A moore code signal denoising method and system

Abstract

The application discloses a Morse code signal denoising method and system, and the method comprises a training stage and a use stage, wherein the training stage comprises: constructing an original dictionary for sparse expression of the Morse code signal; and performing dimension reduction on the constructed original dictionary to obtain a dimension reduction matrix and a low-dimensional dictionary; the use stage comprises: segmenting an input Morse code signal by using a sliding window to obtain a plurality of segmented signals; performing signal dimension reduction on each segmented signal by using the dimension reduction matrix to obtain a low-dimensional signal; establishing an optimization model, and performing operation by using the low-dimensional signal and the low-dimensional dictionary to obtain a sparse expression vector; and combining the original dictionary and the sparse expression vector to restore information after denoising of the input signal. The application can effectively suppress noise in the Morse code signal, improve signal processing performance and processing speed, and reduce required data quantity and training cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of signal denoising, and more particularly to a Morse code signal denoising method and system. BACKGROUND

[0002] Morse code is a kind of telecommunication encoding containing only dot and dash signals, which can be used to send letters, numbers and punctuation marks, and is usually used for wireless transmission of information. In a wireless transmission channel, the transmission of signals will be affected by various interferences, including Gaussian noise, time-varying fading, multipath fading, etc. In this case, if Morse code needs to be transmitted, it needs to be denoised at the receiving end to ensure that the correct information is received.

[0003] At present, in the prior art:

[0004] (1) The denoising technology based on wavelet transform can reduce the influence of noise to a certain extent, but cannot completely remove noise and cannot effectively suppress noise; the signal processing capability is poor. At the same time, for complex signals, there may be a large error when using this method.

[0005] (2) The denoising technology based on compressed sensing can achieve high-performance denoising and can process various types of noise in actual application. However, this technology requires high data cost in the training stage (a large amount of related audio data is needed to set the basis vector), and the solving calculation cost is also high in the use stage (a large-scale optimization problem needs to be solved), and the signal processing speed is also low.

[0006] Therefore, how to improve the processing performance of Morse code signal denoising, effectively suppress noise, improve the signal processing speed, reduce the required data amount and reduce the use cost is a technical problem that needs to be solved by the person skilled in the art. SUMMARY

[0007] Therefore, the present application provides a Morse code signal denoising method and system, which can effectively suppress noise in Morse code signals, improve signal processing performance, improve signal processing speed, reduce required data amount and reduce use cost.

[0008] To achieve the above purpose, the technical scheme adopted by the present application is:

[0009] In a first aspect, the present application provides a Morse code signal denoising method, which comprises a training stage and a use stage, wherein:

[0010] The training stage comprises:

[0011] Construct a raw dictionary for sparse representation of Morse code signals;

[0012] Dimension reduction is performed on the constructed raw dictionary to obtain a dimension reduction matrix and a low-dimensional dictionary;

[0013] The use stage includes:

[0014] The input Morse code signal is segmented by sliding window to obtain a plurality of segmented signals;

[0015] Each segmented signal is subjected to signal dimension reduction using the dimension reduction matrix to obtain a low-dimensional signal;

[0016] An optimization model is established, and the low-dimensional signal and the low-dimensional dictionary are used for operation to obtain a sparse representation vector;

[0017] The raw dictionary and the sparse representation vector are combined to restore the information after noise reduction of the input signal.

[0018] Further, in the training stage, the raw dictionary for sparse representation of Morse code signals includes:

[0019] Prepare a short code signal with a length of L1, and normalize the sample points of the short code signal to obtain a reference signal S;

[0020] A matrix D with a size of L*M is constructed, where L is the size of the window, L is greater than L1, and M is the number of steps;

[0021] The reference signal S is placed in the first column of the matrix D, and is modified by time shift operation, a new signal is generated each time an element is moved, and the new signal is stored in the subsequent columns of the matrix D. The stored matrix D is used as the raw dictionary for Morse code signal recovery.

[0022] Further, in the training stage, the dimension reduction is performed on the constructed raw dictionary to obtain a dimension reduction matrix and a low-dimensional dictionary, including:

[0023] SVD decomposition is performed on the matrix D to obtain D=U*∑*V T ; Wherein U is an LxL matrix, ∑ is an LxL diagonal matrix, and V is an MxL matrix;

[0024] The first k columns of the matrix U are taken out and recorded as the matrix U k ;

[0025] The matrix U k is transposed to obtain a dimension reduction matrix

[0026] The matrix D is subjected to dimension reduction to obtain D1=P*D, wherein D1 is a low-dimensional dictionary matrix with a size of k*M.

[0027] Furthermore, during the usage phase, the input Morse code signal is segmented using a sliding window to obtain multiple segmented signals, including:

[0028] The input Morse code signal is uniformly sampled to obtain a one-dimensional original signal Y, which is represented as:

[0029] Y = [y1, y2, ..., y] n ] T

[0030] Among them, y j Let j represent the signal amplitude at the j-th sampling point, where j = 1, 2, ..., n, and n represents the number of signal sampling points.

[0031] The original signal Y is segmented using a sliding window, with each window being L in size and sliding step size l0; this results in a series of segmented signals Y of length L. i , where i = 1, 2, ..., N, and N represents the number of segmented signals.

[0032] Furthermore, during the usage phase, the formula for obtaining the low-dimensional signal is:

[0033] Z i =P*Y i

[0034] Among them, Z i Let P represent the low-dimensional signal, and let Y represent the dimensionality reduction matrix. i This indicates a segmented signal.

[0035] Furthermore, in the usage phase, the optimization model is established using the basis pursuit denoising method, and solved using the convex optimization solver CVX to obtain a sparse representation vector; the optimization model is as follows:

[0036] min||Z i -D1*X i ||+λ|X i |1

[0037] Where ||·|| denotes the Euclidean norm of the vector, Z i Let D1 represent a low-dimensional signal, and X represent a low-dimensional dictionary matrix. i Let |·|1 represent the sparse representation vector, |·|1 represent the l1 norm of the vector, and λ is the regularization parameter.

[0038] Furthermore, in the usage phase, the process of combining the original dictionary with the sparse representation vector to recover the denoised information of the input signal includes:

[0039] In the loop iteration, the sparse expression vector X of the current time window is obtained i ;

[0040] The sparse expression vector X is multiplied by the original dictionary D to obtain the estimated value of the recovery signal as: i

[0041] The middle part of is placed in the corresponding position of the zero vector to obtain a signal Y equal in length to the output signal * .

[0042] In a second aspect, the present application also provides a Morse code signal denoising system, applied to the above-mentioned Morse code signal denoising method, for realizing Morse code signal denoising; the system comprises:

[0043] An original dictionary construction module is configured to construct an original dictionary for sparse expression of the Morse code signal;

[0044] A dimension reduction matrix and low-dimensional dictionary output module is configured to perform dimension reduction on the constructed original dictionary and output a dimension reduction matrix and a low-dimensional dictionary;

[0045] A sliding window segmentation module is configured to segment the input Morse code signal by sliding window to obtain a plurality of segmented signals;

[0046] A signal dimension reduction module is configured to perform signal dimension reduction on each segmented signal using the dimension reduction matrix to obtain a low-dimensional signal;

[0047] An expression vector solving module is configured to establish an optimization model and perform operation using the low-dimensional signal and the low-dimensional dictionary to obtain a sparse expression vector;

[0048] A recovery signal module is configured to combine the original dictionary and the sparse expression vector to recover information after denoising of the input signal.

[0049] Compared with the prior art, the technical scheme of the present application has at least the following beneficial technical effects:

[0050] 1. The present application combines signal dimension reduction technology and sparse expression technology, which can effectively suppress complex noise in the Morse code audio signal and improve signal processing performance.

[0051] 2. The present application can process various types of noise and effectively suppress noise in the case of continuous change in noise level to recover the Morse code signal.

[0052] 3. The present application realizes real-time processing by appropriately selecting the size of the sliding window and the number of dimension reduction, which can greatly improve the signal processing speed.

[0053] ​4. The present application only needs one reference signal with high signal-to-noise ratio in constructing the dictionary, which is much less than the data amount required by other methods, reduces the amount of training data required, and reduces the training cost.

[0054] Other features and advantages of the present application will be set forth in the following description, and in part will become apparent to those skilled in the art from the description, or can be learned by practice of the application. The objects and other advantages of the application will be realized and attained by the structure particularly pointed out in the written description and claims thereof as well as the appended drawings.

[0055] The technical solutions of the present application will be further described in detail below with the help of the accompanying drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0056] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without any creative effort.

[0057] The accompanying drawings are used to provide a further understanding of the present application, and constitute a part of the specification, which are used together with the embodiments of the present application to explain the present application, and do not constitute a limitation to the present application.

[0058] Figure 1 The training phase flowchart of a mores code signal denoising method provided by the embodiments of the present application.

[0059] Figure 2 The use phase flowchart of a mores code signal denoising method provided by the embodiments of the present application.

[0060] Figure 3 The schematic diagram of a reference signal provided by the embodiments of the present application.

[0061] Figure 4 The schematic diagram of an input signal after denoising and recovery of the original signal provided by the embodiments of the present application.

[0062] Figure 5 The schematic diagram of suppressing various noises including impulse noise provided by the embodiments of the present application.

[0063] Figure 6 The schematic diagram of suppressing noise in the case of continuous change of noise level provided by the embodiments of the present application. DETAILED DESCRIPTION

[0064] Exemplary embodiments of the present disclosure will be described herein below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it is understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the present disclosure to those skilled in the art.

[0065] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of the application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative labor are within the scope of protection of the present application.

[0066] Embodiment 1

[0067] The embodiment of the present application provides a Morse code signal denoising method, which comprises a training stage and a use stage, wherein:

[0068] In this embodiment, the flow of the training stage is as shown in Figure 1 The flow of the training stage mainly includes two steps of constructing a dictionary and reducing the dimension of the dictionary, and the specific implementation process is as follows:

[0069] (1) Construct a dictionary that can be used for sparse representation of Morse code signals:

[0070] In the training stage, a dictionary that can be used for sparse representation of Morse code signals is first constructed. First, a short code signal with a length of L1 (which contains as little noise as possible) needs to be prepared. After normalizing the sample points of the signal (dividing by the modulus of the entire signal), a reference signal S can be obtained. Then, a matrix D with a size of L*M is constructed, where L is greater than L1 and M is the number of step lengths. Then, the reference signal S is placed in the first column of the matrix and modified by time shift operation. Each time an element is moved to the right, a new signal is generated, which is stored in the subsequent columns of the matrix. Specifically, when the moving step length is 1, the new signal is stored in the second column of the matrix; when the moving step length is 2, the new signal is stored in the third column of the matrix; and so on. Ensure that when the step length is M, the last sample of the reference signal is the last element of the last column of the matrix. This way, a set of deformations based on the reference signal can be generated, which are placed in the matrix D, and then the matrix D will be used as a dictionary for Morse code signal recovery.

[0071] The principle of this step is to manually construct a dictionary that can sparsely represent Morse signals by using the sparsity of Morse code signals on the short code shift dictionary. This avoids the need for a large number of Morse code signals to be obtained, reducing the data requirements.

[0072] (2) Dimension reduction is performed on the above dictionary to obtain a dimension reduction matrix and a low-dimensional dictionary. The specific algorithm is as follows:

[0073] SVD decomposition is performed on the matrix D to obtain D = U *∑*V T ; wherein U is an L*L matrix,∑ is an L*L diagonal matrix, and V is an M*L matrix;

[0074] The first k columns of the matrix U are taken out and denoted as the matrix U k ;

[0075] The matrix U k is transposed to obtain a dimension reduction matrix P of size k*L.

[0076] The matrix D is dimension reduced to obtain D1 = P*D, wherein D1 is a low-dimensional dictionary matrix of size k*M.

[0077] Through the above steps, a dimension reduction matrix P that can be used for dimension reduction of Morse code signals is successfully constructed, and a dictionary matrix D1 after dimension reduction. In the algorithm steps in the subsequent use stage, P will be used for dimension reduction of the input segmented signal, and D1 will be used to construct a smaller scale optimization problem to improve the solving efficiency, thereby improving the processing speed of the signal.

[0078] In this embodiment, the flow of the use stage is as shown in Figure 2 , mainly including four steps of sliding window segmentation, signal dimension reduction, solving expression vector, and recovering signal. The specific implementation process is as follows:

[0079] (1) The input signal is segmented by sliding window:

[0080] First, the input signal is uniformly sampled to obtain a one-dimensional original signal Y, which can be expressed as:

[0081] Y = [y1, y2,..., y n ] T (column signal),

[0082] wherein y j represents the signal amplitude at the jth sampling point, wherein j = 1, 2,..., n, and n represents the number of signal sampling points. Then, the original signal Y is segmented by sliding window, and the size of each window is L and the step length of the window sliding is l0 (for example, l0 = 0.8L). Thus, a series of segmented signals Y i of length L are obtained, wherein i = 1, 2,..., N, and N represents the number of segmented signals.

[0083] In this embodiment, it is suggested to have overlapping sliding windows, and only the signal in the middle part of the window is taken, and there is no overlap when the signal is recovered. If it is a non-overlapping sliding window; or the complete signal in the sliding window (including the signal start and end part samples) is taken, and the overlapping part of the window is weighted and averaged, and added to the finally recovered signal. If non-overlapping sliding window or complete signal in the window is taken, it is possible that the sliding window cuts a long pulse into two short pulses, causing defects in the recovered signal.

[0084] (2) Signal dimension reduction:

[0085] For each segmented signal Y i , dimension reduction is performed on it using a dimension reduction matrix P, that is, Z i = P * Y i , where i represents the i-th segmented signal, Y i represents the original data of the i-th segmented signal, and P represents the dimension reduction matrix; N low-dimensional signals Z i of length k can be obtained.

[0086] Through dimension reduction, the dimension of the signal can be reduced, the redundant information in the signal can be reduced, and the processing of the signal can be more efficient and simple. At the same time, by segmenting the long signal for processing, the requirement for computer computing power can be reduced, and the calculation time and resource consumption can be reduced. In addition, it also prepares for the small-scale optimization problem of the following step (3), and provides strong support for the implementation of the subsequent algorithm.

[0087] (3) Solve the expression vector:

[0088] In this step, the low-dimensional signal Z i is operated with the low-dimensional dictionary D1, so as to obtain the sparse expression vector X i .

[0089] Specifically, the sparse expression vector X i of length M is obtained by solving the solution of the classical basis pursuit denoising (BPDN) optimization problem min||Z i -D1*X i ||+λ|X i |1. Wherein, ||·|| represents the Euclidean norm (i.e. l2 norm) of the vector, |·|1 represents the l1 norm of the vector, and λ is a regularization parameter.

[0090] In this embodiment, the sparsity of the l1 norm is used, and the objective function is constrained by using the regularization method, so that most elements of the sparse expression vector X i are 0. Through this method, the expression vector X i obtained can be used to describe the input signal Z iThe linear combination result on the low-dimensional dictionary D1, while also having compression representation and de-noising capabilities.

[0091] By solving the sparse expression vector X i , the amount of data of the input signal Z i can be effectively reduced, the processing speed of the data can be improved, and the noise in the signal can be removed. Since Z i can be processed independently and does not depend on the signals at the previous and subsequent time points, this step can be carried out in parallel by means of a multi-core processor to improve the processing speed.

[0092] In this embodiment, X i can also be solved by other similar optimization problems:

[0093] For example, min |X i |1, s.t. Z i = D1*X i , or min ||Z i -D1X i ||+λ||X i || p (0≤p<1), or min ||X i || p , s.t. Z i = D1X i , and the like. The X i solved by the alternatives differ slightly, but the impact on the signal recovery performance is not great. Therefore, it is recommended to solve by BPDN, because the size of the regularization parameter can be adjusted to control the suppression effect on the noise, and the l1 norm optimization problem of BPDN is a convex optimization problem, which is faster to solve than the l p norm optimization problem.

[0094] (4) Recovering the signal:

[0095] The main purpose of this step is to recover the information of the input signal after de-noising by combining the original dictionary D with the sparse expression vector X i . In this step, a zero vector of the same length as the input signal is first defined, and then the segmented signal in the sliding window (length L) is recovered, and the central part (for example, from 0.1L to 0.9L samples) is selected and placed in the corresponding position of the zero vector.

[0096] Specifically, the implementation process of this step is as follows. First, the sparse expression vector X i of the current time window is obtained in the loop iteration. Next, X i is multiplied by the original dictionary D to obtain the estimated value of the recovered signal: Subsequently, the The middle part of the signal Y is placed into the corresponding position of the zero vector, obtaining a signal Y with the same length as the output signal * Through this step, the segmented signal obtained in the second step can be integrated to generate an output signal with the same length as the input signal.

[0097] The specific implementation of the above method is further described below with a specific embodiment:

[0098] This embodiment is aimed at the Morse code transmission and reception scenario based on wireless communication, and the system is deployed at the receiving end to improve the detection performance by noise reduction on the received signal.

[0099] The specific business scenario is divided into two parts: the sending end and the receiving end. First, the sending end will perform the following encoding operation: a sound pulse signal with a short duration (e.g. 0.03-0.06s) represents a "dot" in Morse code, and a sound pulse signal with a long duration (e.g. 0.3-0.5s) represents a "dash" in Morse code. The sound signal will be transmitted through a wireless channel, and will be naturally attenuated and noisy. Then, the wireless signal is demodulated at the receiving end, and then sampled at a sampling rate of 44.1kHz. The sampled signal is used as the input of the system.

[0100] The specific implementation is as follows:

[0101] 1. Construct a dictionary:

[0102] a. From the data received at the receiving end, select a sound pulse signal with low noise level (representing the shortest "dot" in Morse code) as the reference signal. In this embodiment, it is assumed that no audio pulse signal shorter than 0.05s will appear in the business, so a 0.056s (2481 sample points) audio pulse signal is selected as the reference signal, as shown in Figure 3 The horizontal axis represents the sampling points, and the horizontal axis with a length of 2500 represents the length of the entire signal, which is 2500 sampling points. The vertical axis represents the amplitude of the signal.

[0103] b. Refer to step (1) of the training phase of the method of the present application to construct a dictionary that can be used for sparse representation of Morse code signals: an L*M matrix D. In this embodiment, L=11025 (0.25s) and M=8544 are preferably selected.

[0104] 2. Construct a dimension reduction matrix and a low-dimensional dictionary

[0105] Refer to step (2) of the training phase of the method of the present application to obtain the dimension reduction matrix P and the low-dimensional dictionary D1. In this embodiment, k=50 is preferably selected.

[0106] 3. Sliding window segmentation

[0107] The input signal is segmented by sliding window according to step (1) in the using stage of the method of the present application, and a plurality of segmented signals are obtained. The length of the overlapping window is set to 0.025 s (1103 samples), and for an input signal with a length of 15.97 s, the total number of segmented signals is 70.

[0108] 4. Signal dimension reduction: the dimension of each segmented signal is reduced, and Z is calculated i = P * Y i , and a low-dimensional signal Z i is obtained.

[0109] 5. Solve the expression vector: for each low-dimensional signal Z i , an optimization model min||Z i - D1 * X i || + λ |X i |1 is established, and a convex optimization solver CVX is used to solve it, and a sparse expression vector X i is obtained.

[0110] 6. Recover the signal: combine the original dictionary with the sparse expression vector to recover the information of the input signal after denoising. In this step, the sliding window is slid according to a certain step size, and the central part (1103 to 9923 samples) is selected and placed in the zero vector at the corresponding position. The situation after the input signal is denoised and the result of recovering the original signal are shown in Figure 4 (Black in the figure represents the input noisy signal, gray represents the output denoised signal, the horizontal axis represents time, unit: s, and the vertical axis represents the amplitude of the signal).

[0111] Further, in this embodiment, the present application is also verified to suppress various noises including impulse noise and to suppress noise in the case of continuous change of noise level; the results are shown in Figure 5 and Figure 6 (Black in the figure represents the input noisy signal, gray represents the output denoised signal, the horizontal axis represents time, and the vertical axis represents the amplitude of the signal). It can be seen from Figure 5 that the scheme of the present application can effectively suppress various types of noise, and from Figure 6 it can be seen that the scheme of the present application can also effectively suppress noise in the case of continuous change of noise level, and even in the case of low local signal-to-noise ratio, the Morse code signal can be well recovered.

[0112] The Morse code signal denoising method provided by the application can effectively suppress complex noise in a Morse code audio signal and improve signal processing performance by combining a signal dimension reduction technique and a sparse expression model. The method can process various types of noise and effectively suppress noise in the case of continuous noise level change to restore a Morse code signal. The method can achieve real-time processing by appropriately selecting a sliding window size and a dimension reduction number, thereby greatly improving signal processing speed. The method only needs one reference signal with high signal-to-noise ratio when constructing a dictionary, and the amount of required training data is much smaller than that required by other methods, thereby reducing the amount of required training data.

[0113] From the description of the above embodiments, those skilled in the art can know that the application provides a Morse code signal denoising method, which combines a signal dimension reduction technique and a sparse expression model, can effectively suppress complex noise in a Morse code audio signal, and improves signal processing performance. The method can process various types of noise and effectively suppress noise in the case of continuous noise level change to restore a Morse code signal. The method can achieve real-time processing by appropriately selecting a sliding window size and a dimension reduction number, thereby greatly improving signal processing speed. The method only needs one reference signal with high signal-to-noise ratio when constructing a dictionary, and the amount of required training data is much smaller than that required by other methods, thereby reducing the amount of required training data.

[0114] Embodiment 2

[0115] The application also provides a Morse code signal denoising system, which is applied to the Morse code signal denoising method described in Embodiment 1 and realizes Morse code signal denoising. The system comprises:

[0116] An original dictionary construction module constructs an original dictionary for sparse expression of a Morse code signal.

[0117] A dimension reduction matrix and low-dimensional dictionary output module is used for dimension reduction of the constructed original dictionary and outputs a dimension reduction matrix and a low-dimensional dictionary.

[0118] A sliding window segmentation module is used for sliding window segmentation of an input Morse code signal to obtain a plurality of segmented signals.

[0119] A signal dimension reduction module is used for signal dimension reduction of each segmented signal using a dimension reduction matrix to obtain a low-dimensional signal.

[0120] The expression vector solving module is configured to establish an optimization model, and use the low-dimensional signal and the low-dimensional dictionary to obtain a sparse expression vector;

[0121] The recovery signal module is configured to combine the original dictionary with the sparse expression vector to recover information after noise reduction of the input signal.

[0122] The Morse code signal noise reduction system provided by the embodiment of the present application has the same implementation principle and technical effects as the method embodiment, and for brevity, the part not mentioned in the embodiment will be described with reference to the corresponding content in the method embodiment.

[0123] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system or a computer program product. Therefore, the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can be in the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program code.

[0124] The above detailed description of the embodiments of the present application, the principles and implementation modes of the present application are described, and the above embodiment description is only used to help understand the method of the present application and its core idea.

[0125] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of noise reduction of a Morse code signal, characterized by, The method comprises a training stage and a use stage, wherein: The training stage comprises: constructing an original dictionary for sparse expression of the Morse code signal; dimension reduction is performed on the constructed original dictionary to obtain a dimension reduction matrix and a low-dimensional dictionary; The use stage comprises: segmenting the input Morse code signal by sliding window to obtain a plurality of segmented signals; dimension reduction is performed on each segmented signal using the dimension reduction matrix to obtain a low-dimensional signal; an optimization model is established, and the low-dimensional signal and the low-dimensional dictionary are used for operation to obtain a sparse expression vector; the original dictionary and the sparse expression vector are combined to recover information after noise reduction of the input signal; In the training stage, the original dictionary for sparse expression of the Morse code signal comprises: a short code signal with a length of L1 is prepared, and a reference signal S is obtained by normalizing sample points of the short code signal; a matrix D with a size of L*M is constructed, wherein L is the size of the window, L is greater than L1, and M is the number of steps; the reference signal S is placed in the first column of the matrix D, and is modified by time shift operation, a new signal is generated each time an element is moved, and the new signal is sequentially stored in the subsequent columns of the matrix D, and the stored matrix D is used as the original dictionary for Morse code signal recovery.

2. The method of claim 1, wherein, In the training stage, the dimension reduction is performed on the constructed original dictionary to obtain a dimension reduction matrix and a low-dimensional dictionary, comprising: SVD decompose the matrix D to obtain D = U *∑* V T ; wherein U is an LxL matrix,∑ is an LxL diagonal matrix, and V is an MxL matrix. Take the first k columns of the matrix U and call it the matrix U k ; transpose the matrix U k to obtain a reduced dimension matrix of size k*L dimension reduction is performed on the matrix D to obtain D1=P*D, wherein D1 is a low-dimensional dictionary matrix with a size of k*M.

3. The method of claim 2, wherein, In the use stage, the input Morse code signal is segmented by sliding window to obtain a plurality of segmented signals, comprising: the input Morse code signal is uniformly sampled to obtain a one-dimensional original signal Y, and the original signal Y is represented as: Y = [y1, y2,..., y n ] T wherein y j represents the signal amplitude at the jth sampling point, wherein j = 1, 2,..., n, and n represents the number of signal sampling points; The original signal Y is segmented by sliding window, each window has a size of L, and the step size of window sliding is lo; thus a series of segmented signals Y with a length of L is obtained i where i = 1, 2, …, N, and N represents the number of segmented signals.

4. The method of claim 3, wherein, In the use stage, the formula for obtaining the low-dimensional signal is: Z i = P * Y i wherein Z i represents a low-dimensional signal, P represents a dimension reduction matrix, Y i represents a segmented signal.

5. The method of claim 4, wherein, In the use stage, the optimization model is established by the basis pursuit denoising method, and a convex optimization solver CVX is used to solve the optimization model to obtain the sparse expression vector; the optimization model is as follows: min ||z i -D1*X i ||+λ|X i |1 where ||·|| denotes the Euclidean norm of a vector, Z i represents a low-dimensional signal, D1 represents a low-dimensional dictionary matrix, X i represents a sparse representation vector, |·|1 denotes the l1 norm of a vector, and λ is a regularization parameter.

6. The method of claim 5, wherein, In the use stage, the original dictionary and the sparse expression vector are combined to recover information after noise reduction of the input signal, comprising: obtaining a sparse representation vector X of the current time window in the loop iteration i ; The sparse representation vector X is obtained by i The multiplication operation with the original dictionary D is performed to obtain the estimated value of the recovery signal: The intermediate part of Y is placed into the corresponding position in the zero vector, obtaining a signal Y * of the same length as the output signal.

7. A system for noise reduction of Morse code signals, characterized by The system comprises: an original dictionary construction module for constructing an original dictionary for sparse expression of the Morse code signal; a dimension reduction matrix and low-dimensional dictionary output module for performing dimension reduction on the constructed original dictionary to output a dimension reduction matrix and a low-dimensional dictionary; a sliding window segmentation module for segmenting the input Morse code signal by sliding window to obtain a plurality of segmented signals; a signal dimension reduction module for performing signal dimension reduction on each segmented signal using the dimension reduction matrix to obtain a low-dimensional signal; an expression vector solving module for establishing an optimization model, using the low-dimensional signal and the low-dimensional dictionary for operation to obtain a sparse expression vector; a recovered signal module for combining the original dictionary and the sparse expression vector to recover information after noise reduction of the input signal; The original dictionary for sparse expression of the Morse code signal comprises: A short code signal with a length of L1 is prepared, and a reference signal S is obtained by normalizing sample points of the short code signal; A matrix D with a size of L*M is constructed, where L is the size of the window, L is greater than L1, and M is the number of steps; The reference signal S is placed in the first column of the matrix D, and is modified by a time shift operation, a new signal is generated each time an element is moved, and the new signal is stored in the subsequent columns of the matrix D in turn, and the stored matrix D is used as the original dictionary for Morse code signal recovery.

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