model is guided to continuously adjust parameters through error back propagation until the optimal solution is reached. The objective function may be a cost function, a loss function, or the like.
The optimal dictionary can have good distortion restoration effects on all types of distortion signals.
In one possible implementation, S102 specifically includes sub-steps S1021 and S1022:
s1021: determining an objective function of a single layer in the deep convolutional neural network model:
wherein ,Z0 The input is represented by a representation of the input,representing F norm>Representing 1 norm>Representing 2 norms, D representing the basis of the dictionary D, λ representing the hyper-parameters.
Wherein, the super parameters can be obtained by random search, and the super parameters are manually set parameters before model training, and control the learning process and complexity of the model. The reasonable selection of the super parameters can improve the model effect.
The specific meaning of the single-layer objective function is that the sum of the error matrix and the current layer output is small enough. The error matrix is to reduce the error between the actual result and the predicted result, and the current layer output is introduced into the objective function, so that the model can be helped to better control the output of each layer. In deep neural networks, the output of each layer is often the input of the next layer, so controlling the output of each layer can effectively control the complexity and expressive power of the overall model. By introducing the product of the current layer into the objective function, the stability of the model can be increased, and a stable convergence state can be more easily achieved, so that better model performance can be obtained.
S1022: introducing a nonlinear activation function into the objective function, promoting the objective function of a single layer to an L layer, and changing the objective function of the deep convolutional neural network model to be:
。
among them, the nonlinear memory activation functions are of a wide variety, including Sigmoid functions, tanh functions, reLU functions, leakyReLU functions, and ELU functions. The invention can use a ReLU function, which is a commonly used nonlinear activation function that outputs equal to the input when the input is positive and 0 when the input is negative, and has the following function form: f (x) =max (0, x).
In the model of the neural network, the activation function is a very important component. The nonlinear activation function is introduced to perform nonlinear transformation on the result after linear transformation, so that the neural network can learn more complex characteristics. If the activation function is not introduced, the neural network can only perform linear transformation, and a nonlinear mode cannot be fitted. Further, in deep neural networks, the activation function may cause the output of each layer to have some nonlinear properties, so that the entire model may fit a more complex function. If the activation function is not introduced, the deep neural network is degenerated into a linear model, and the advantage of deep learning cannot be reflected.
According to the invention, by introducing the nonlinear activation function into the objective function of the single layer and popularizing the nonlinear activation function to the L layer, on one hand, the deep neural network can be prevented from being degenerated into a linear model, and on the other hand, the optimal dictionary of each layer can be trained according to the objective function after popularizing the nonlinear activation function to the L layer.
Further, in one possible implementation, S102 further includes:
s1023: introducing intra-class constraint conditions into the objective function, and changing the objective function of the deep convolutional neural network model into the following steps:
wherein ,is a super parameter.
Wherein, in the improved objective function, the error is minimized for each layer of each sample of each category, so as to obtain a universal dictionary as much as possible. It is no longer necessary to generate a specific dictionary for a particular type. The generated dictionary can be used in all satellite signals through intra-class constraint, and the problem that the signal model is too strong in constraint is solved.
Further, by introducing intra-class constraint conditions into the objective function, an optimal dictionary can be found, all types of signals can be processed, similarity of data features under the signals of the same class can be ensured as much as possible, and non-similarity of features among signals of different classes can be ensured. Therefore, the method can ensure that signals of different types have differences when in distortion restoration, and the signals of the same type have similarity when in distortion restoration, so that the method has universality and accuracy, and can meet the requirements of both the distortion restoration of each type of signal and the good distortion restoration of each type of signal when in distortion restoration. The intra-class constraint conditions can also effectively reduce decision boundaries among classes, and can further improve generalization capability of the model.
The intra-class constraint can be introduced into the objective function by means of intra-class co-distribution constraint, intra-class variance constraint or intra-class distance constraint.
S103: and training the deep convolutional neural network model by taking the objective function as a target.
In one possible implementation, S103 includes sub-steps S1031 and S1032:
s1031: generating a distorted training image X through a fuzzy matrix H:
where Y represents the original time-frequency image and N represents white noise.
The fuzzy matrix can be set arbitrarily according to actual needs, and different selected fuzzy matrices can generate different distortion training images so as to fit dictionaries with different functions.
Specifically, the blur matrix may employ at least one of: gaussian blur matrix, mean blur matrix, median blur matrix, gradient blur matrix and linear blur matrix.
The distorted training image is generated by the fuzzy matrix to amplify the training set and improve the generalization performance of the model. Blur matrices are one of the commonly used data enhancement techniques that can generate a set of blurred images by applying a series of blur filters on the original image. These blurred images are similar to the original images but have different degrees of blurring and noise levels, so that the diversity of the training data can be increased. By using the training image generated by the fuzzy matrix, the model can learn more different characteristics and classification accuracy under the noise condition, so that the robustness and generalization capability of the model are improved.
S1032: and training the deep convolutional neural network model by distorting the training image X and taking an objective function as a target.
In practical application, a large amount of labeling data is usually needed to improve the performance of the model when training the deep learning model, but obtaining a large amount of labeling data is a difficult and expensive matter. In the invention, the distorted training image is generated through the fuzzy matrix, the training set is amplified, the diversity of training data is increased, and the robustness and generalization capability of the model are further improved.
S104: and extracting parameters of each layer after training is completed to form an optimal dictionary.
The parameters of each layer are extracted mainly as internal parameters of a convolution kernel, and the convolution kernel of each channel is regarded as an independent dictionary.
S105: a distorted signal in the satellite signal is acquired.
In one possible implementation, S105 includes sub-steps S1051 and S1052:
s1051: a frequency domain signal of the original satellite signal is acquired.
S1052: and analyzing the continuity of the frequency domain signals, and screening out distortion signals according to the continuity of the frequency domain signals.
Wherein the frequency domain characteristics are generally continuous for a normal frequency domain signal. And for distorted signals, it usually appears as a sudden high frequency component or discontinuous frequency domain structure. Therefore, the distortion signal can be accurately screened out according to the continuity of the frequency domain signal.
In one possible embodiment, S1052 specifically includes:
performing power spectrum analysis on the frequency domain signal to obtain power spectrum density：
Where N represents the total number of samples, k represents the frequency value,representing the frequency separation between adjacent frequency components,represents the sampling frequency, +.>，X[k]Representing the frequency domain signal values.
Fourth moment M of calculating power spectral density 4 ：
An average of the power spectral densities is calculated.
And obtaining a corresponding fourth-order accumulated quantity according to the fourth-order moment, calculating a difference value between the fourth-order accumulated quantity and an average value of the power spectrum density, and confirming the signal under the corresponding frequency as a distortion signal under the condition that the difference value is larger than a first preset value.
It should be noted that the distorted signal is often accompanied by discontinuous jump points or spikes, etc. The power spectral density is more sensitive to the detection of energy peaks, and if the higher-order moment of a frequency domain signal is far greater than that of a normal signal, the signal can be confirmed as a distorted signal, so that a good distorted signal detection effect can be achieved. Meanwhile, the fourth-order moment of the power spectrum density and the fourth-order moment accumulation calculating method are relatively simple, the power spectrum density is calculated firstly, then square sum average is carried out, and excessive complex operation is not needed in the calculating process. Further, the fourth moment method of the power spectrum density can be combined with other signal processing technologies, such as wavelet transformation, time-frequency analysis and the like, so that the detection effect and the reliability are improved.
S106: for a pair ofThe distorted signal is transformed to obtain a time-frequency image Z of the distorted signal 0 。
In one possible implementation, S106 is specifically: the time-frequency image of the distorted signal is obtained by Short-time fourier transform (Short-Time Fourier Transform, STFT).
Where training directly with the original signal as input may result in the model over fitting these particular signals due to the specificity of some satellite signals, resulting in a trivial solution. According to the invention, the time-frequency image is obtained through short-time Fourier transform, so that deep learning failure caused by the fact that the specificity of certain satellite signals is subjected to trivial solution in the deep learning process can be avoided.
S107: time-frequency image Z of input distortion signal 0 Obtaining a time-frequency image Y of the restored signal through the optimal dictionary:
wherein L represents the number of layers of the deep convolutional neural network model, L represents the number of each layer,，Z l-1 represents the output of layer 1, < >>Representing the optimal dictionary of the first layer.
S108: and transforming the time-frequency image of the restored signal to obtain the restored signal.
In one possible implementation, S108 is specifically: and performing Short-time inverse Fourier transform (Short-Time Inverse Fourier Transform, STIFT) on the time-frequency image of the restored signal to obtain the restored signal.
The method has the advantages that the optimal dictionary is obtained through training of the deep convolutional neural network model, the deep convolutional neural network model can be automatically fitted, parameters of the whole model are in optimal parameters, the problem that parameters are difficult to adjust in traditional dictionary learning is avoided, the recovery effect on distorted signals is good, various distorted signals can be recovered universally by using the optimal dictionary, the constraint of the model is small, the generalization is strong, the application range of signal recovery is wide, and the popularization of technology is facilitated.
In describing embodiments of the present invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "center", "top", "bottom", "inner", "outer", "inside", "outside", etc. indicate orientations or positional relationships based on the drawings are merely for convenience in describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Wherein "inside" refers to an interior or enclosed area or space. "peripheral" refers to the area surrounding a particular component or region.
In the description of embodiments of the present invention, the terms "first," "second," "third," "fourth" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first", "a second", "a third" and a fourth "may explicitly or implicitly include one or more such feature. In the description of the present invention, unless otherwise indicated, the meaning of "a plurality" is two or more.
In describing embodiments of the present invention, it should be noted that the terms "mounted," "connected," and "assembled" are to be construed broadly, as they may be fixedly connected, detachably connected, or integrally connected, unless otherwise specifically indicated and defined; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.
In the description of embodiments of the invention, a particular feature, structure, material, or characteristic may be combined in any suitable manner in one or more embodiments or examples.
In describing embodiments of the present invention, it will be understood that the terms "-" and "-" are intended to be inclusive of the two numerical ranges, and that the ranges include the endpoints. For example, "A-B" means a range greater than or equal to A and less than or equal to B. "A-B" means a range of greater than or equal to A and less than or equal to B.
In the description of embodiments of the present invention, the term "and/or" is merely an association relationship describing an association object, meaning that three relationships may exist, e.g., a and/or B, may represent: a exists alone, A and B exist together, and B exists alone. In addition, the character "/" herein generally indicates that the front and rear associated objects are an "or" relationship.
Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (8)
1. A distortion signal restoration method based on priori knowledge, comprising:
s101: constructing a deep convolutional neural network model, wherein the deep convolutional neural network model is of a multi-layer structure, and each layer is provided with a dictionary to be learned;
s102: determining an objective function of the deep convolutional neural network model, wherein the objective function is used for searching an optimal dictionary;
s103: training the deep convolutional neural network model by taking the objective function as a target;
s104: extracting parameters of each layer after training is completed, and forming the optimal dictionary;
s105: obtaining a distortion signal in a satellite signal;
S106: transforming the distorted signal to obtain a time-frequency image of the distorted signalZ 0 ；
S107: time-frequency image of input distortion signalZ 0 Obtaining a time-frequency image of the restored signal through the optimal dictionaryY：
；
wherein ,Lrepresenting the number of layers of the deep convolutional neural network model,lthe number of each layer is indicated,，Z l-1 represent the firstl-output of layer 1,>represent the firstlAn optimal dictionary of layers;
s108: transforming the time-frequency image of the restored signal to obtain a restored signal;
wherein, dictionary of each layer in the deep convolutional neural network modelD l Can be expressed as:；
wherein ,D l represent the firstlThe dictionary of the layers is set up to,Lrepresenting the number of layers of the deep convolutional neural network model,k l represent the firstlSample dimensions of the layers;
classifying signals according to different signal sources, and classifying each category in the deep convolutional neural network model into a first categorylLayer outputZ l Expressed as:
；
；
；
wherein ,Cthe total number of categories is indicated,ca number representing the class of the sample,nrepresenting the number of samples for each category,represent the firstcClass signal at the firstlOutput of layer->Represent the firstcClass 1jThe first sample is atlLayer output;
wherein, the S102 includes:
s1021: determining an objective function of a single layer in the deep convolutional neural network model:
；
；
wherein ,Z 0 the input is represented by a representation of the input,representation ofFNorms (F/F)>Representing 1 norm>The number of 2 norms is indicated,drepresentation dictionaryDIs used as a base for the (c) of the (c),λrepresenting the super-parameters;
s1022: introducing a nonlinear activation function into the objective function to make a single layerPromotion of objective function toLAnd a layer for changing the objective function of the deep convolutional neural network model as follows:
。
2. the distorted signal restoration method according to claim 1, wherein S102 further comprises:
s1023: introducing intra-class constraint conditions into the objective function, and changing the objective function of the deep convolutional neural network model into:
； wherein ,/>Is a super parameter.
3. The distorted signal restoration method according to claim 1, wherein the S103 includes:
s1031: by blurring the matrixHGenerating distorted training imagesX：；
wherein ,Yrepresenting the original time-frequency image of the image,Nrepresenting white noise;
s1032: training an image through the distortionXAnd training the deep convolutional neural network model by taking the objective function as a target.
4. A distorted signal restoration method according to claim 3, wherein the blur matrix may employ at least one of:
gaussian blur matrix, mean blur matrix, median blur matrix, gradient blur matrix and linear blur matrix.
5. The distorted signal restoration method according to claim 1, wherein S105 includes:
s1051: acquiring a frequency domain signal of an original satellite signal;
s1052: and analyzing the continuity of the frequency domain signals, and screening out distortion signals according to the continuity of the frequency domain signals.
6. The distorted signal restoration method according to claim 5, wherein S1052 specifically comprises:
performing power spectrum analysis on the frequency domain signal to obtain power spectrum density：
；
wherein ,Nrepresenting the number of total sampling points,kthe value of the frequency is indicated,representing the frequency separation between adjacent frequency components, +.>Represents the sampling frequency, +.>，X[k]Representing frequency domain signal values;
calculating fourth moment of the power spectral densityM 4 ：
Calculating an average value of the power spectral density;
and obtaining a corresponding fourth-order accumulated quantity according to the fourth-order moment, calculating a difference value between the fourth-order accumulated quantity and an average value of the power spectrum density, and confirming a signal at a corresponding frequency as a distortion signal under the condition that the difference value is larger than a first preset value.
7. The distorted signal restoration method according to claim 1, wherein S106 specifically is:
and obtaining the time-frequency image of the distorted signal through short-time Fourier transform.
8. The distorted signal restoration method according to claim 1, wherein S108 specifically comprises:
and performing short-time inverse Fourier transform on the time-frequency image of the restored signal to obtain the restored signal.
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