CN111401236A - Underwater sound signal denoising method based on self-coding neural network - Google Patents

Underwater sound signal denoising method based on self-coding neural network Download PDF

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CN111401236A
CN111401236A CN202010180738.6A CN202010180738A CN111401236A CN 111401236 A CN111401236 A CN 111401236A CN 202010180738 A CN202010180738 A CN 202010180738A CN 111401236 A CN111401236 A CN 111401236A
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曾向阳
薛灵芝
王海涛
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Northwestern Polytechnical University
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Abstract

The invention provides an underwater sound signal denoising method based on a self-coding neural network, which comprises the steps of training self-coding to obtain an activation function model, optimizing the value of parameters in the neural network according to a loss function, updating all weights by using a gradient descent method, enabling the value of the weights to accord with the mapping from a noisy sample to a clean sample, obtaining the parameters of a mapping relation, and then obtaining the model with the parameters after the training of the self-coding model to realize the denoising function of the noisy sample. The invention solves the problem of poor system robustness caused by the assumption made on the independence of signals and noise in the traditional denoising algorithm, and increases the denoising robustness.

Description

Underwater sound signal denoising method based on self-coding neural network
Technical Field
The invention relates to the technical field of underwater sound denoising, and extracts useful underwater sound signals in a complex underwater environment.
Background
The underwater acoustic signal denoising technology is a key research object in the field of signal processing, and is mainly used for feature extraction of underwater acoustic signals, in water, propagation of electromagnetic wave signals is limited, main information carriers are changed into acoustic signals, however, compared with the electromagnetic wave signals, the acoustic signals are more easily interfered by the external environment and present features similar to noise signals, and useful information is carried in the signal features, so that the research on underwater acoustic signal denoising is a key research content in the field of signal processing and the field of underwater signal research.
In the existing underwater sound signal denoising method, the traditional underwater sound denoising method, the wavelet denoising method and the adaptive filtering denoising method are mainly adopted, and the machine learning-based method is applied to underwater sound denoising in a small amount at present.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides an underwater sound signal denoising method based on a self-coding neural network, the traditional underwater sound signal denoising method, such as a wavelet denoising algorithm and an integrated empirical mode decomposition algorithm, has certain assumed conditions for samples before denoising, but the assumed conditions cannot be completely met in the actual underwater environment, the self-coding denoising network based on deep learning is a supervised training model, specific label information needs to be given in advance, in addition, no assumption is made for the environment and the samples, therefore, the training process of the self-coding network does not depend on the assumed conditions, and the trained model has better robustness.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: in the training stage of self-coding, the self-coding network is assumed to have three elements in the input layer, two elements in the hidden layer and three elements in the output layer, and variables are defined
Figure BDA0002412438010000011
Is a weight, wherein a represents the a-th element in the upper network connecting the weight, b represents the b-th element in the lower network connecting the weight, c takes 1 or 2, 1 represents the weight from the input layer to the hidden layer, 2 represents the weight from the hidden layer to the output layer, and the variable is
Figure BDA0002412438010000012
For the bias term, q is 1 or 2, q-1 represents the bias of the hidden layer, q-2 represents the bias of the output layer, p represents the bias term of the p-th term in the layer, and the input layer is represented by xiRepresenting i denotes the ith element of the input layer, e.g.
Figure BDA0002412438010000013
Representing a weight between a first element in an input layer to a first element of a hidden layer of the self-coding network,
Figure BDA0002412438010000014
representing a weight from a first element in an input layer to a second element in a hidden layer of the encoded network,
Figure BDA0002412438010000015
representing the weight between the first element in the hidden layer to the first element in the output layer of the self-coding network,
Figure BDA0002412438010000021
represents an offset from the first element of the hidden layer of the coded network,
Figure BDA0002412438010000022
an offset representing a second element of the hidden layer of the self-coding network,
Figure BDA0002412438010000023
represents the offset of the first element of the output layer from the coding, h represents the output of the hidden layer from the coding network,
Figure BDA00024124380100000211
an output representing a first element of a hidden layer of a self-coding network,
Figure BDA0002412438010000024
representing the output of a second element of the hidden layer of the self-coding network, y being the output of the output layer, y1The first output element of the output layer is represented, so the forward-propagating self-coding network is represented by the following relation:
Figure BDA0002412438010000025
Figure BDA0002412438010000026
the method comprises the following steps that formula (1) is an encoding process of a self-encoding network, formula (2) is a decoding process of the self-encoding network, f is an activation function, each layer of the self-encoding network is provided with one activation function, the activation functions select sigmoid functions, and the mathematical expressions of the sigmoid functions are as follows:
Figure BDA0002412438010000027
step 2: the back propagation algorithm is a core algorithm for training the neural network, and the values of parameters in the neural network are optimized according to a defined loss function, so that the loss function of the neural network model on a training data set reaches a minimum value, and the loss function is expressed as c ═ f (x, w, b) -x]2Wherein x is an input matrix in the self-coding network model, w is a weight matrix, b is a bias matrix,
Figure BDA0002412438010000028
is the output value from the encoded output layer, wherein,
Figure BDA0002412438010000029
for the input values after adding noise, the loss function is expressed as:
Figure BDA00024124380100000210
wherein, N is the frame number after the underwater sound signal Fourier transform, lambda, β, and rho are model hyperparameters, wherein lambda is a weight attenuation parameter used for controlling the relative importance of a weight attenuation term in a formula, β is a sparsity punishment term parameter used for controlling the weight of a sparsity punishment factor, yiFor the output value, x, of the self-coding network at the ith neuroniIs the input value of the i-th neuron of the self-coding network, w is the weight of the coding layer, w' is the weight of the decoding layer, FThe weights of all elements when the function is lost are referred, and for the sparse penalty term in the formula (4), the specific expression is as follows:
Figure BDA0002412438010000031
wherein rho is a sparsity parameter representing the average liveness closeness of the hidden neuron;
Figure BDA0002412438010000032
taking target activation sparsity parameter rho as mean value and activation degree of hidden neuron j of self-coding neural network
Figure BDA0002412438010000033
Relative entropy between two bernoulli random variables that are mean values, where ρ is an empirical value, taken as 100;
the gradient descent algorithm is that the point where the derivative is 0 is the minimum point of a function, and since the independent variables of the loss function are all weights and offsets, the derivative expression of the loss function is solved as follows:
Figure BDA0002412438010000034
wherein
Figure BDA0002412438010000035
For small variations in the weights from the first element of the input layer of the encoding network to the first element of the hidden layer,
Figure BDA0002412438010000036
for small variations in the weights from the first element of the encoded network input layer to the second element of the hidden layer,
Figure BDA0002412438010000037
biasing the slight variation of the term for the first element of the hidden layer of the self-coding network,
Figure BDA0002412438010000038
the slight change of the second element bias term of the hidden layer of the self-coding network is taken as a gradient in the gradient direction,
Figure BDA0002412438010000039
the expression is as follows:
Figure BDA00024124380100000310
each weight is updated according to equation (7), wherein η is the learning rate,
Figure BDA00024124380100000311
the weight is updated with the variance, and the update formula is:
Figure BDA00024124380100000312
wherein,
Figure BDA00024124380100000313
for the updated weight, subtracting the increment of the weight from the original weight to obtain the updated weight, wherein the updating method of each weight is similar to the formula (8), and each weight is updated correspondingly;
and updating all weights by using a gradient descent method, so that the values of the weights conform to the mapping from the noisy sample to a clean sample, and after the parameters of the mapping relation are obtained, the model with the parameters obtained after the self-coding model is trained realizes the denoising function of the noisy sample.
The method has the beneficial effects that the DNN denoising self-coding algorithm is adopted, so that the problem of poor system robustness caused by the assumption of independence of signals and noise in the traditional denoising algorithm is solved. The method solves the problem that the noise type of the underwater sound signal with noise and the coherence of the underwater sound signal and the noise signal are assumed in advance in the denoising process of the traditional underwater sound denoising algorithm, and some assumptions cannot be established in practical application, so that the denoising range is narrow.
Drawings
FIG. 1 is a diagram of a training architecture for a single self-encoding network of the present invention.
Fig. 2 is a flow chart of an implementation of the present invention.
FIG. 3 is a time domain contrast diagram before and after denoising according to the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
The invention provides a denoising algorithm based on a self-coding network, and the denoising method based on the self-coding network utilizes a training self-coding model to enable the self-coding model to form a mapping relation between the characteristics of a signal with noise and the characteristics of a clean sound signal, and the mapping relation can be utilized to effectively remove the noise of the signal with noise, thereby recovering the original clean sound signal.
(1) In the training stage of self-coding, the self-coding network is assumed to have three elements in the input layer, two elements in the hidden layer and three elements in the output layer, and variables are defined
Figure BDA0002412438010000041
Is a weight, wherein a represents the a-th element in the upper network connecting the weight, b represents the b-th element in the lower network connecting the weight, c takes 1 or 2, 1 represents the weight from the input layer to the hidden layer, 2 represents the weight from the hidden layer to the output layer, and the variable is
Figure BDA0002412438010000042
For the bias term, q is 1 or 2, q-1 represents the bias of the hidden layer, q-2 represents the bias of the output layer, p represents the bias term of the p-th term in the layer, and the input layer is represented by xiRepresenting i denotes the ith element of the input layer, e.g.
Figure BDA0002412438010000043
Representing a weight between a first element in an input layer to a first element of a hidden layer of the self-coding network,
Figure BDA0002412438010000044
representing a weight from a first element in an input layer to a second element in a hidden layer of the encoded network,
Figure BDA0002412438010000045
representing the weight from the first element in the hidden layer to the first element in the output layer of the encoded network,
Figure BDA0002412438010000046
represents an offset from the first element of the hidden layer of the coded network,
Figure BDA0002412438010000047
an offset representing a second element of the hidden layer of the self-coding network,
Figure BDA0002412438010000048
represents the offset of the first element of the output layer from the coding, h represents the output of the hidden layer from the coding network,
Figure BDA0002412438010000049
an output representing a first element of a hidden layer of the self-coding network,
Figure BDA00024124380100000410
representing the output of the second element of the hidden layer of the self-coding network, y being the output of the output layer, y1The first output element of the output layer is represented, so the forward-propagating self-coding network is represented by the following relation:
Figure BDA0002412438010000051
Figure BDA0002412438010000052
the method comprises the following steps that (1) is an encoding process of a self-encoding network, (2) is a decoding process of the self-encoding network, f is an activation function, the activation function is an important embodiment of personification of the neural network, just as a neuron of a person gives an arbitrary excitation, if the excitation is larger than a certain threshold value, the excitation is transmitted to a brain, if the excitation is smaller than the threshold value, the excitation is automatically ignored, and a linearization effect is achieved, each layer of the self-encoding network is provided with the activation function, the activation function selects a sigmoid function, and the mathematical expression of the sigmoid function is as follows:
Figure BDA0002412438010000053
(2) the back propagation algorithm is a core algorithm for training the neural network, and the values of parameters in the neural network are optimized according to a defined loss function, so that the loss function of the neural network model on a training data set reaches a minimum value, and the loss function is expressed as c ═ f (x, w, b) -x]2Wherein x is an input matrix in the self-coding network model, w is a weight matrix, b is a bias matrix,
Figure BDA0002412438010000054
is the output value from the encoded output layer, wherein,
Figure BDA0002412438010000055
for the input values after adding noise, the influence on the weight attenuation on the loss function and the effect of the sparse penalty in the self-coding model are considered, and the loss function is expressed as:
Figure BDA0002412438010000056
wherein N is the frame number after the underwater sound signal Fourier transform, lambda, β, and rho are model hyper-parameters, wherein lambda is a weight attenuation parameter used for controlling the relative weight of the weight attenuation term in the formulaEssential, β is a sparsity penalty parameter, weight used to control sparsity penalty factor, yiFor the output value, x, of the self-coding network at the ith neuroniFor the input value of the self-coding network in the ith neuron, w is the weight of the coding layer, w' is the weight of the decoding layer, F refers to the weight of all elements when the function is lost, and for the sparse penalty term in the formula (4), the overfitting phenomenon of the self-coding network in the training process is effectively removed, and the specific expression is as follows:
Figure BDA0002412438010000061
wherein rho is a sparsity parameter representing the average liveness closeness of the hidden neuron;
Figure BDA0002412438010000062
taking target activation sparsity parameter rho as mean value and activation degree of hidden neuron j of self-coding neural network
Figure BDA0002412438010000063
Relative entropy between two bernoulli random variables that are mean values, where ρ is an empirical value, taken as 100;
the gradient descent algorithm is one of important methods for solving the minimization of a loss function, and the main idea is that the position where the derivative is 0 is a minimum value point of the function, and since the independent variables of the loss function are all weights and offsets, the derivative expression for solving the loss function is as follows:
Figure BDA0002412438010000064
wherein
Figure BDA0002412438010000065
For small variations in the weights from the first element of the input layer of the encoding network to the first element of the hidden layer,
Figure BDA0002412438010000066
for small variations in the weights from the first element of the encoded network input layer to the second element of the hidden layer,
Figure BDA0002412438010000067
biasing the slight variation of the term for the first element of the hidden layer of the self-coding network,
Figure BDA0002412438010000068
the method is a small variation of a second element bias term of a hidden layer of the self-coding network, the direction of the small variation is the direction with the fastest variation, the minimum value of a loss function is found at the fastest speed, the transformation is the fastest in the direction of a gradient, the small variation is taken as the gradient, and the small variation is taken
Figure BDA0002412438010000069
The expression is as follows:
Figure BDA00024124380100000610
the update of each weight is performed in accordance with equation (7), where η is the learning rate,
Figure BDA00024124380100000611
the weight is updated with the variance, and the update formula is:
Figure BDA00024124380100000612
wherein,
Figure BDA00024124380100000613
for the updated weight, subtracting the increment of the weight from the original weight to obtain the updated weight, wherein the updating method of each weight is similar, and each weight is updated correspondingly, so that the mapping relation of the self-coding is slowly close to the real mapping relation.
And updating all weights by using a gradient descent method, so that the values of the weights conform to the mapping from the noisy sample to a clean sample, and after the parameters of the mapping relation are obtained, the model with the parameters obtained after the self-coding model is trained realizes the denoising function of the noisy sample.
The present invention is further described with reference to fig. 2, which is a flow chart of a denoised self-encoding network.
Step 1: firstly, framing a sample, adding a Hanning window with the length of 400, fixing each frame of the sample at the distance of 400 sample points, then assuming that the 400 sample points are a stable process, adopting short-time Fourier transform, and respectively adopting the short-time Fourier transform for each frame, wherein because the frequency spectrum leakage of two edge sections of the Hanning window is serious, the overlapping rate of two adjacent frames is fifty percent, the overlapping can also ensure that a recovery signal is smooth, taking phase information of a noisy sample, then extracting a characteristic value, and taking a characteristic function as:
Y(d)＝log|Y(d)|2(9)
y (d) is a signal of a sample after short-time Fourier transform, d is a frequency dimension, after a characteristic value is extracted, information is sent to a constructed nominal DNN model for training, the DNN denoising network model comprises 5 layers, an input layer, an output layer and 4 hidden layers, 11 frames of noisy samples are taken to extract one frame of useful information, so that the input neuron node of the input layer is 4400 points, the point number of a first neuron is 2048, the point number of a second neuron is 2048, the point number of a third neuron is 1024, the point number of a neuron of the output layer is 400, the sparse parameter of each layer is 0.2, and the activation function of each layer is a sigmoid function, which is shown in a formula (3).
Step 2: intercepting a section of underwater sound signals of 80 minutes, selecting the underwater sound signals of the first 40 minutes as a training set, selecting the underwater sound signals of the last 40 minutes as a testing set, and selecting the underwater sound signals with the learning rate of 0.02 and the sparse function of 0.5.
And step 3: according to the method in the step 1 and the model of the self-coding neural network shown in the figure (1), a training set is added with noise and sent into a DNN model for training, in order to prevent gradient disappearance, 64 groups of data are selected as a batch, loop iteration is carried out for 20 times, each training is completed, a group of test sets are sent into for testing, and the training set error and the test set error of each training set are recorded.
And 4, step 4: and (3) performing back propagation calculation by using the formulas (7) and (8), and performing parameter updating by solving the gradient to finely adjust the mapping relation of the whole network so as to obtain the noise-reduced self-coding network model.
And 5: and obtaining a denoising self-coding model after all the updating steps are completed, wherein all parameters of the denoising self-coding model are used as parameters for mapping from a noisy sample to a clean sample.
Step 6: testing the test set by using the trained denoising DNN model, and reconstructing the sample after estimating the power spectrum of the clean sample by using the DNN model, wherein in the reconstruction stage, as shown in formula (10):
Figure RE-GDA0002484920350000071
wherein
Figure BDA0002412438010000072
The power spectrum of the clean samples is estimated for DNN, ∠ y (d) is the phase information extracted from the noisy samples.
The result is shown in FIG. 3, where loss is the error between the clean sample and the predicted sample after each training of the training set, and val _ loss is the error between the clean sample and the predicted sample after each training of the testing set.

Claims (1)

1. An underwater sound signal denoising method based on a self-coding neural network is characterized by comprising the following steps:
step 1: in the training stage of self-coding, the self-coding network is assumed to have three elements in the input layer, two elements in the hidden layer and three elements in the output layer, and variables are defined
Figure FDA0002412436000000011
Is a weight, wherein a represents the a-th element in the upper network connecting the weight, b represents the b-th element in the lower network connecting the weight, c takes 1 or 2, 1 represents the weight from the input layer to the hidden layer, 2 represents the weight from the hidden layer to the output layer, and the variable is
Figure FDA0002412436000000012
For the bias term, q is 1 or 2, q-1 represents the bias of the hidden layer, q-2 represents the bias of the output layer, p represents the bias term of the p-th term in the layer, and the input layer is represented by xiRepresenting i denotes the ith element of the input layer, e.g.
Figure FDA0002412436000000013
Representing a weight between a first element in an input layer to a first element of a hidden layer of the self-coding network,
Figure FDA0002412436000000014
representing a weight from a first element in an input layer to a second element in a hidden layer of the encoded network,
Figure FDA0002412436000000015
representing the weight between the first element in the hidden layer to the first element in the output layer of the self-coding network,
Figure FDA0002412436000000016
represents an offset from the first element of the hidden layer of the coded network,
Figure FDA0002412436000000017
an offset representing a second element of the hidden layer of the self-coding network,
Figure FDA0002412436000000018
represents the offset of the first element of the output layer from the coding, h represents the output of the hidden layer from the coding network,
Figure FDA0002412436000000019
an output representing a first element of a hidden layer of the self-coding network,
Figure FDA00024124360000000110
representing the output of a second element of the hidden layer of the self-coding network, y being the output of the output layer, y1The first output element of the output layer is represented, so the forward-propagating self-coding network is represented by the following relation:
Figure FDA00024124360000000111
Figure FDA00024124360000000112
the method comprises the following steps that formula (1) is an encoding process of a self-encoding network, formula (2) is a decoding process of the self-encoding network, f is an activation function, each layer of the self-encoding network is provided with one activation function, the activation functions select sigmoid functions, and mathematical expressions of the sigmoid functions are as follows:
Figure FDA00024124360000000113
step 2: the back propagation algorithm is a core algorithm for training the neural network, and the values of parameters in the neural network are optimized according to a defined loss function, so that the loss function of the neural network model on a training data set reaches a minimum value, and the loss function is expressed as c ═ f (x, w, b) -x]2Wherein x is an input matrix in the self-coding network model, w is a weight matrix, b is a bias matrix,
Figure FDA0002412436000000021
is the output value from the encoded output layer, wherein,
Figure FDA0002412436000000022
for the input values after adding noise, the loss function is expressed as:
Figure FDA0002412436000000023
wherein, N is the frame number after the underwater sound signal Fourier transform, lambda, β, and rho are model hyperparameters, wherein lambda is a weight attenuation parameter used for controlling the relative importance of a weight attenuation term in a formula, β is a sparsity penalty term parameter used for controlling the weight of a sparsity penalty factor, and y isiFor the output value, x, of the self-coding network at the ith neuroniFor the input value of the self-coding network in the ith neuron, w is the weight of the coding layer, w' is the weight of the decoding layer, F refers to the weight of all elements when the function is lost, and for the sparse penalty term in the formula (4), the specific expression is as follows:
Figure FDA0002412436000000024
wherein rho is a sparsity parameter representing the average liveness closeness of the hidden neuron;
Figure FDA0002412436000000025
taking target activation sparsity parameter rho as mean value and activation degree of hidden neuron j of self-coding neural network
Figure FDA0002412436000000026
Relative entropy between two bernoulli random variables that are mean values, where ρ is an empirical value, taken as 100;
the gradient descent algorithm is that the point where the derivative is 0 is the minimum point of a function, and since the independent variables of the loss function are all weights and offsets, the derivative expression of the loss function is solved as follows:
Figure FDA0002412436000000027
wherein
Figure FDA0002412436000000028
For small variations in the weights from the first element of the encoded network input layer to the first element of the hidden layer,
Figure FDA0002412436000000029
for small variations in the weights from the first element of the encoded network input layer to the second element of the hidden layer,
Figure FDA00024124360000000210
biasing the slight variation of the term for the first element of the hidden layer of the self-coding network,
Figure FDA00024124360000000211
the slight variation of the second element bias term of the hidden layer of the self-coding network is taken as a gradient in the gradient direction,
Figure FDA00024124360000000212
the expression is as follows:
Figure FDA00024124360000000213
each weight is updated according to equation (7), wherein η is the learning rate,
Figure FDA0002412436000000031
the weight is updated with the variance, and the update formula is:
Figure FDA0002412436000000032
wherein,
Figure FDA0002412436000000033
in order to update the weight of the weight after the update,the weight after the update is obtained by subtracting the increment of the weight from the original weight, the updating method of each weight is similar to the formula (8), and each weight is updated correspondingly;
and updating all weights by using a gradient descent method, so that the values of the weights conform to the mapping from the noisy sample to a clean sample, and after the parameters of the mapping relation are obtained, the model with the parameters obtained after the self-coding model is trained realizes the denoising function of the noisy sample.
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CN113205050A (en) * 2021-05-09 2021-08-03 西北工业大学 Ship radiation noise line spectrum extraction method based on GRU-AE network
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