Weak signal enhancement algorithm based on non-convex regularization

Abstract

The present application provides a kind of weak life signal enhancement algorithm based on non-convex regularization, by minimizing approximate decomposition error time-frequency signal decomposition, solve the required high signal-to-noise ratio of life signal in which sparse component, improve the output signal-to-noise ratio of life signal.The present application is fast in operation, provides the possibility for real-time extraction of weak life signal under low signal-to-noise ratio condition.

Description

Technical Field

[0001] This invention belongs to the field of through-wall human life signal detection, specifically involving a weak life signal enhancement algorithm based on non-convex regularization. Background Technology

[0002] In earthquake rescue (or through-wall) life detection, the amplitude of chest vibrations caused by human respiration is relatively weak, and penetrating walls also significantly attenuates the signal, resulting in a low signal-to-noise ratio (SNR) for human life echo signals. Furthermore, ambient noise and radar instability also reduce the output SNR of life signals. Traditional life signal extraction algorithms use Fast Fourier Transform (FFT), but this method struggles to eliminate the influence of ambient noise. Some researchers have developed a processing method for respiration detection under low SNR conditions. The main step is to extract the respiration signal from the noisy time-frequency signal using Singular Value Decomposition (SVD). SVD assumes that the respiration signal is concentrated in large singular values, but some noise remains in these singular values, resulting in noise in the same frequency band as the respiration signal still being present. In addition, some researchers have proposed a weak life signal enhancement algorithm based on Robust Principal Component Analysis (RPCA). High signal-to-noise ratio (SNR) vital signals can be obtained by solving the low-rank components of time-frequency signals using RPCA. However, the denoising effect is poor at low SNR and the computation time is long. Therefore, it is necessary to develop a method for real-time extraction of human vital signals under low SNR conditions. Summary of the Invention

[0003] In view of the above-mentioned technical problems, this invention proposes a weak life signal enhancement algorithm based on non-convex regularization. It decomposes the time-frequency signal by minimizing the approximate decomposition error, solves the sparse components to obtain the required high signal-to-noise ratio life signal, improves the output signal-to-noise ratio of the life signal, and has a fast operation speed, which provides the possibility for real-time extraction of weak life signals under low signal-to-noise ratio conditions.

[0004] To achieve the above objectives, the present invention adopts the following technical solution:

[0005] A weak life signal enhancement algorithm based on non-convex regularization includes the following steps:

[0006] Step S1: Use a single-transmitter, single-receiver ultra-wideband radar to collect life signals, wherein the life signals are time-domain echo signals;

[0007] Step S2: Preprocess the time-domain echo signal to remove fixed background, suppress linear drift caused by temperature and radar system, and filter out high-frequency noise;

[0008] Step S3: Perform a Fourier transform on the time-domain echo signal along slow time to obtain the time-frequency signal, and window the frequency domain to extract the frequency range of the target breathing frequency.

[0009] Step S4: Using a non-convex regularization method, the time-frequency signal is decomposed by minimizing the approximate decomposition error, and the sparse components are solved to obtain the desired clean life signal.

[0010] Furthermore, in step S1, the echo model of the time-domain echo signal is expressed as:

[0011] x(m,n)=s(m,n)+c(m,n)+g(m,n)+n(m,n) (1)

[0012] Where s(m,n) represents the life signal, c(m,n) is the reflected waveform of other fixed targets, g(m,n) is the non-stationary echo noise, and n(m,n) is environmental clutter; m and n represent the sampling in the fast and slow time dimensions, respectively, m = 1, 2, ..., M, n = 1, 2, ..., N, and the size of the time-domain echo signal matrix is ​​M×N.

[0013] Furthermore, in step S2, the echo model of the time-domain signal after preprocessing is expressed as:

[0014] x(m,n)=s(m,n)+g(m,n)+n(m,n) (2)

[0015] The preprocessing includes the following three steps:

[0016] (1) Use an adaptive background removal method to remove reflected waves from a fixed environment;

[0017] (2) A linear trend suppression method is used to compensate for the linear trend caused by the radar system and temperature in the slow time dimension;

[0018] (3) Design a range filter to filter out high-frequency noise caused by oversampling and unwanted low-frequency signals.

[0019] Furthermore, in step S3, the time-domain signal echo model is windowed after being transformed to the frequency domain by a slow-time Fourier transform:

[0020] X(m,k)=S(m,k)+N(m,k)+G(m,k) (3)

[0021] Where X(m,k), S(m,k), N(m,k) and G(m,k) correspond to the frequency domain signals of x(m,n), s(m,n), n(m,n) and g(m,k) after slow-time Fourier transform, respectively;

[0022] Based on the actual frequency of human respiratory signals, the designed frequency band is limited to a narrow window, where k is the index of the frequency dimension, k = 1, 2, ..., K, and K is the maximum frequency value of the narrow window. After preprocessing and slow-time Fourier transform, the background is eliminated. At this time, the time-frequency signal X of the radar received data consists of the Fourier transformed life signal S, the background signal N, and the entry-level error G.

[0023] Further, in step S4, the time-frequency signal X of the radar received data in equation (3) represents the noisy life signal, S is the clean life signal after noise reduction and is regarded as a sparse component, the background signal N is the low-rank environmental signal, and G represents the entry-level error; using a non-convex regularization method, the low-rank and sparse solutions are obtained by minimizing the approximate decomposition error:

[0024]

[0025] Where g1(·) and g2(·) are the generalized nonconvex penalties for the low-rank and sparse parts, λ is used to weigh the trade-off parameters between these two specifications to achieve the condition of data fidelity; β is the penalty parameter with respect to the entry-level error G; ||*|| F The F-norm of a matrix; This represents the value that minimizes * within the range of values ​​for N and S;

[0026] In equation (3), there are separable structures in the objective function and constraint terms. Using the non-convex optimization method, the three parts in equation (3) are separated by minimizing the approximation error. At this time, in equation (4), g1(·) = rank(·) and g2(·) = card(·), where rank(*) represents the rank of * and card(*) represents the number of elements in * that meet the requirements.

[0027] The solution function for equation (4) is expressed as:

[0028]

[0029] Where r represents the low-rank threshold and l represents the sparse threshold.

[0030] Furthermore, minimizing the approximation error in equation (5) includes:

[0031] Step 1: Solve the low-rank part N obtained in the t-th iteration using the bilateral random projection method. t At this point, S and G are fixed;

[0032]

[0033] in, This represents the value of N that minimizes * within the range of values ​​for N;

[0034] use To replace the time-frequency signal X received by the radar, the convergence speed is accelerated. The left and right random projections of the data matrix are... Where A1∈R n×r A2∈R m×r It is a random Gaussian matrix;

[0035] That is:

[0036]

[0037] Where Q1, R1, Q2, and R2 are the QR decomposition results of P1 and P2, respectively, and q is a non-negative integer representing the value of q during the process from X to P2. XX during conversion T The number of operations, where the superscript T indicates the transpose of the matrix.

[0038] Step 2: Solving the sparse part in the t-th iteration Now, with N and G fixed, we further convert the problem to a hard thresholding method. We select a sparse threshold l and use Otsu's method (also known as the maximum inter-class variance method) to find this value. After binarizing the image using the obtained threshold, the inter-class variance between the foreground and background images is maximized.

[0039]

[0040] in, It refers to the element belonging to Ω in the filter selection*, where Ω is |XN t |The set of sampling subscripts;

[0041] Step 3: Solve for the error noise component G obtained in the t-th iteration. t :

[0042] G t =XN t -S t (9)

[0043] Step 4: Calculate S = S + S t Determine G t If the preset threshold is met, output the result; otherwise, return to step one and update X = N. t +G t .

[0044] Beneficial effects:

[0045] This invention is used for enhancing weak vital signals from humans passing through walls. It avoids bias problems in the solution process by using a non-convex regularization method; it captures sparse vital signal components by minimizing the approximate decomposition error for time-frequency signal decomposition; it uses a random bilateral projection method to solve the low-rank part and applies a power scheme to accelerate the solution while ensuring computation time; this invention can improve the output signal-to-noise ratio of vital signals, has a fast computation speed, and provides the possibility for real-time extraction of weak vital signals under low signal-to-noise ratio conditions. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of a weak life signal enhancement algorithm based on non-convex regularization according to the present invention.

[0047] Figure 2 This is a simulation scene diagram;

[0048] Figure 3a The time-frequency diagram of the life signal after traditional Fourier transform processing;

[0049] Figure 3b The time-frequency diagram of the life signal after singular value decomposition;

[0050] Figure 3c The time-frequency diagram of the life signal after robust principal component analysis;

[0051] Figure 3d Frequency diagram of the life signal processed by the method provided in this disclosure;

[0052] Figure 4 The results of the four methods are shown in the figure for different signal-to-noise ratios. Detailed Implementation

[0053] To further clarify the technical solution, experimental results, and advantages of this invention, the implementation steps of this invention are described in detail below with specific examples. In an exemplary embodiment of this invention, a weak life signal enhancement algorithm based on non-convex regularization is provided, which is a weak life signal enhancement algorithm based on minimizing approximate decomposition error.

[0054] like Figure 1 As shown, a weak life signal enhancement algorithm based on non-convex regularization in this embodiment includes the following steps:

[0055] Step S1: Acquire life signals using a single-transmitter, single-receiver ultra-wideband radar. The life signals are time-domain echo signals. The echo model of the time-domain echo signal is represented as follows:

[0056] x(m,n)=s(m,n)+c(m,n)+g(m,n)+n(m,n) (1)

[0057] Where s(m,n) represents the human respiratory signal, c(m,n) is the reflected waveform of other fixed targets, g(m,n) is the non-stationary echo noise, and n(m,n) is environmental clutter. m and n represent the sampling in the fast and slow time dimensions, respectively, m = 1, 2, ..., M, n = 1, 2, ..., N, and the size of the time-domain echo signal matrix is ​​M × N.

[0058] Step S2: Preprocess the time-domain echo signal to remove fixed background, suppress linear drift caused by temperature and radar system, and filter out high-frequency noise. After processing, the time-domain signal echo model can be expressed as:

[0059] x(m,n)=s(m,n)+g(m,n)+n(m,n) (2)

[0060] The preprocessing mainly includes the following three steps: (1) using an adaptive background removal method to remove reflected waves from a fixed environment; (2) using a linear trend suppression method to compensate for the linear trend caused by the radar system and temperature in the slow time dimension; (3) designing a range filter to filter out high-frequency noise caused by oversampling and unwanted low-frequency signals.

[0061] Step S3: Perform a Fourier transform on the time-domain echo signal along slow time to obtain the time-frequency signal, and window the frequency domain to extract the frequency range of the target breathing frequency.

[0062] The time-domain signal echo model can be transformed to the frequency domain using a slow-time FFT and then windowed.

[0063] X(m,k)=S(m,k)+N(m,k)+G(m,k) (3)

[0064] Where X(m,k), S(m,k), N(m,k), and G(m,k) correspond to the frequency domain signals of x(m,n), s(m,n), n(m,n), and g(m,k) after slow-time FFT transformation, respectively. Based on the actual frequency of human respiratory signals, the designed frequency band is limited to a narrow window, where k is the index of the frequency dimension, k = 1, 2, ..., K, and K is the maximum frequency value of the narrow window. After preprocessing and slow-time Fourier transform, the background is essentially eliminated. At this point, the time-frequency signal X of the radar received data consists of the Fourier-transformed vital signal S, the background signal N, and the entry-level error G.

[0065] Step S4: Using a non-convex regularization method, the time-frequency signal is decomposed by minimizing the approximate decomposition error, and the sparse components are solved to obtain the desired clean life signal.

[0066] In equation (3), the time-frequency signal X of the radar received data represents the noisy life signal, S is the clean life signal after noise reduction, which can be regarded as a sparse component, N is the low-rank environmental signal, and G represents the entry-level error. A non-convex regularization method can be used to obtain the low-rank and sparse solution by minimizing the approximate decomposition error:

[0067]

[0068] Where g1(·) and g2(·) are the generalized nonconvex penalties for the low-rank and sparse parts, and λ is used to weigh the trade-offs between these two specifications to achieve the data fidelity condition. β is the penalty parameter with respect to the entry-level error G. F The F-norm of a matrix. This represents the value that minimizes * within the range of values ​​for N and S.

[0069] It can be observed that there are separable structures in the objective function and constraint terms of equation (3). The three parts in equation (3) can be separated by minimizing the approximation error using a non-convex optimization method. At this time, g1(·) = rank(·) and g2(·) = card(·) in equation (4), where rank(*) represents the rank of * and card(*) represents the number of elements in * that meet the requirements. This invention has a small computational load and a fast computation speed.

[0070] The solution function for equation (4) can be further expressed as:

[0071]

[0072] Where r represents the low-rank threshold and l represents the sparse threshold. Minimizing the approximation error and solving equation (5) can be divided into four steps:

[0073] Step 1: Solve the low-rank part N obtained in the t-th iteration using the bilateral random projection method. t At this point, S and G are fixed;

[0074]

[0075] in, This represents the value of N that minimizes * within the range of values ​​for N;

[0076] use To replace the time-frequency signal X received by the radar, the convergence speed is accelerated. The left and right random projections of the data matrix are... Where A1∈R n×r A2∈R m×r For random Gaussian matrices:

[0077] That is:

[0078]

[0079] Where Q1, R1, Q2, and R2 are the QR decomposition results of P1 and P2, respectively, and q is a non-negative integer representing the value of q during the process from X to P2. XX during conversion T The number of operations, where the superscript T indicates the transpose of the matrix.

[0080] Step 2: Solve for the sparse part obtained in the t-th iteration. With N and G fixed, this can be further transformed into a hard thresholding method, the core of which is the selection of the sparse threshold l. Otsu's method is then used to solve for this value.

[0081]

[0082] in, The filter selects the elements belonging to Ω from the * array, where Ω is |XN t The sampling index set | is used in Otsu's method, also known as the maximum inter-class variance method. After the threshold is obtained and the image is binarized, the inter-class variance between the foreground and background images is maximized.

[0083] Step 3: Solve for the error noise component G obtained in the t-th iteration. t :

[0084] G t =XN t -S t (9)

[0085] Step 4: Calculate S = S + S t Determine G t If the preset threshold is met, output the result; otherwise, return to step one and update X = N. t +G t .

[0086] Table 1 shows the iterative process of the proposed life signal enhancement algorithm:

[0087] Table 1

[0088]

[0089] In the proposed life signal enhancement algorithm, the parameter ε = 10 was set and adjusted based on experimental data results. -4 r = 4 and q = 2.

[0090] In this embodiment, Figure 2 A simulation diagram of penetrating-wall life detection is provided; Figure 3a , Figure 3b , Figure 3c , Figure 3dThese are the life detection results after processing by the proposed enhancement algorithms, which are based on traditional FFT, SVD enhancement algorithms, and RPCA enhancement algorithms, under the same signal-to-noise ratio. Figure 3a The image shows the time-frequency diagram of the life signal after traditional Fourier transform processing. Figure 3b This is the time-frequency plot of the life signal after singular value decomposition. Figure 3c This is the time-frequency plot of the life signal after robust principal component analysis. Figure 3d Frequency diagram of the life signal after processing by the method provided in this disclosure. Figure 4 The output signal-to-noise ratios of the proposed enhancement algorithms are given by the traditional FFT, SVD enhancement, and RPCA enhancement algorithms under different input signal-to-noise ratios.

[0091] In summary, this invention uses a non-convex regularization method to solve for the sparse components of the time-frequency signal after the slow-time Fourier transform by minimizing the approximate decomposition error. This method has a fast solution speed, improves the output signal-to-noise ratio of the life signal, and makes it possible to extract weak life signals in real time under low signal-to-noise ratio conditions.

Claims

1. A weak life signal enhancement algorithm based on non-convex regularization, characterized in that, Includes the following steps: Step S1: Use a single-transmitter, single-receiver ultra-wideband radar to collect life signals, wherein the life signals are time-domain echo signals; Step S2: Preprocess the time-domain echo signal to remove fixed background, suppress linear drift caused by temperature and radar system, and filter out high-frequency noise; Step S3: Perform a Fourier transform on the time-domain echo signal along slow time to obtain the time-frequency signal, and window the frequency domain to extract the frequency range of the target respiration frequency, including: The time-domain signal echo model is transformed to the frequency domain using a slow-time Fourier transform and then windowed. (3) in, , , and Corresponding to the preprocessing , , and Frequency domain signal after slow-time Fourier transform; Based on the actual frequency of human respiratory signals, the designed frequency band is limited to a narrow window. It is an index along the frequency dimension. , This is the maximum frequency value of the narrow window; after preprocessing and slow-time Fourier transform, the background is eliminated; at this point, the time-frequency signal of the radar received data... Life signals after Fourier transform Background signal and entry-level error composition; Step S4: Using a non-convex regularization method, decompose the time-frequency signal by minimizing the approximate decomposition error, solve for the sparse components, and obtain the desired clean life signal, including: The time-frequency signal of the radar received data in equation (3) This represents a noisy life signal. It is a clean life signal after noise reduction, regarded as a sparse component, background signal. It is a low-rank environmental signal. Representing the entry-level error; using a non-convex regularization method, low-rank and sparse solutions are obtained by minimizing the approximate decomposition error: (4) in, , It is a generalized non-convex penalty for the low-rank and sparse parts. The trade-off parameters used to balance these two specifications to achieve the conditions for data fidelity; It's about entry-level error. The penalty parameter; The F-norm of a matrix; Indicates in and Within the range of values ​​of , Minimum value; In equation (3), the objective function and constraint terms contain separable structures. Using a non-convex optimization method, the three parts of equation (3) are separated by minimizing the approximation error; at this time, in equation (4) , ,in express rank, express The number of elements that meet the requirements; The solution function for equation (4) is expressed as: (5) in, Low-rank threshold, This represents the sparsity threshold.

2. The weak life signal enhancement algorithm based on non-convex regularization according to claim 1, characterized in that, In step S1, the echo model of the time-domain echo signal is expressed as: (1) in, Indicates a life signal. It is the reflected waveform of other fixed targets. It is non-stationary echo noise. It is environmental clutter; and These represent sampling in the fast and slow time dimensions, respectively. , The size of the time-domain echo signal matrix is .

3. The weak life signal enhancement algorithm based on non-convex regularization according to claim 2, characterized in that, In step S2, the echo model of the time-domain signal after preprocessing is expressed as: (2) The preprocessing includes the following three steps: (1) Use an adaptive background removal method to remove reflected waves from a fixed environment; (2) A linear trend suppression method is used to compensate for the linear trend caused by the radar system and temperature in the slow time dimension; (3) Design a range filter to filter out high-frequency noise caused by oversampling and unwanted low-frequency signals.

4. The weak life signal enhancement algorithm based on non-convex regularization according to claim 1, characterized in that, The solution to minimize the approximation error in equation (5) includes: Step 1: Solve the problem using the bilateral random projection method. The low-rank part is solved in the next iteration. At this time, it is fixed ; (6) in, Indicates in Within the range of values ​​of , smallest The value; use To replace the time-frequency signal for receiving radar data To accelerate convergence, the left and right random projections of the data matrix are... , ,in , It is a random Gaussian matrix; That is: (7) in, They are respectively The QR decomposition results It is a non-negative integer, indicating that it is in progress. arrive During conversion The number of operations, superscript Represents the transpose of a matrix; Step Two: The sparse part is solved in the next iteration. At this time, it is fixed This is further transformed into a hard thresholding method for sparse thresholding. The selection process involves using Otsu's method, also known as the maximum inter-class variance method, to find the threshold value. This threshold, after image binarization segmentation, maximizes the inter-class variance between the foreground and background images. (8) in, Filter selection China belongs to elements, yes The set of sampling subscripts; Step 3: Solve the... Error noise component of the next iteration solution : (9) Step 4: Calculation ,judge If the preset threshold is met, output the result; otherwise, return to step one and update the settings. .

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