Self-adaptive variational mode noise reduction method and system based on bit plane decomposition

Abstract

The invention discloses an adaptive variational mode noise reduction method and system based on bit plane decomposition, and belongs to the field of signal processing. According to the technology, binary conversion is carried out on a time domain signal through an innovative bit plane decomposition method, the signal is decomposed into time domain components under different bit resolutions, and the optimal decomposition parameter of VMD is adaptively determined based on component characteristics. The method comprises the following steps: firstly, carrying out bit plane decomposition on a noisy signal to obtain time domain components of different bits; calculating an autocorrelation test value of each component, and distinguishing a signal component and a noise component; dynamically calculating the modal number and penalty factor of the VMD according to the number of signal components and the energy entropy; and finally, performing VMD decomposition and reconstructing a noise reduction signal. Transient features are reserved through bit plane decomposition, and the feature retention rate is remarkably improved; vMD parameters are directly calculated, iterative optimization is avoided, and the processing speed is greatly increased; hardware resource occupation is greatly reduced, and power consumption is greatly reduced; and in a strong noise environment, the accuracy is greatly improved.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and specifically to an adaptive variational mode denoising method and system based on bit-plane decomposition. Background Technology

[0002] Compared with traditional noise reduction techniques, Variational Mode Decomposition (VMD) offers advantages such as adaptive decomposition and mode aliasing control, making it a promising technology for dynamic real-time systems and high-dimensional data processing. Specifically, VMD transforms signal decomposition into a constrained variational optimization problem, thereby achieving adaptive frequency band division and ensuring the decomposition results have clear physical meaning, facilitating signal noise reduction.

[0003] In the variational optimization problem of VMD, two parameters need to be determined: the number of decomposition modes and the penalty factor. Currently, improved methods for VMD have been proposed to automatically determine these parameters. The calculation scheme for these parameters mainly involves iteratively running and comparing the results of the VMD method under different parameters to determine the optimal parameters.

[0004] However, this method of determining parameters solely based on frequency domain decomposition mode information easily overlooks the capture of transient features and abrupt changes. This transient information is crucial in detection equipment, such as identifying bearing failures, recognizing human fall postures, and identifying sudden drops in blood pressure based on PPG signals. Furthermore, iterative use of the VMD method significantly impacts the real-time noise reduction speed, hindering its practical application in hardware.

[0005] Existing technologies determine the two parameters, the number of decomposition modes and the penalty factor, by calculating the VMD decomposition results under multiple different parameter combinations and calculating corresponding evaluation indicators, such as the characteristics of the decomposition modes and their application effects, to determine the optimal parameter combination.

[0006] Because frequency domain analysis is prone to noise interference or frequency aliasing, and is insensitive to non-stationary features such as impulse signals and step changes, this method of calculating VMD decomposition parameters based on frequency domain decomposition results cannot ensure that the final decomposition results can contain transient change information.

[0007] Due to the high computational complexity of VMD, this iterative approach significantly increases the overall signal processing time, failing to meet real-time noise reduction requirements. Furthermore, solving the variational problem through multiple iterations presents a significant computational challenge for hardware implementation, hindering the practical application of noise reduction algorithms in hardware.

[0008] Therefore, it is necessary to design an adaptive variational mode denoising method and system based on bit-plane decomposition to solve the above problems. Summary of the Invention

[0009] The present invention aims to provide an adaptive variational mode denoising method and system based on bit-plane decomposition to solve at least one technical problem existing in the prior art.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] An adaptive variational mode denoising method and system based on bit-plane decomposition includes the following steps:

[0012] S1: Perform bit-plane decomposition on the noisy original signal, convert the signal into binary representation, and generate multiple time-domain components, where the high-bit components correspond to the low-frequency energy distribution and the low-bit components correspond to the high-frequency energy distribution.

[0013] S2: Based on the energy randomness and energy concentration of the bit plane components, adaptively determine the number of decomposition modes K and the penalty factor α of the variational mode decomposition;

[0014] S3: Using the determined parameters K and α, the original signal is decomposed using VMD to obtain multiple intrinsic mode functions;

[0015] S4: Select the K′ with the highest energy. signal The eigenmode function components are reconstructed to obtain the denoised signal.

[0016] Preferably, the specific steps of the mid-plane decomposition in S1 include:

[0017] Each sample value of the signal sequence is converted into binary form to generate bit-plane coefficients composed of weight vectors; the low-frequency and high-frequency components of the signal are separated by the distribution of high- and low-frequency components.

[0018] Preferably, the energy randomness in S2 is calculated as follows:

[0019] Calculate the autocorrelation test value p for the weight vector of each bit plane component. j If p j If the value is ∈[-0.5,0.5], it is determined to be a noise component; otherwise, it is a signal component.

[0020] Preferably, the energy concentration of the main signal component in S2 is calculated as follows: the energy entropy H of the highest 3-bit component is calculated. The lower the entropy value, the more concentrated the energy; the higher the entropy value, the more dispersed the energy distribution.

[0021] Preferably, the variational optimization problem of VMD decomposition in S3 is defined as:

[0022] Minimize the sum of bandwidths of all modes, with the constraint that the sum of bandwidths of all modes equals the original signal; solve iteratively using the augmented Lagrangian function and the alternating direction multiplier method until the convergence condition is met.

[0023] Preferably, the signal reconstruction method in S4 is as follows: selecting the K′ with the highest energy. signal The intrinsic mode function components are directly superimposed, and the remaining components are discarded to suppress noise.

[0024] An adaptive variational mode denoising system based on bit-plane decomposition includes: a bit-plane decomposition module, a parameter calculation module, a VMD decomposition module, and a signal reconstruction module; the bit-plane decomposition module is used to convert the input signal into binary bit-plane components; the parameter calculation module is used to calculate the optimal parameters K and α of VMD based on the characteristics of the bit-plane components; the VMD decomposition module is used to perform variational mode decomposition and output intrinsic mode function components; the signal reconstruction module is used to filter and reconstruct the denoised signal.

[0025] Preferably, the parameter calculation module further includes an autocorrelation test unit, an energy entropy calculation unit, and a penalty factor adjustment unit. The autocorrelation test unit is used to distinguish between signal and noise components; the energy entropy calculation unit is used to assess the degree of signal energy concentration; and the penalty factor adjustment unit dynamically adjusts α according to the noise jump frequency.

[0026] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method of adaptive variational mode denoising based on bit-plane decomposition.

[0027] An electronic device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the program to implement the method of adaptive variational mode denoising based on bit-plane decomposition.

[0028] Compared with existing technologies, the adaptive variational mode denoising method and system based on bit-plane decomposition provided by this invention has the following beneficial effects:

[0029] 1. Overcoming the limitations of traditional frequency domain analysis methods in their insensitivity to transient features, this method accurately captures non-stationary features such as impact signals and step changes from a time domain perspective through bit-plane decomposition. It is particularly suitable for applications requiring the preservation of abrupt change information, such as: mechanical fault diagnosis (impact feature preservation), medical signal processing (sudden drop in blood pressure detection), and human behavior recognition (fall posture determination).

[0030] 2. Innovatively, key VMD parameters are directly determined through bit-plane decomposition: the signal and noise components are automatically distinguished based on the autocorrelation test value, the number of decomposed modes is dynamically adjusted by combining energy entropy, and the penalty factor is adaptively calculated based on the noise intensity.

[0031] 3. This invention significantly improves real-time processing performance, determining optimal parameters in a single calculation, resulting in a substantial increase in processing speed. Compared to traditional optimization algorithms, computational efficiency is significantly improved.

[0032] 4. Noise separation is achieved during the bit-plane decomposition stage, which has strong anti-interference ability. Bit-plane decomposition only requires shift registers and adders, which consumes few resources. It supports flexible balance between accuracy and efficiency by adjusting the bit-plane analysis depth. Attached Figure Description

[0033] Figure 1 This is a flowchart of an adaptive variational mode denoising method based on bit-plane decomposition according to the present invention;

[0034] Figure 2 This invention simulates clean signals and noisy signals with transient characteristics;

[0035] Figure 3 The waveforms of the noise-reduced signal and the clean signal are shown in this invention. Detailed Implementation

[0036] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0037] In the description of this invention, it should be understood that the terms "upper", "lower", "front", "rear", "left", "right", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0038] First, let's explain the technical terms used in this application:

[0039] VMD: Variational Mode Decomposition.

[0040] Please see the appendix Figure 1 As shown, this embodiment provides an adaptive variational mode denoising method based on bit-plane decomposition, including the following steps:

[0041] S1: Perform bit-plane decomposition on the noisy original signal, convert the signal into binary representation, and generate multiple time-domain components, where the high-bit components correspond to the low-frequency energy distribution and the low-bit components correspond to the high-frequency energy distribution.

[0042] S2: Based on the energy randomness and energy concentration of the bit plane components, adaptively determine the number of decomposition modes K and the penalty factor α of the variational mode decomposition;

[0043] S3: Using the determined parameters K and α, the original signal is decomposed using VMD to obtain multiple intrinsic mode functions;

[0044] S4: Select the K′ with the highest energy. signal The eigenmode function components are reconstructed to obtain the denoised signal.

[0045] The specific steps of the sub-plane decomposition in step S1 include:

[0046] Each sample value of the signal sequence is converted into binary form to generate bit-plane coefficients composed of weight vectors; the low-frequency and high-frequency components of the signal are separated by the distribution of high- and low-frequency components.

[0047] In this embodiment, the noisy original signal is decomposed into bit-plane components: the signal is decomposed into multiple time-domain components.

[0048] Let a noisy original signal sequence of length N be x = [x1 … x2]. N ] T Perform a binary conversion on each value, that is... For the entire x, it can be decomposed into x = 2. 0 ·a0+…+2 K ·a K , where a j =[a 1j … a Nj ] T j = 0, ..., K, representing the weight vector, 2 j (j=0,…,K) represents the bit plane coefficients. See the figure below.

[0049]

[0050] Therefore, x can be represented by a plane composed of weights at each bit resolution, i.e., a bit plane. The weights closer to the top of the plane represent the energy distribution of the signal at higher bit amplitudes; the weights closer to the bottom of the plane represent the energy distribution of the signal at lower bit amplitudes. The higher bit components account for the majority of the signal's energy and can be understood as low-frequency components, while the lower bit components account for a smaller portion of the signal's energy and can be understood as high-frequency components.

[0051] Bit-plane decomposition can decompose the original time-domain signal into time-domain components at different bit resolutions, and can roughly decompose the high-frequency and low-frequency parts.

[0052] The energy randomness in S2 is calculated as follows: For each bit-plane component, an autocorrelation test value p is calculated using its weight vector. j If p j If the value is ∈ [-0.5, 0.5], it is determined to be a noise component; otherwise, it is a signal component. The calculation method for the energy concentration of the main signal component in step S2 is as follows: calculate the energy entropy H of the highest 3-bit component. The lower the entropy value, the more concentrated the energy; the higher the entropy value, the more dispersed the energy distribution.

[0053] In this embodiment, the energy randomness of each component is calculated. Through bit-plane decomposition, the weight vector under different bit-plane coefficients is composed of 0 or 1, where the position of 1 reflects the energy randomness of the corresponding amplitude level. Here, the autocorrelation test value p of the weight vector aj is calculated. j As a criterion for sparsity, p j ∈[-1,1]. When p j The closer a value is to 0, the more the sequence leans towards a random sequence, meaning the energy of that component has a higher degree of randomness. For a delay d, a certain weight vector a... j autocorrelation test value in This represents the weight vector a j The average value.

[0054] Calculate the number of signal components. First, determine whether each component is a signal component or a noise component based on the randomness of its energy. Set thresholds of -0.5 and 0.5. When the p-value of the component's autocorrelation test value... j If the value is within the range [-0.5, 0.5], then the component is considered a noise component; otherwise, it is considered a signal component. Let num be the number of signal components and the number of noise components, respectively. signal With num noise .

[0055] Calculate the concentration of the main signal energy. The main signal energy is concentrated in the highest 3 bits, which typically account for over 90% of the signal energy. Calculate the energy entropy represented by the weight vector of the highest 3 bits. When H high The closer H is to 0, the higher the concentration of the main energy of the signal, and the closer the signal is to a single principal component type. high The closer the value is to log23, the lower the energy concentration, indicating a tendency for uniform dispersion, and the closer the signal is to a multi-principal component type.

[0056] Adaptive calculation of the number of VMD decomposition modes K′. Since the number of frequency domain decomposition modes needs to be determined using time domain information, therefore num... signal It can only serve as a rough estimate of the number of signal modes in the frequency domain. It is also necessary to combine the degree of energy concentration of the main signal to estimate the number of signal modes in the frequency domain.

[0057] In this invention, K′ signal =round(num signal ·H high ), soon num signal ·H high The value is rounded. The number of noise modes is related to num. noise Consistency, i.e., K′ noise =num noise Therefore, K′=K′ signal +K′ noise .

[0058] Adaptively calculate the VMD decomposition penalty factor α. Calculate the frequency of 1 occurrences in all noise components; a higher frequency indicates more frequent 0 / 1 transitions, stronger noise, and a larger α is needed to suppress noise propagation. The frequency value freq is calculated as follows: Where num bit1 This represents the number of occurrences of 1. Set the base penalty factor α. base This is five times the signal sampling frequency. In this invention, α is set to freq·α. base .

[0059] The variational optimization problem of VMD decomposition in S3 is defined as follows: minimize the sum of the bandwidths of each mode, with the constraint that the sum of the bandwidths of each mode is equal to the original signal; it is solved iteratively by augmented Lagrangian function and alternating direction multiplier method until the convergence condition is met.

[0060] In this embodiment, the signal is automatically decomposed into multiple intrinsic mode functions using a variational optimization framework.

[0061] Parameter settings. Based on the above results, set the key decomposition parameters: number of modes K′ and penalty factor α. Convergence tolerance tol = 10. -6 The center frequencies of each mode {w} k Both} and the Lagrange multiplier λ are initialized to 0.

[0062] Construct a variational model. By minimizing the sum of the bandwidths of all modes and ensuring that the sum of the bandwidths of all modes equals the original signal, the following variational problem can be constructed. Where u k (t) represents the intrinsic mode function. δ(t) represents the derivative with respect to time t, δ(t) represents the unit impulse function, * represents the convolution calculation, and ||·||2 represents the L2 norm.

[0063] By introducing α and λ to construct an augmented Lagrangian function, the constrained optimization problem described above is transformed into the following unconstrained problem. in, and u k Fourier transforms of (t) and x(w), ∈ 2 These are slack variables, and you can decide whether or not to use them.

[0064] Iteratively update each mode, center frequency, and Lagrange multiplier, repeating until convergence. The update order and formula for each variable are as follows: update the k-th mode. Update center frequency Update Lagrange multipliers Where τ is the update step size, which can be set according to requirements. When the iteration satisfies... Then stop iterating.

[0065] Output the intrinsic mode functions. After terminating the iteration, K′ intrinsic mode functions will be obtained, i.e., the signal components {u1(t), u2(t), ..., u...}. K′ (t)}.

[0066] The signal reconstruction method in S4 is as follows: select the K′ with the highest energy. signal The intrinsic mode function components are directly superimposed, and the remaining components are discarded to suppress noise.

[0067] In this embodiment, the denoised signal is calculated by selecting components based on energy calculation and reconstructing them into a denoised signal.

[0068] We need to filter out K′ signal Each signal component. Calculate the energy of each mode. Choose the first K′ signal The component with the highest energy is taken as the signal component, and the summation is used to obtain the noise-reduced signal.

[0069] An adaptive variational mode denoising system based on bit-plane decomposition includes: a bit-plane decomposition module, a parameter calculation module, a VMD decomposition module, and a signal reconstruction module; the bit-plane decomposition module is used to convert the input signal into binary bit-plane components; the parameter calculation module is used to calculate the optimal parameters K and α of VMD based on the characteristics of the bit-plane components; the VMD decomposition module is used to perform variational mode decomposition and output intrinsic mode function components; the signal reconstruction module is used to filter and reconstruct the denoised signal.

[0070] The parameter calculation module further includes an autocorrelation test unit, an energy entropy calculation unit, and a penalty factor adjustment unit. The autocorrelation test unit is used to distinguish between signal and noise components; the energy entropy calculation unit is used to assess the degree of signal energy concentration; and the penalty factor adjustment unit dynamically adjusts α according to the noise jump frequency.

[0071] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the method of adaptive variational mode denoising based on bit-plane decomposition.

[0072] An electronic device includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the program to implement the method of adaptive variational mode denoising based on bit-plane decomposition.

[0073] like Figure 2-3 As shown in the experiment, the present invention can capture prominent transient features and retain them in the denoised signal, and the peak appears at the same time as the original signal.

[0074] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. An adaptive variational mode denoising method based on bit-plane decomposition, characterized in that, Includes the following steps: S1: Perform bit-plane decomposition on the noisy original signal, convert the signal into binary representation, and generate multiple time-domain components, where the high-bit components correspond to the low-frequency energy distribution and the low-bit components correspond to the high-frequency energy distribution. S2: Based on the energy randomness and energy concentration of the bit plane components, the number of decomposition modes K and the penalty factor α of the variational mode decomposition are adaptively determined; S3: Using the determined parameters K and α, the original signal is decomposed using VMD to obtain multiple intrinsic mode functions; S4: Select the K′ with the highest energy. signal The eigenmode function components are reconstructed to obtain the denoised signal.

2. The adaptive variational mode denoising method based on bit-plane decomposition according to claim 1, characterized in that... The specific steps of the mid-plane decomposition in S1 include: Each sample value of the signal sequence is converted into binary form to generate bit-plane coefficients composed of weight vectors; the low-frequency and high-frequency components of the signal are separated by the distribution of high- and low-frequency components.

3. The adaptive variational mode denoising method based on bit-plane decomposition according to claim 1, characterized in that, The method for calculating the energy randomness in S2 is as follows: Calculate the autocorrelation test value p for the weight vector of each bit plane component. j If p j If the value is ∈[-0.5,0.5], it is determined to be a noise component; otherwise, it is a signal component.

4. The adaptive variational mode denoising method based on bit-plane decomposition according to claim 1, characterized in that... The calculation method for the energy concentration of the main signal in S2 is as follows: calculate the energy entropy H of the highest 3-bit components. The lower the entropy value, the more concentrated the energy; the higher the entropy value, the more dispersed the energy distribution.

5. The adaptive variational mode denoising method based on bit-plane decomposition according to claim 1, characterized in that... The variational optimization problem of VMD decomposition in S3 is defined as follows: Minimize the sum of bandwidths of all modes, with the constraint that the sum of bandwidths of all modes equals the original signal; solve iteratively using the augmented Lagrangian function and the alternating direction multiplier method until the convergence condition is met.

6. The adaptive variational mode denoising method based on bit-plane decomposition according to claim 1, characterized in that, The signal reconstruction method in S4 is as follows: select the K′ with the highest energy. signal The intrinsic mode function components are directly superimposed, and the remaining components are discarded to suppress noise.

7. An adaptive variational mode denoising system based on bit-plane decomposition, characterized in that... It includes: a bit-plane decomposition module, a parameter calculation module, a VMD decomposition module, and a signal reconstruction module; the bit-plane decomposition module is used to convert the input signal into binary bit-plane components; the parameter calculation module is used to calculate the optimal parameters K and α of VMD based on the characteristics of the bit-plane components; the VMD decomposition module is used to perform variational mode decomposition and output intrinsic mode function components; the signal reconstruction module is used to filter and reconstruct the denoised signal.

8. The adaptive variational mode denoising system based on bit-plane decomposition according to claim 7, characterized in that: The parameter calculation module further includes an autocorrelation test unit, an energy entropy calculation unit, and a penalty factor adjustment unit. The autocorrelation test unit is used to distinguish between signal and noise components; the energy entropy calculation unit is used to assess the degree of signal energy concentration. The penalty factor adjustment unit dynamically adjusts α according to the noise jump frequency.

9. A computer-readable storage medium storing a computer program, characterized in that, When the program is executed by the processor, it implements the method described in any one of claims 1-6.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory, characterized in that, When the processor executes the program, it implements the method according to any one of claims 1-9.

Images