Adaptive singular value decomposition method for underwater acoustic signal denoising and application

Abstract

This application discloses an adaptive singular value decomposition method for underwater acoustic signal denoising and its application. The method includes: Step 1) acquiring the noisy underwater acoustic signal to be analyzed; Step 2) constructing an m×n dimensional Hankel matrix based on the underwater acoustic signal, performing singular value decomposition on the Hankel matrix to obtain a singular value diagonal matrix; Step 3) obtaining the curvature of each singular value in the singular value diagonal matrix, determining a threshold based on the curvature, and acquiring the singular values ​​within the threshold as valid singular values; Step 4) retaining the valid singular values ​​in the singular value diagonal matrix, setting the other singular values ​​to zero, and updating the singular value diagonal matrix; Step 5) reconstructing the denoised Hankel matrix using the updated singular value diagonal matrix, selecting all elements of the first row of the denoised Hankel matrix and the m-1 elements from the nth column of the second row to the nth column of the mth row for restoration, to obtain the denoised underwater acoustic signal.

Description

Technical Field

[0001] This application relates to the field of signal processing technology, specifically to an adaptive singular value decomposition method for underwater acoustic signal noise reduction and its application. Background Technology

[0002] Underwater acoustic signal denoising is an important technology with wide applications in underwater communication, underwater acoustic sensing, and marine surveying. In underwater environments, due to the conductive properties of water and the complexity of the underwater environment, underwater acoustic signals are often interfered with by various noises, such as current noise, underwater biological sounds, and ship noise. These noises cause significant problems for the transmission, detection, and analysis of underwater acoustic signals. The background of underwater acoustic signal denoising can be traced back to the early 20th century, when researchers began studying underwater acoustic communication technology. Because underwater acoustic signals are easily interfered with by noise during underwater transmission, reducing the impact of noise on underwater acoustic signals has become a key research focus. Early underwater acoustic signal denoising methods mainly relied on filters for noise suppression, but the fixed parameters of these filters could not adapt to different underwater acoustic environments and noise characteristics, resulting in limited denoising effectiveness.

[0003] With the advancement of technology, underwater acoustic signal denoising technology has developed rapidly. Wavelet transform is a commonly used signal denoising method that can convert underwater acoustic and noise signals to the time-frequency domain. By selecting appropriate wavelet basis functions, noise can be eliminated or suppressed to extract clear underwater acoustic signals. The key to wavelet transform lies in the selection of threshold and wavelet basis functions, which leads to the need for empirical parameter setting in wavelet filtering, resulting in poor self-adjustment. In addition, EMD filtering suffers from endpoint effects during decomposition, which distorts the waveforms of some modal components. Furthermore, EMD filtering is often ineffective in signals with complex frequency components. Singular value decomposition (SVD) filtering overcomes the shortcomings of the above methods. The key to SMD denoising lies in the selection of singular values, i.e., selecting points where singular values ​​change abruptly. Methods for selecting singular values ​​include singular value difference spectrum, singular value characteristic mean, singular value median method, and methods that select the peak value with the maximum curvature of the singular value. However, the aforementioned underwater acoustic signal noise reduction methods all share a problem: while achieving good noise reduction results in simulated signals, they fail to consider the strong Gaussian white noise, high-frequency noise, and complex frequency components of underwater acoustic signals. Therefore, the filtering effect is often better in lower frequency segments, but strong Gaussian white noise still exists in the high-frequency range. Summary of the Invention

[0004] The purpose of this application is to provide an adaptive singular value decomposition method for underwater acoustic signal denoising and its application, in order to address the shortcomings of existing underwater acoustic signal denoising methods. While these methods achieve good denoising results in simulated signals, they fail to consider the strong Gaussian white noise, high-frequency noise, and complex frequency components of underwater acoustic signals. Consequently, they often achieve better filtering results in lower frequency segments, but strong Gaussian white noise still exists in the high-frequency range.

[0005] To achieve the above objectives, this application provides an adaptive singular value decomposition method for underwater acoustic signal denoising, comprising the following steps:

[0006] Step 1) Obtain the underwater acoustic signal containing noise to be analyzed;

[0007] Step 2) Based on the underwater acoustic signal, construct an m×n dimensional Hankel matrix, and perform singular value decomposition on the Hankel matrix to obtain a singular value diagonal matrix;

[0008] Step 3) Obtain the curvature of each singular value in the singular value diagonal matrix, determine a threshold based on the curvature, and obtain the singular values ​​within the threshold as valid singular values;

[0009] Step 4) Retain the valid singular values ​​in the singular value diagonal matrix, set the other singular values ​​to zero, and update the singular value diagonal matrix;

[0010] Step 5) Using the updated singular value diagonal matrix, reconstruct the denoised Hankel matrix, select all elements in the first row of the denoised Hankel matrix and m-1 elements from the nth column of the second row to the nth column of the mth row to restore the denoised underwater acoustic signal.

[0011] Optionally, step 2) specifically includes:

[0012] Using the formula: H m×n =U m×m ·D m×n ·V n×n For the Hankel matrix H m×n Perform singular value decomposition to obtain the singular value diagonal matrix D. m×n The Hankel matrix is ​​constructed based on the underwater acoustic signal x, U m×m and V n×n Let represent normalized orthogonal matrices of dimensions m×m and n×n, respectively.

[0013] Optionally, in step 2),

[0014] The Hankel matrix H m×n With the singular value diagonal matrix D m×n The expression is:

[0015]

[0016]

[0017] Among them, σ=[σ1, σ2, σ3,…,σ p ] is a sequence of non-zero singular values, p = min(m, n).

[0018] Optionally,

[0019] In step 2), the criteria for determining the number of rows m and columns n of the Hankel matrix are as follows:

[0020] m and n satisfy N is the number of samples of the underwater acoustic signal, n = N - m + 1, and 1 < n < N. In addition, m ≥ 2 and n ≥ 2.

[0021] Optionally, in step 3),

[0022] The step of determining the threshold based on the curvature specifically includes:

[0023] Obtain the singular values ​​σ1, σ2, ..., σ p The corresponding curvature C i , will [0, max(C i Divide the scale into equal parts and count the number of curvature values ​​Q corresponding to each scale range. j Starting with Q1, we obtain the first Q with only one curvature value. j Make a judgment;

[0024] The criteria for making the judgment are as follows:

[0025] Among them, Q j-1 Q j Q j+1 These are the number of curvature values ​​contained in the (j-1), j, and j+1th scale ranges, respectively.

[0026] If all of the above conditions are met, then select Q. j The lower boundary of the scale range is used as the threshold; otherwise, Q is selected. j The singular value corresponding to the unique curvature value is used as the threshold.

[0027] Optionally, the preset scale is 0.01.

[0028] To achieve the above objectives, this application also provides an underwater acoustic signal noise reduction device with adaptive singular value decomposition, comprising:

[0029] A data acquisition device for acquiring noisy underwater acoustic signals and a server communicating with the data acquisition device, wherein the server is configured to perform the following operations:

[0030] Acquire the underwater acoustic signal containing noise to be analyzed;

[0031] Based on the underwater acoustic signal, an m×n dimensional Hankel matrix is ​​constructed, and singular value decomposition is performed on the Hankel matrix to obtain a singular value diagonal matrix.

[0032] Obtain the curvature of each singular value in the singular value diagonal matrix, determine a threshold based on the curvature, and obtain the singular values ​​within the threshold as valid singular values.

[0033] The valid singular values ​​in the singular value diagonal matrix are retained, the other singular values ​​are set to zero, and the singular value diagonal matrix is ​​updated.

[0034] Using the updated singular value diagonal matrix, the denoised Hankel matrix is ​​reconstructed. All elements in the first row of the denoised Hankel matrix and m-1 elements from the nth column of the second row to the nth column of the mth row are selected for restoration to obtain the denoised underwater acoustic signal.

[0035] Optionally, it also includes a terminal that communicates with the server, and the server is further configured to visualize the noise-reduced underwater acoustic signal through the terminal.

[0036] Optionally, the acquisition device can be any one of the following: an underwater acoustic buoy, an underwater acoustic recorder, and an underwater acoustic sonar.

[0037] To achieve the above objectives, this application also provides a computer storage medium having a computer program stored thereon, wherein the computer program, when executed by a machine, implements the steps of the method described above.

[0038] The embodiments of this application have the following advantages:

[0039] This application provides an adaptive singular value decomposition method for underwater acoustic signal denoising, comprising: step 1) acquiring a noisy underwater acoustic signal to be analyzed; step 2) constructing an m×n dimensional Hankel matrix based on the underwater acoustic signal, performing singular value decomposition on the Hankel matrix to obtain a singular value diagonal matrix; step 3) acquiring the curvature of each singular value in the singular value diagonal matrix, determining a threshold based on the curvature, and acquiring singular values ​​within the threshold as valid singular values; step 4) retaining the valid singular values ​​in the singular value diagonal matrix, setting other singular values ​​to zero, and updating the singular value diagonal matrix; step 5) reconstructing a denoised Hankel matrix using the updated singular value diagonal matrix, selecting all elements of the first row of the denoised Hankel matrix and the m-1 elements from the nth column of the second row to the nth column of the mth row for restoration, to obtain the denoised underwater acoustic signal.

[0040] By employing the above method and adopting an adaptive threshold selection criterion, the boundary between effective and noise signals can be accurately determined. This method has strong universality and adaptability. Compared with other methods, this application is more stable and effective in noise reduction. It solves the problem that many existing underwater acoustic signal noise reduction methods have good noise reduction effects on simulated signals, but do not take into account the strong Gaussian white noise, high-frequency noise, and complex frequency components of underwater acoustic signals. Therefore, the filtering effect is often better in the lower frequency segments, but strong Gaussian white noise still exists in the high-frequency part. Attached Figure Description

[0041] To more clearly illustrate the embodiments of this application or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary, and those skilled in the art can derive other embodiments based on the provided drawings without creative effort.

[0042] Figure 1 A flowchart of an adaptive singular value decomposition underwater acoustic signal denoising method provided in this application embodiment:

[0043] Figure 2 A logic block diagram of an adaptive singular value decomposition underwater acoustic signal denoising method provided in this application embodiment is as follows:

[0044] Figure 3 The spectrum diagrams of the simulated signal before and after denoising by the method of this application are shown, wherein (a) is the spectrum diagram of the noisy signal and (b) is the spectrum diagram of the signal after denoising by the method of this application.

[0045] Figure 4(a) is the spectrum of the original engineering signal after processing; (b) is the spectrum of the signal after wavelet transform denoising; (c) is the spectrum of the signal after EMD decomposition denoising; (d) is the spectrum of the signal after singular value curvature maximum peak filtering; (e) is the spectrum of the signal after singular value median filtering; and (f) is the spectrum of the signal processed by the method of this application. Detailed Implementation

[0046] The following specific embodiments illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0047] Furthermore, the technical features involved in the different embodiments of this application described below can be combined with each other as long as they do not conflict with each other.

[0048] One embodiment of this application provides an adaptive singular value decomposition method for underwater acoustic signal noise reduction, referencing... Figure 1 and Figure 2 , Figure 1 This is a flowchart illustrating an adaptive singular value decomposition method for underwater acoustic signal denoising, provided in one embodiment of this application. Figure 2 The diagram below illustrates a logic block diagram of an adaptive singular value decomposition method for underwater acoustic signal denoising, as provided in an embodiment of this application. It should be understood that the method may also include additional boxes not shown and / or the boxes shown may be omitted, and the scope of this application is not limited in this respect.

[0049] In step 1), the underwater acoustic signal containing noise to be analyzed is acquired.

[0050] Specifically, the noisy underwater acoustic signal to be analyzed is denoted as x.

[0051] In step 2), based on the underwater acoustic signal, an m×n-dimensional Hankel matrix is ​​constructed, and singular value decomposition is performed on the Hankel matrix to obtain a singular value diagonal matrix.

[0052] Specifically, an m×n dimensional Hankel matrix is ​​constructed according to the criterion of maximizing the product of the number of rows and columns, and singular value decomposition is performed: H m×n =U m×m ·D m×n ·V n×n The singular value diagonal matrix D is obtained. m×n U m×m and V n×nLet H represent the normalized orthogonal matrices of dimensions m×m and n×n, respectively; additionally, H m×n and D m×n The expression is:

[0053]

[0054]

[0055] In some embodiments, the criteria for determining the optimal number of rows m and columns n of the Hankel matrix are: N is the number of samples of the underwater acoustic signal, and m and n satisfy... n = N - m + 1, and 1 < n < N, and m ≥ 2, n ≥ 2.

[0056] In step 3), the curvature of each singular value in the singular value diagonal matrix is ​​obtained, a threshold is determined based on the curvature, and singular values ​​within the threshold are obtained as valid singular values.

[0057] Specifically, in the singular value diagonal matrix D m×n The non-zero singular value sequence σ = [σ1, σ2, σ3, ..., σ] that can be obtained is σ = [σ1, σ2, σ3, ... ...4]. p p = min(m, n), calculate the curvature of each singular value, obtain the threshold according to the curvature judgment criterion, and obtain the order i of the effective singular value.

[0058] In some embodiments, the optimal method for selecting the threshold includes the following steps:

[0059] Obtain the singular values ​​σ1, σ2, ..., σ p The corresponding curvature C i , will [0, max(C i Divide the scale into preset increments (e.g., 0.01) and count the number Q of curvature values ​​corresponding to each increment. j Starting with Q1, we obtain the first Q with only one curvature value. j Make a judgment;

[0060] The judgment criteria are:

[0061]

[0062] If all of the above conditions are met, then select Q. j The lower boundary of the scale range is used as the threshold; otherwise, Q is selected. j The singular value corresponding to the unique curvature value is used as the threshold;

[0063] In the above formula, Q j-1 Q j Q j+1 These are the number of curvature values ​​contained in the (j-1), j, and j+1th scale ranges, respectively.

[0064] At step 4), the valid singular values ​​in the singular value diagonal matrix are retained, the other singular values ​​are set to zero, and the singular value diagonal matrix is ​​updated.

[0065] Specifically, valid singular values ​​are retained, and all other singular values ​​are set to zero: σ k =0, where k = i+1, i+2, ..., p, i is the order of the singular value, and a new diagonal matrix D′ is obtained.

[0066] In step 5), the noise-reduced Hankel matrix is ​​reconstructed using the updated singular value diagonal matrix. All elements in the first row of the noise-reduced Hankel matrix and m-1 elements from the nth column of the second row to the nth column of the mth row are selected for restoration to obtain the noise-reduced underwater acoustic signal.

[0067] Specifically, the Hankel matrix is ​​reconstructed using the new diagonal matrix D′ to obtain the denoised Hankel matrix H′=U. m×m ·D′·V n×n Based on the reconstructed denoised Hankel matrix H′, the denoised underwater acoustic signal is obtained.

[0068] See Figure 3 This embodiment uses a specific example for simulation verification:

[0069] 1. Determine the analog signal construction matrix

[0070] Taking signal x1 as an example, a signal denoising simulation experiment based on singular value decomposition is carried out. The expression of x1 is: x1=(sin(20πt)) 2 +0.5(sin(80πt)) 3 The number of samples is 1000, and zero-mean Gaussian white noise with a standard deviation of 1 is added to x1 to obtain the signal x. The Hankel matrix constructed according to the maximum product criterion of rows and columns has m=500 rows and n=501 columns.

[0071] 2. Determine the selected threshold.

[0072] Singular value decomposition is performed on the Hankel matrix, and the curvature of each singular value is calculated. According to the judgment criterion, the singular value i=5 corresponding to the unique curvature value is selected as the threshold, so only the first 5 singular values ​​are selected.

[0073] 3. Reconstruct the Hankel matrix and restore the signal.

[0074] Retain valid singular values ​​and set all other singular values ​​to zero: σ k =0, where k = i+1, i+2, ... p, to obtain a new diagonal matrix D′, and then reconstruct the Hankel matrix H′ = U. m×m ·D′·Vn×n We select all elements in the first row of H′ and m-1 elements from the nth column of the second row to the nth column of the mth row to restore the signal after noise reduction, which is the signal x′ after noise reduction.

[0075] Figure 3 The simulation results are shown, with (a) representing the signal x and (b) representing the denoised signal x′. It can be seen that this application has a good denoising effect. From... Figure 4 As can be seen, by comparing the common methods for selecting the singular value separation order, the noise reduction effect of this application is significantly better than other methods, and it clearly describes the dividing line between Gaussian white noise and useful signal. Moreover, compared with other methods, it does not affect the actual noise reduction effect due to the abrupt change of singular values, highlighting its advantages in underwater acoustic signal noise reduction.

[0076] This application also provides an adaptive singular value decomposition underwater acoustic signal noise reduction device. The device includes:

[0077] A data acquisition device for acquiring noisy underwater acoustic signals and a server communicating with the data acquisition device, wherein the server is configured to perform the following operations:

[0078] Acquire the underwater acoustic signal containing noise to be analyzed;

[0079] Based on the underwater acoustic signal, an m×n dimensional Hankel matrix is ​​constructed, and singular value decomposition is performed on the Hankel matrix to obtain a singular value diagonal matrix.

[0080] Obtain the curvature of each singular value in the singular value diagonal matrix, determine a threshold based on the curvature, and obtain the singular values ​​within the threshold as valid singular values.

[0081] The valid singular values ​​in the singular value diagonal matrix are retained, the other singular values ​​are set to zero, and the singular value diagonal matrix is ​​updated.

[0082] Using the updated singular value diagonal matrix, the denoised Hankel matrix is ​​reconstructed. All elements in the first row of the denoised Hankel matrix and m-1 elements from the nth column of the second row to the nth column of the mth row are selected for restoration to obtain the denoised underwater acoustic signal.

[0083] In some embodiments, the system further includes a terminal that communicates with the server, and the server is further configured to visualize the noise-reduced underwater acoustic signal via the terminal.

[0084] In some embodiments, the device for acquiring underwater acoustic signals containing noise may include: (1) a hydrophone: a hydrophone is a sensor device (essentially a sensor) used to receive underwater acoustic signals, which typically operates by floating underwater. It can measure acoustic vibrations in the water and convert them into electrical signals for processing and analysis.

[0085] (2) Underwater Acoustic Recorder: An underwater acoustic recorder is a device specifically designed for long-term or short-term recording of underwater sounds. It typically features a large-capacity memory and a highly sensitive underwater acoustic sensor, which can be used to capture and store sounds in the underwater environment.

[0086] (3) Sonar: Sonar is an active device for detecting underwater targets. It emits sound pulses and receives echo signals. Sonar is widely used in marine surveying, underwater navigation, fish detection, and other fields.

[0087] For specific implementation methods, please refer to the aforementioned method embodiments, which will not be repeated here.

[0088] This application may be a method, apparatus, system, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for performing various aspects of this application.

[0089] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example, but not limited to, electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0090] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0091] The computer program instructions used to perform the operations of this application may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuits, such as programmable logic circuits, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), are personalized by utilizing the status information of the computer-readable program instructions. These electronic circuits can execute the computer-readable program instructions to implement various aspects of this application.

[0092] Various aspects of this application are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0093] These computer-readable program instructions can be provided to a processing unit of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processing unit of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner. Thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0094] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions that execute on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0095] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those marked in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0096] Note that, unless otherwise explicitly stated, all features disclosed in this specification (including any appended claims, abstract, and drawings) may be replaced by alternative features for achieving the same, equivalent, or similar purpose. Therefore, unless explicitly stated otherwise, each disclosed feature is merely one example of a set of equivalent or similar features. Where used, "further," "preferably," "even further," and "more preferably" are simple starting points for describing another embodiment based on the foregoing embodiments, the combination of which with the foregoing embodiments constitutes the complete configuration of another embodiment. Any combination of several "further," "preferably," "even further," or "more preferably" settings following the same embodiment constitutes yet another embodiment.

[0097] Although this application has been described in detail above with general descriptions and specific embodiments, some modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of this application fall within the scope of protection claimed in this application.

Claims

1. A method for denoising underwater acoustic signals using adaptive singular value decomposition, characterized in that, Includes the following steps: Step 1) Obtain the underwater acoustic signal containing noise to be analyzed; Step 2) Construct based on the underwater acoustic signal A Hankel matrix of dimension 1 is obtained by performing singular value decomposition on the Hankel matrix to obtain a singular value diagonal matrix. Step 3) Obtain the curvature of each singular value in the singular value diagonal matrix, determine a threshold based on the curvature, and obtain the singular values ​​within the threshold as valid singular values; The step of determining the threshold based on the curvature specifically includes: Obtain each singular value , … Corresponding curvature ,Will Divide the scale into equal parts and count the number of curvature values ​​corresponding to each scale range. ,from Initially, we obtain the first value containing only one curvature value. Make a judgment; The criteria for making the judgment are as follows: ,in, , , They are the first , , The number of curvature values ​​contained within a scale range If all of the above conditions are met, then select... The lower boundary of the scale range is used as the threshold; otherwise, select... The singular value corresponding to the unique curvature value is used as the threshold. Step 4) Retain the valid singular values ​​in the singular value diagonal matrix, set the other singular values ​​to zero, and update the singular value diagonal matrix; Step 5) Using the updated singular value diagonal matrix, reconstruct the denoised Hankel matrix, select all elements in the first row of the denoised Hankel matrix and m-1 elements from the nth column of the second row to the nth column of the mth row to restore the denoised underwater acoustic signal.

2. The underwater acoustic signal noise reduction method based on adaptive singular value decomposition according to claim 1, characterized in that, Step 2) specifically includes: Using the formula: For the Hankel matrix Perform singular value decomposition to obtain the singular value diagonal matrix. The Hankel matrix is ​​based on the underwater acoustic signal. structure, and They represent and A normalized orthogonal matrix of dimension 1.

3. The underwater acoustic signal noise reduction method based on adaptive singular value decomposition according to claim 2, characterized in that, In step 2), The Hankel matrix With the singular value diagonal matrix The expression is: ， ， in, It is a sequence of non-zero singular values. .

4. The underwater acoustic signal noise reduction method based on adaptive singular value decomposition according to claim 2, characterized in that, In step 2), the criteria for determining the number of rows m and columns n of the Hankel matrix are as follows: m and n satisfy N is the number of samples of the underwater acoustic signal. ,and ,in addition , .

5. The underwater acoustic signal noise reduction method based on adaptive singular value decomposition according to claim 1, characterized in that, In step 3), The preset scale is 0.

01.

6. A noise reduction device for underwater acoustic signals with adaptive singular value decomposition, characterized in that, include: A data acquisition device for acquiring noisy underwater acoustic signals and a server communicating with the data acquisition device, wherein the server is configured to perform the following operations: Acquire the underwater acoustic signal containing noise to be analyzed; Based on the aforementioned underwater acoustic signal, construct A Hankel matrix of dimension 1 is obtained by performing singular value decomposition on the Hankel matrix to obtain a singular value diagonal matrix. Obtain the curvature of each singular value in the singular value diagonal matrix, determine a threshold based on the curvature, and obtain the singular values ​​within the threshold as valid singular values. The step of determining the threshold based on the curvature specifically includes: Obtain each singular value , … Corresponding curvature ,Will Divide the scale into equal parts and count the number of curvature values ​​corresponding to each scale range. ,from Initially, we obtain the first value containing only one curvature value. Make a judgment. The criteria for making the judgment are as follows: ,in, , , They are the first , , The number of curvature values ​​contained within a scale range If all of the above conditions are met, then select... The lower boundary of the scale range is used as the threshold; otherwise, select... The singular value corresponding to the unique curvature value is used as the threshold. The valid singular values ​​in the singular value diagonal matrix are retained, the other singular values ​​are set to zero, and the singular value diagonal matrix is ​​updated. Using the updated singular value diagonal matrix, the denoised Hankel matrix is ​​reconstructed. All elements in the first row of the denoised Hankel matrix and m-1 elements from the nth column of the second row to the nth column of the mth row are selected for restoration to obtain the denoised underwater acoustic signal.

7. The underwater acoustic signal noise reduction device with adaptive singular value decomposition according to claim 6, characterized in that, Also includes: A terminal that communicates with the server, and the server is also configured to visualize the noise-reduced underwater acoustic signal through the terminal.

8. The underwater acoustic signal noise reduction device with adaptive singular value decomposition according to claim 6, characterized in that, The acquisition device can be any one of the following: an underwater acoustic buoy, an underwater acoustic recorder, or an underwater acoustic sonar.

9. A computer storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a machine, it implements the steps of the method as described in any one of claims 1 to 5.

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