A method for denoising a detection signal of a mechanical perfusion isolated heart based on a dual-domain transformation

Abstract

This invention relates to the field of signal denoising, specifically to a method for denoising detection signals from mechanically perfused isolated hearts based on dual-domain transform. The method first decomposes the original detection signal from the isolated heart under mechanical perfusion conditions into multiple signal components. Based on spectral kurtosis, the signal components characterizing fluid noise are removed. A preliminary denoised signal is reconstructed using the retained signal components. Wavelet decomposition is then performed on the preliminary denoised signal to obtain a wavelet coefficient vector. This vector is then optimized using a constructed loss function to obtain the optimal wavelet coefficient vector for the preliminary denoised signal. Based on the optimal wavelet coefficient vector, the signal is reconstructed to obtain the denoised detection signal. This invention effectively removes noise from the detection signal while better preserving the key morphological features of the signal, thus improving the denoising quality of the isolated heart detection signal under mechanical perfusion conditions.

Description

Technical Field

[0001] This invention relates to the field of signal denoising, and specifically to a method for denoising signals from mechanically perfused isolated hearts based on dual-domain transformation. Background Technology

[0002] Heart transplantation is the most effective surgical treatment for end-stage heart failure. However, the shortage of donor hearts and limitations in preservation techniques have been key bottlenecks hindering its development. Traditional organ preservation methods involve static cryopreservation, placing the heart in a low-temperature preservation solution to prolong ischemia tolerance by reducing metabolism. However, this method has inherent drawbacks; when blood flow is restored after transplantation, it can lead to severe cell damage and functional impairment, affecting the early functional recovery of the transplanted heart. To overcome these limitations, ex vivo mechanical perfusion technology has emerged. This system can simulate the in vivo physiological environment during heart ex vivo, significantly extending preservation time, reducing preservation damage, and enabling real-time assessment.

[0003] During mechanical perfusion, real-time and accurate assessment of the viability of isolated hearts is crucial for ensuring donor heart quality and the success rate of subsequent experiments. Traditional assessment methods often rely on biochemical indicators or visual observation of the heart's pulsation state. These methods generally have inherent limitations such as response lag, limited information dimensions, or strong subjectivity. Cardiac optical mapping technology uses voltage-sensitive dyes to convert the dynamic changes in myocardial cell membrane potential into high spatiotemporal resolution fluorescence signals, thereby achieving direct, non-destructive, and real-time recording of the electrical wave conduction process on the heart surface. The detection signals acquired by this technology can accurately reflect core electrophysiological parameters such as the morphology, duration, and conduction velocity of action potentials, and are widely considered the gold standard for assessing cardiac electrophysiological activity and viability. By quantitatively analyzing key features in the detection signals (such as action potential duration, conduction velocity heterogeneity, and diastolic potential stability), researchers can comprehensively and objectively assess the changes in the donor heart's state, the degree of damage, and the recovery effect during mechanical perfusion, providing a theoretical basis for pre-transplant quality assessment. However, acquiring high-quality detection signals under the non-ideal environment of mechanical perfusion presents significant challenges, as the acquired signals are often subject to various noise interferences. The superposition of these noises severely distorts the detection signal waveform. The direct consequence is that researchers cannot accurately assess the true electrophysiological state of the heart based on the contaminated signals. Therefore, efficient and high-fidelity noise removal of the acquired raw detection signals under mechanical perfusion conditions to recover high-quality signal waveforms is of great importance.

[0004] In related technologies, wavelet transform is usually used to filter and denoise the acquired noisy detection signals. By setting a threshold, some of the decomposed wavelet coefficients are zeroed out, and the processed wavelet coefficients are reconstructed to denoise the original detection signal. However, in the process of acquiring detection signals from an isolated heart under mechanical perfusion, there is a specific type of noise, namely fluid noise generated by the flow of perfusion fluid. Its energy is concentrated in a specific low-frequency band that overlaps with the heart rate, and its main frequency completely overlaps with the spectrum of cardiac mechanical activity (pressure, tension) and electrophysiological slow wave components (such as the T wave and diastole of ECG). If wavelet threshold denoising is directly applied to the unprocessed isolated heart signal containing fluid noise, unreasonable threshold settings may lead to insufficient or excessive denoising, resulting in denoising failure or signal distortion. Summary of the Invention

[0005] To address the technical problem that directly applying wavelet threshold denoising to unprocessed isolated heart signals containing fluid noise can lead to insufficient or excessive denoising due to inappropriate threshold settings, resulting in denoising failure or signal distortion, this invention aims to provide a denoising method for mechanically perfused isolated heart detection signals based on dual-domain transform. The specific technical solution adopted is as follows:

[0006] This invention proposes a method for denoising signals from mechanically perfused isolated hearts based on dual-domain transform, the method comprising:

[0007] Obtain raw detection signals from isolated hearts under mechanical perfusion conditions;

[0008] The original detection signal is decomposed into multiple signal components. The spectral kurtosis is calculated for each signal component. Based on the spectral kurtosis, the signal components that characterize fluid noise are removed from the signal components. The preliminary denoised signal is reconstructed using the remaining signal components.

[0009] The initial denoised signal is subjected to wavelet decomposition to obtain the wavelet coefficient vector of the initial denoised signal; a loss function for wavelet decomposition is constructed, and the wavelet coefficient vector is optimized using the loss function to obtain the optimal wavelet coefficient vector of the initial denoised signal.

[0010] Based on the optimal wavelet coefficient vector, the signal is reconstructed to obtain a denoised detection signal.

[0011] Furthermore, the step of decomposing the original detection signal into multiple signal components includes:

[0012] The original detection signal is input into the variational mode decomposition algorithm, and the original detection signal is decomposed into multiple signal components through the variational optimization framework.

[0013] Furthermore, the calculation of spectral kurtosis for each signal component includes:

[0014] For any signal component, windowing is applied to the signal component to obtain multiple local stationary segments of the signal component;

[0015] Perform a short-time Fourier transform on each local stationary segment of the signal component to obtain the spectral amplitude of each local stationary segment at different frequency points;

[0016] Calculate the statistical moments of the spectral amplitudes of all the local stationary segments of the signal component at the same frequency point, and substitute them into the spectral kurtosis calculation formula to obtain the single-point spectral kurtosis of the signal component at each frequency point;

[0017] The average of the single-point spectral kurtosis of the signal component at all frequency points is taken as the spectral kurtosis of the signal component.

[0018] Further, the step of removing the signal components used to characterize fluid noise from the signal components based on the spectral kurtosis includes:

[0019] Signal components with spectral kurtosis greater than a preset spectral kurtosis threshold are used as signal components characterizing fluid noise and are removed.

[0020] Furthermore, the process of reconstructing the initial denoised signal using the retained signal components includes:

[0021] The retained signal components are linearly superimposed to obtain the initial denoised signal.

[0022] Furthermore, the wavelet coefficient vector for obtaining the initial denoised signal includes:

[0023] Based on the filter coefficients of the wavelet function used in wavelet decomposition, and combined with the length of the initial denoised signal and the number of wavelet decomposition layers, the transformation matrix of the wavelet function used in wavelet decomposition is obtained.

[0024] The product of the transformation matrix and the initial denoised signal is used as the wavelet coefficient vector of the initial denoised signal, wherein the wavelet function used in the wavelet decomposition is orthogonal, and the transformation matrix is ​​an orthogonal matrix.

[0025] Furthermore, the loss function for constructing the wavelet decomposition includes:

[0026] Based on the wavelet coefficient vector of the initial denoised signal, a data fitting term for the loss function is constructed;

[0027] The noise intensity of the initial denoised signal is obtained by performing noise estimation on the initial denoised signal. Based on the noise intensity of the initial denoised signal and the scale corresponding to each wavelet decomposition layer, a non-convex sparse regularization term of the loss function is constructed.

[0028] Based on the transformation matrix of the wavelet function used in wavelet decomposition, the noise intensity of the initial denoised signal, and the length of the initial denoised signal, the total variation regularization term of the loss function is constructed.

[0029] The sum of the data fitting term, the non-convex sparse regularization term, and the total variation regularization term is used as the loss function of wavelet decomposition, wherein the data fitting term, the non-convex sparse regularization term, and the total variation regularization term contain independent variables used to indicate the wavelet coefficient vector.

[0030] Furthermore, the optimal wavelet coefficient vector for obtaining the initial denoised signal includes:

[0031] Based on the Lagrange multiplier method, an augmented Lagrange function is constructed for the loss function;

[0032] The ADMM algorithm is used to optimize the augmented Lagrangian function of the loss function, and the value of the independent variable corresponding to the minimum value of the loss function is used as the optimal wavelet coefficient vector of the initial denoised signal.

[0033] Furthermore, the augmented Lagrangian function of the loss function is:

[0034] By introducing auxiliary variables and replacing the independent variables used in the total variation regularization term with auxiliary variables, a total variation regularization term containing auxiliary variables is obtained.

[0035] Based on the difference between the auxiliary variable and the independent variable used to indicate the wavelet coefficient vector, an augmentation term for the augmented Lagrangian function is constructed;

[0036] The augmented Lagrangian function is obtained by adding the data fitting term and the non-convex sparse regularization term, which contain independent variables indicating the wavelet coefficient vector, the total variation regularization term containing auxiliary variables, and the augmented term.

[0037] Further, obtaining the denoised detection signal includes:

[0038] The optimal wavelet coefficient vector is subjected to inverse wavelet transform to obtain the denoised detection signal.

[0039] The present invention has the following beneficial effects:

[0040] 1. Variational mode decomposition is used to replace traditional empirical mode decomposition. Through iterative optimization of variational inference, the effective pressure signal (periodic, low frequency) and fluid noise (random, high frequency) are accurately segmented into independent intrinsic mode functions (IMF), i.e. signal components, which completely solves the "mode aliasing" problem. After decomposition, the signal components have no energy leakage, the effective signal and fluid noise are completely separated, the decomposition accuracy is improved, and a better signal source is provided for subsequent wavelet denoising.

[0041] 2. The total variation regularization term in the loss function constructed in this invention applies piecewise smoothing constraints in the signal domain, effectively filling and correcting oscillations near discontinuities caused by wavelet coefficients being incorrectly thresholded to zero. Employing non-convex sparse regularization, its corresponding threshold function more closely approximates the ideal hard threshold behavior than a soft threshold, more decisively reducing small-amplitude noise coefficients to zero. Simultaneously, the unified optimization framework allows for joint optimization of all coefficients, avoiding the inherent problems of excessively high or low thresholds in the first step of the two-step method, thereby suppressing isolated spikes caused by noise coefficients exceeding the threshold.

[0042] 3. This invention has a significant effect on suppressing motion artifacts and baseline drift that overlap with the effective signal frequency band in mechanical perfusion environments. The total variation regularization term has a natural smoothing effect on such slowly varying noise, while the unified optimization model can automatically coordinate the regularization intensity in the wavelet domain and the time domain to adapt to different noise levels.

[0043] 4. The optimization algorithm used in this invention has the characteristics of decomposition and coordination, which decomposes the complex unified optimization problem into multiple sub-problems that can be solved quickly. It has high real-time performance and can meet the online processing requirements of data streams during the experiment. Attached Figure Description

[0044] To more clearly illustrate the technical solutions and advantages in the embodiments of the present invention or 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 only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 A flowchart of a method for denoising detection signals of mechanically perfused isolated heart based on dual-domain transformation, provided in an embodiment of the present invention;

[0046] Figure 2 This is a schematic diagram of a raw detection signal provided in one embodiment of the present invention;

[0047] Figure 3 This is a schematic diagram of a denoising detection signal provided in one embodiment of the present invention. Detailed Implementation

[0048] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a method for denoising mechanically perfused isolated heart detection signals based on dual-domain transform proposed in accordance with the present invention. In the following description, different "one embodiment" or "another embodiment" do not necessarily refer to the same embodiment. Furthermore, specific features, structures, or characteristics in one or more embodiments can be combined in any suitable form.

[0049] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0050] The following description, in conjunction with the accompanying drawings, details a specific scheme for a method of denoising detection signals from an isolated mechanically perfused heart based on dual-domain transformation, provided by the present invention.

[0051] Please see Figure 1 The diagram illustrates a flowchart of a method for denoising signals from an isolated mechanically perfused heart based on dual-domain transform, according to an embodiment of the present invention. The method includes:

[0052] Step S1: Obtain the raw detection signal of the isolated heart under mechanical perfusion environment.

[0053] This invention uses a Langendorff-perfused rat isolated heart as an example. First, a fluorescence detection system is used to record the fluorescence signal of a voltage-sensitive dye on the heart surface at a rate of 800 frames per second. This signal is then subjected to initial Gaussian smoothing preprocessing to obtain a noisy raw detection signal. (See [link to relevant documentation]). Figure 2 It shows a schematic diagram of a raw detection signal provided in an embodiment of the present invention, from Figure 2 As can be seen, the original detection signal is affected by noise, resulting in severe waveform distortion, which requires noise reduction processing.

[0054] It should be noted that the original detection signal is a discrete signal sequence for subsequent mathematical calculations and analysis. Furthermore, since the amplitude of the perfusion fluid flow noise may fluctuate due to variations in perfusion flow rate and viscosity, the original detection signal needs to be normalized to map it to the [-1,1] interval, thereby eliminating amplitude differences and preventing mode aliasing caused by uneven amplitude during subsequent signal decomposition. In one embodiment of the invention, the normalization process can specifically be, for example, maximum-minimum value normalization. Moreover, the normalization in subsequent steps can all employ maximum-minimum value normalization. In other embodiments of the invention, other normalization methods can be selected based on the specific numerical range, which will not be elaborated further.

[0055] Step S2: Decompose the original detection signal into multiple signal components, calculate the spectral kurtosis for each signal component, remove the signal components that characterize fluid noise based on the spectral kurtosis, and reconstruct the preliminary denoised signal using the retained signal components.

[0056] During the acquisition of isolated heart detection signals under mechanical perfusion conditions, there is a major specific noise, namely fluid noise generated by the flow of perfusion fluid. Its energy is concentrated in a specific low-frequency band that overlaps with the heart rate, and its main frequency completely overlaps with the spectrum of cardiac mechanical activity (pressure, tension) and electrophysiological slow wave components (such as the T wave and diastole of ECG). If wavelet threshold denoising is directly applied to the unprocessed isolated heart signal containing fluid noise, there will be unreasonable threshold settings leading to insufficient or excessive denoising. Therefore, in this embodiment of the invention, the original detection signal is first decomposed into multiple signal components. The decomposed signal components are free of mode aliasing, and the effective signal and fluid noise are located in different signal components. Subsequently, the signal component representing fluid noise can be accurately removed from the multiple signal components, thereby eliminating fluid noise.

[0057] Preferably, in one embodiment of the present invention, the method for obtaining the wavelet coefficient vector of the initial denoised signal specifically includes:

[0058] The original detection signal is input into the variational mode decomposition algorithm, and the original detection signal is decomposed into multiple signal components, i.e., multiple intrinsic mode functions (IMFs), through a variational optimization framework. The use of the variational mode decomposition algorithm relies on three core parameters: the number of modes, the penalty factor, and the convergence accuracy. The number of modes should not be set too large or too small. If the number of modes is too small, the effective signal and noise cannot be completely separated; if the number of modes is too large, redundant modes will be generated, increasing the computational load. In this embodiment of the invention, the value range of the number of modes is set to 4~6. In one embodiment of the invention, the number of modes is set to 5. The specific value of the number of modes can also be determined according to specific requirements. The implementation scenario is set by the implementer or determined using existing energy ratio methods, and is not limited here. The penalty factor is used to balance the compactness of the modes and the signal reconstruction error. If the penalty factor is too small, the mode bandwidth is too wide, leading to aliasing of "effective signal + noise." If the penalty factor is too large, the mode bandwidth is too narrow, causing the reconstructed signal to lose effective features. In this embodiment, the penalty factor is set to a range of 1000~3000. In one embodiment, the penalty factor is set to 2000, resulting in a compact mode bandwidth and low reconstruction error. Simultaneously, in another embodiment, the convergence accuracy is set to... This is to ensure the iterative stability of the algorithm.

[0059] Since fluid noise is essentially a random signal generated by turbulence, it has strong non-Gaussianity (i.e., the signal distribution deviates from a normal distribution), while the effective signal component is a periodic signal from the beating of an isolated heart, it has weak non-Gaussianity (close to a normal distribution). Spectral kurtosis is the optimal indicator for quantifying non-Gaussianity, superior to traditional indicators such as variance and kurtosis. It can objectively distinguish between random noise modes and periodic effective signal modes. Since the spectral kurtosis of fluid noise is relatively large compared to the effective signal component, the spectral kurtosis can be calculated for each signal component to quantify the noise attribute of each signal component. Subsequently, based on the spectral kurtosis, the signal components used to characterize fluid noise can be removed from the signal components, while the effective signal components are retained.

[0060] Preferably, in one embodiment of the present invention, the method for obtaining the spectral kurtosis of each signal component specifically includes:

[0061] First, for any signal component, windowing is applied to the signal component to obtain multiple locally stationary segments of the signal component. Although the signal component, i.e. the intrinsic mode function (IMF), is a single-mode signal, it may still be locally non-stationary due to fluctuations in the perfusion fluid flow rate (such as changes in pump speed) (such as a sudden shift in the frequency of a certain segment). Therefore, in one embodiment of the present invention, a Hanning window is selected instead of a rectangular window for windowing. The "cosine roll-off" characteristic of the Hanning window can significantly reduce spectral leakage, avoid signal abrupt changes caused by window boundary truncation, and improve the continuity of subsequent frequency domain analysis.

[0062] Then, a short-time Fourier transform is performed on each local stationary segment of the signal component to obtain the spectral amplitude of each local stationary segment at different frequency points. The short-time Fourier transform preserves the local time-frequency information of the signal through the "sliding window + Fourier transform" method, while the full-segment Fourier transform loses the changes in the time dimension and cannot capture the dynamic characteristics of fluid noise.

[0063] Next, the statistical moments of the spectral amplitude of all local stationary segments of the signal component at the same frequency point are calculated and substituted into the spectral kurtosis calculation formula to obtain the single-point spectral kurtosis of the signal component at each frequency point. The spectral kurtosis calculation formula is well known to those skilled in the art and will not be elaborated here. It uses a combination of fourth-order moments and second-order moments to calculate spectral kurtosis. Compared with the kurtosis index that only uses the fourth-order moment, spectral kurtosis is normalized by the second-order moment, which eliminates the influence of signal amplitude fluctuations (such as the increase in signal amplitude caused by changes in the viscosity of the perfusion fluid).

[0064] Finally, the average of the single-point spectral kurtosis of the signal component at all frequency points is taken as the spectral kurtosis of the signal component.

[0065] The above analysis shows that the spectral kurtosis of fluid noise is relatively large compared to the effective signal components. Therefore, based on the spectral kurtosis, the signal components that characterize fluid noise can be removed from the signal components. Subsequently, the remaining signal components can be used to reconstruct the initial denoised signal with the fluid noise removed.

[0066] Preferably, in one embodiment of the present invention, the method for removing the signal component used to characterize fluid noise from the signal component specifically includes:

[0067] Signal components with spectral kurtosis greater than a preset spectral kurtosis threshold are used as signal components characterizing fluid noise and are removed. Since the spectral kurtosis of signal components characterizing fluid noise is usually greater than 3, while the spectral kurtosis of effective signal components is usually less than 1.5, the preset spectral kurtosis threshold is set to a range of 1.5 to 3. In one embodiment of the present invention, the preset spectral kurtosis threshold is set to 2. The preset spectral kurtosis threshold can also be set by the implementer according to the specific implementation scenario, and is not limited here.

[0068] After removing the signal components that characterize fluid noise, the remaining signal components can be used to reconstruct the initial denoised signal, thereby effectively removing fluid noise from the original detection signal and making the subsequent wavelet transform denoising effect better.

[0069] Preferably, in one embodiment of the present invention, all retained signal components can be linearly superimposed to obtain a preliminary denoised signal. Here, linear superposition refers to adding the amplitudes of each signal component at the same time point as the amplitude of the preliminary denoised signal at that time point.

[0070] Thus, the fluid noise in the original detection signal was effectively removed, and a preliminary denoised signal was obtained.

[0071] Step S3: Perform wavelet decomposition on the initial denoised signal to obtain the wavelet coefficient vector of the initial denoised signal; construct the loss function of wavelet decomposition, and use the loss function to optimize the wavelet coefficient vector to obtain the optimal wavelet coefficient vector of the initial denoised signal.

[0072] The preliminary denoised signal obtained through the above steps only removes fluid noise. In order to perform more thorough denoising on the original detection signal, this embodiment of the invention further performs wavelet decomposition on the preliminary denoised signal, thereby transforming the preliminary denoised signal from the signal domain to the wavelet domain and obtaining the wavelet coefficient vector of the preliminary denoised signal. The wavelet coefficient vector contains wavelet coefficients of all decomposition levels and all time points. The wavelet coefficients include two types: approximation coefficients and detail coefficients. Subsequently, a loss function can be constructed based on the wavelet coefficient vector to optimize the wavelet coefficient vector, avoiding the direct zeroing of some decomposed wavelet coefficients by setting a threshold, thus improving the final signal denoising effect.

[0073] Preferably, in one embodiment of the present invention, the method for obtaining the wavelet coefficient vector of the initial denoised signal specifically includes:

[0074] First, based on the filter coefficients of the wavelet function used in wavelet decomposition, and combined with the length of the initial denoised signal and the number of wavelet decomposition layers, the transformation matrix of the wavelet function used in wavelet decomposition is obtained. In the embodiments of the present invention, the wavelet function used in wavelet decomposition is orthogonal, so its corresponding transformation matrix is ​​also an orthogonal matrix, that is, the transpose of the transformation matrix is ​​equal to the inverse matrix. In one embodiment of the present invention, the Symlets8 wavelet function is selected, and the number of decomposition layers is set to 5. The wavelet function and the number of decomposition layers can also be set by the implementer according to the specific implementation scenario, and are not limited here.

[0075] It should be noted that the filter coefficients of a certain wavelet function are a fixed set of known values ​​specific to that wavelet function. The wavelet transform matrix is ​​essentially a combination of the length of the original signal and the number of decomposition levels, and is organized into a large sparse matrix by cyclically shifting and downsampling the filter coefficients. The length of the original signal determines the size of the transform matrix, and the complete transform matrix under multi-level wavelet decomposition is a cascade of decomposition matrices at each level. The number of decomposition levels determines the number of decomposition matrices at each level. The construction of the transform matrix of the wavelet function is a technique well known to those skilled in the art, and will not be elaborated here.

[0076] The product of the transformation matrix and the initial denoised signal is then used as the wavelet coefficient vector of the initial denoised signal.

[0077] In one embodiment of the present invention, the expression for the wavelet coefficient vector of the initial denoised signal can be, for example, as follows:

[0078]

[0079] in, The wavelet coefficient vector represents the initial denoised signal, and its length is equal to the length of the initial denoised signal. This represents the transformation matrix of the wavelet function used in wavelet decomposition; This represents the initial denoised signal, presented as a column vector.

[0080] Traditional wavelet denoising methods typically involve setting a threshold to zero out some of the decomposed wavelet coefficients and then reconstructing them to denoise the initial signal. However, this approach suffers from the problem of unreasonable threshold settings, leading to incorrect zeroing of some wavelet coefficients. This results in the loss of key features in the denoised detection signal, failing to meet real-time requirements and producing poor denoising performance. Therefore, this invention abandons the threshold-based approach. Instead, it constructs a wavelet decomposition loss function based on the wavelet coefficient vector, the length of the initial denoised signal, and the scale corresponding to each wavelet decomposition layer. This loss function, through joint constraints of data fidelity, wavelet domain sparsity, and signal domain smoothing, successfully resolves the contradiction between "feature preservation" and "noise suppression" in denoising signals from mechanically perfused isolated hearts. Ultimately, it achieves a high signal-to-noise ratio and high waveform fidelity denoising effect, laying a solid foundation for real-time and accurate assessment of cardiac electrophysiological function.

[0081] Preferably, in one embodiment of the present invention, the method for obtaining the loss function of wavelet decomposition specifically includes:

[0082] First, based on the wavelet coefficient vector of the initial denoised signal, a data fitting term for the loss function is constructed. The data fitting term ensures data fidelity and guarantees that the subsequently obtained denoised signal is "undistorted".

[0083] Preferably, in one embodiment of the present invention, the data fitting term of the loss function is:

[0084]

[0085] in, This represents the data fitting term, and its independent variable is... ; This represents the wavelet coefficient vector of the initially denoised signal; The vector to be solved, i.e. the independent variable, is also presented in the form of a column vector; Indicates the modulo symbol.

[0086] This term acts as an "anchor" or "constraint" to prevent the denoising process from "overcorrecting." Its core is to calculate the Euclidean distance (i.e., the square of the magnitude of the difference between the two) between the wavelet transform E of the noisy initial denoised signal and the current optimization objective B (i.e., the wavelet coefficients after denoising). Subsequently, by minimizing this distance, the algorithm is forced not to deviate too far from the initial denoised signal. This ensures that the denoised signal can still retain the true physiological information in the initial denoised signal to the greatest extent, avoiding signal distortion caused by over-processing. It is the fundamental guarantee for signal fidelity.

[0087] Then, noise estimation is performed on the initial denoised signal to obtain the noise intensity of the initial denoised signal. Based on the noise intensity of the initial denoised signal and the scale corresponding to each wavelet decomposition layer, a non-convex sparse regularization term of the loss function is constructed. The non-convex sparse regularization term is used to achieve sparse denoising in the wavelet domain and accurately remove noise.

[0088] In one embodiment of the present invention, the existing minimum value controlled recursive averaging method can be used to estimate the noise of the initial denoised signal, thereby obtaining the noise intensity of the initial denoised signal. In other embodiments of the present invention, methods such as sample variance method, difference method or Kalman filtering method can also be used to estimate the noise of the initial denoised signal, which will not be limited here.

[0089] Preferably, in one embodiment of the present invention, the non-convex sparse regularization term of the loss function is:

[0090]

[0091]

[0092]

[0093] in, This represents the non-convex sparse regularization term of the loss function; Indicates the first Non-convex sparse regularization parameters for layer wavelet decomposition; The vector to be solved In the first Layer wavelet decomposition and time point location The wavelet coefficients to be solved, i.e., the vector to be solved. The elements to be solved in; This represents the predefined non-convex penalty function; Indicates the first The parameters used in the non-convex penalty function under layer wavelet decomposition; This indicates the noise intensity of the initially denoised signal; Indicates the first The scale corresponding to the layer wavelet decomposition, the first Scale corresponding to layer wavelet decomposition and decomposition layer number The relationship is ; This represents the preset trade-off parameter, whose value range is: In one embodiment of the present invention, the following is used: Set to 0.9, The specific values ​​can be set by the implementer according to the specific implementation scenario, and are not limited here.

[0094] In one embodiment of the present invention, the arctangent penalty function is selected as the preset non-convex penalty function, wherein the arctangent penalty function is: ,in, It is the independent variable of the arctangent penalty function. These are the parameters used in the arctangent penalty function, and , It directly determines the "curvature" of the arctangent penalty function, thereby controlling the threshold behavior of its corresponding threshold function.

[0095] The arctangent penalty function is applied in the embodiments of this invention as follows: .

[0096] The principle of the non-convex sparse regularization term is based on a key assumption: useful electrophysiological signals are sparsity in the wavelet domain (i.e., only a small number of wavelet coefficients have large amplitudes), while noise is widely distributed across all wavelet coefficients. A non-convex arctangent penalty function is chosen, which has the characteristic of applying a strong penalty force close to a hard threshold to wavelet coefficients with small amplitudes (which are likely noise), resolutely "resetting" them to zero; while for wavelet coefficients with large amplitudes (which are likely real signals), the penalty force is weaker, allowing for better preservation. This has better feature preservation capabilities than traditional soft thresholding. Furthermore, the parameters of the arctangent penalty function in this embodiment of the invention... It exhibits scale-adaptive properties, employing different shape controls for different decomposition scales to achieve fine-grained adjustment, and non-convex sparse regularization parameters. It also exhibits scale-adaptive properties, for high-frequency scales ( (Low value), high noise ratio, larger setting Perform powerful noise reduction; for low-frequency scales ( (Large value), more signal components, smaller setting It performs gentle processing to protect low-frequency characteristics such as signal plateaus, and preset trade-off parameters. The larger the value, the greater the non-convex sparse regularization parameter. The larger the value, the stronger the denoising effect in the wavelet domain, and the lower the noise intensity. It serves as the "benchmark" for the entire parameter adjustment system, quantifying the overall energy level of noise in the original noisy signal. All other parameter settings are based on the noise intensity. .

[0097] Next, based on the transformation matrix of the wavelet function used in wavelet decomposition, the noise intensity of the initial denoised signal, and the length of the initial denoised signal, a total variation regularization term for the loss function is constructed. The total variation regularization term ensures smooth segmentation of the signal domain, effectively performing filling and smoothing.

[0098] Preferably, in one embodiment of the present invention, the total variation regularization term of the loss function is:

[0099]

[0100]

[0101] in, Represents the total variation regularization term of the loss function; This represents the total variation regularization parameter; Represents a first-order difference matrix; This represents the transformation matrix of the wavelet function used in wavelet decomposition; Indicates the transpose symbol; This represents the vector to be solved, i.e., the independent variable; Indicates the modulo symbol; Indicates the preset trade-off parameters; Indicates the length of the initially denoised signal; This indicates the noise intensity of the initial denoised signal.

[0102] This term imposes constraints in the signal domain, which first pass through... Wavelet coefficients are reconstructed into a time-domain signal, and then the gradient of this signal (i.e., the difference between adjacent sampling points) is calculated using a first-order difference matrix D. Subsequently, gradient sparsity is promoted by minimizing the modulus of the product of the three coefficients, achieving piecewise smoothing. This effectively fills and corrects spurious oscillations near discontinuities (such as the start of action potentials) caused by wavelet domain thresholding, eliminating artifact oscillations and smoothing the overall trend of the signal (low-frequency components). It significantly combats slow baseline drift caused by mechanical perfusion and, while smoothing noise, preserves key features such as sharp edges like the rising limb of the action potential. The total variation regularization parameter... Used to balance signal smoothness and signal fidelity, it directly controls the weight of the total variation regularization term in the overall loss function, which is determined by... , and Joint decision, A larger value means the algorithm will highly value the smoothness of the signal. It will strongly penalize the signal gradient (i.e., drastic changes between adjacent sampling points), thus producing a very smooth denoising result. This effectively suppresses baseline drift and fill artifact oscillations. A smaller value means the algorithm requires less signal smoothness and focuses more on sparse denoising and data fidelity in the wavelet domain. This helps preserve sharp signal characteristics. Meanwhile, when... When the size is large, the algorithm mainly relies on wavelet domain sparse denoising. It automatically shrinks, and total variation smoothing is only used as an auxiliary means to slightly correct artifacts. This setting is particularly suitable for preserving sharp features, while when When the signal is small, the algorithm will reduce wavelet domain denoising while enhancing total variation smoothing. This is suitable for scenarios where baseline drift is very severe but signal edge requirements are not extreme.

[0103] Finally, the sum of the data fitting term, the non-convex sparse regularization term, and the total variation regularization term is used as the loss function for wavelet decomposition.

[0104] As an example, in one embodiment of the present invention, the expression for the loss function of wavelet decomposition can be specifically as follows:

[0105]

[0106] in, This represents the loss function of wavelet decomposition.

[0107] Once the loss function of wavelet decomposition is obtained, it can be solved. That is, the problem is transformed into finding the value of the independent variable corresponding to the minimum value of the loss function, thereby obtaining the optimal wavelet coefficient vector of the initial denoised signal. Subsequently, a signal with better denoising effect can be reconstructed based on the optimal wavelet coefficient vector.

[0108] Preferably, in one embodiment of the present invention, the method for obtaining the optimal wavelet coefficient vector of the initial denoised signal specifically includes:

[0109] The process of finding the optimal wavelet coefficient vector is the process of minimizing the loss function. However, since the non-convex sparse regularization term and the total variation regularization term of the loss function act on variable B at the same time, directly solving the two together would be very complicated and could not meet the real-time requirements. Therefore, this embodiment of the invention introduces the variable splitting technique and solves the problem by constructing an augmented Lagrangian function.

[0110] First, based on the Lagrange multiplier method, an augmented Lagrange function is constructed for the loss function.

[0111] This invention introduces an auxiliary variable U, which becomes a copy of B, and equivalently transforms the original problem into the following constrained optimization problem:

[0112]

[0113] The constraints are:

[0114] The augmented Lagrangian function constructed for the above problem is:

[0115]

[0116] in, The augmented Lagrangian function represents the loss function; Indicates the data fitting term; This represents the non-convex sparse regularization term of the loss function; The total variation regularization term of the loss function has the following independent variable: ; Indicates auxiliary variables; Indicates the penalty parameter; Indicates scaling dual variables; Indicates the modulo symbol.

[0117] For the augmented Lagrangian function, the first two terms are in terms of B, the third term is in terms of U, and through variable splitting, the task of total variation regularization is assigned to the new variable U. The fourth term... As an augmentation term, the difference between U and B is penalized, and the scaling of the dual variable d is used to force U and B to eventually become equal during iteration.

[0118] Then, the ADMM algorithm is used to optimize the augmented Lagrangian function of the loss function, and the value of the independent variable corresponding to the minimum value of the loss function is taken as the optimal wavelet coefficient vector of the initial denoised signal. The ADMM algorithm can decompose the optimization problem into two subproblems that can be solved exactly, and iterate them alternately, thereby realizing the rapid solution of the optimal wavelet coefficient vector and ensuring the real-time performance of signal denoising. The ADMM algorithm is a well-known technique in the art and will not be elaborated here.

[0119] Step S4: Based on the optimal wavelet coefficient vector, reconstruct the signal to obtain the denoised detection signal.

[0120] After obtaining the optimal wavelet coefficient vector, the signal can be reconstructed based on the optimal wavelet coefficient vector to obtain a denoised detection signal. In this embodiment of the invention, the denoised signal avoids artifacts and sparse noise spikes, while preserving key morphological features such as the rapid rise and plateau phase of the action potential. The signal-to-noise ratio and waveform fidelity are significantly improved. Please refer to [link to relevant documentation]. Figure 3 It shows a schematic diagram of a denoising detection signal provided in an embodiment of the present invention, in comparison. Figure 2 It can be clearly seen that the embodiments of the present invention effectively remove noise while preserving key morphological features.

[0121] Preferably, in one embodiment of the present invention, the method for acquiring the denoising detection signal specifically includes:

[0122] The inverse wavelet transform of the optimal wavelet coefficient vector is performed to obtain the denoised detection signal. The specific calculation process is as follows:

[0123]

[0124] in, Indicates the noise reduction detection signal; This represents the transformation matrix of the wavelet function used in wavelet decomposition; Indicates the transpose symbol; This represents the optimal wavelet coefficient vector, which is the independent variable after the solution is obtained. The value of .

[0125] It should be noted that the order of the above embodiments of the present invention is merely for descriptive purposes and does not represent the superiority or inferiority of the embodiments. The processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0126] The various embodiments in this specification are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

Claims

1. A method for denoising signals from isolated mechanically perfused hearts based on dual-domain transform, characterized in that, The method includes: Obtain raw detection signals from isolated hearts under mechanical perfusion conditions; The original detection signal is decomposed into multiple signal components. The spectral kurtosis is calculated for each signal component. Based on the spectral kurtosis, the signal components that characterize fluid noise are removed from the signal components. The preliminary denoised signal is reconstructed using the remaining signal components. The initial denoised signal is subjected to wavelet decomposition to obtain the wavelet coefficient vector of the initial denoised signal; a loss function for wavelet decomposition is constructed, and the wavelet coefficient vector is optimized using the loss function to obtain the optimal wavelet coefficient vector of the initial denoised signal. Based on the optimal wavelet coefficient vector, the signal is reconstructed to obtain a denoised detection signal.

2. The method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 1, characterized in that, The step of decomposing the original detection signal into multiple signal components includes: The original detection signal is input into the variational mode decomposition algorithm, and the original detection signal is decomposed into multiple signal components through the variational optimization framework.

3. The method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 1, characterized in that, The calculation of spectral kurtosis for each signal component includes: For any signal component, windowing is applied to the signal component to obtain multiple local stationary segments of the signal component; Perform a short-time Fourier transform on each local stationary segment of the signal component to obtain the spectral amplitude of each local stationary segment at different frequency points; Calculate the statistical moments of the spectral amplitudes of all the local stationary segments of the signal component at the same frequency point, and substitute them into the spectral kurtosis calculation formula to obtain the single-point spectral kurtosis of the signal component at each frequency point; The average of the single-point spectral kurtosis of the signal component at all frequency points is taken as the spectral kurtosis of the signal component.

4. The method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 1, characterized in that, The step of removing the signal components used to characterize fluid noise from the signal components based on the spectral kurtosis includes: Signal components with spectral kurtosis greater than a preset spectral kurtosis threshold are used as signal components characterizing fluid noise and are removed.

5. The method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 1, characterized in that, The process of reconstructing the initial denoised signal using the retained signal components includes: The retained signal components are linearly superimposed to obtain the initial denoised signal.

6. The method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 1, characterized in that, The wavelet coefficient vector for obtaining the initial denoised signal includes: Based on the filter coefficients of the wavelet function used in wavelet decomposition, and combined with the length of the initial denoised signal and the number of wavelet decomposition layers, the transformation matrix of the wavelet function used in wavelet decomposition is obtained. The product of the transformation matrix and the initial denoised signal is used as the wavelet coefficient vector of the initial denoised signal, wherein the wavelet function used in the wavelet decomposition is orthogonal, and the transformation matrix is ​​an orthogonal matrix.

7. The method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 6, characterized in that, The loss function for constructing wavelet decomposition includes: Based on the wavelet coefficient vector of the initial denoised signal, a data fitting term for the loss function is constructed; The noise intensity of the initial denoised signal is obtained by performing noise estimation on the initial denoised signal. Based on the noise intensity of the initial denoised signal and the scale corresponding to each wavelet decomposition layer, a non-convex sparse regularization term of the loss function is constructed. Based on the transformation matrix of the wavelet function used in wavelet decomposition, the noise intensity of the initial denoised signal, and the length of the initial denoised signal, the total variation regularization term of the loss function is constructed. The sum of the data fitting term, the non-convex sparse regularization term, and the total variation regularization term is used as the loss function of wavelet decomposition, wherein the data fitting term, the non-convex sparse regularization term, and the total variation regularization term contain independent variables used to indicate the wavelet coefficient vector.

8. The method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 1, characterized in that, The optimal wavelet coefficient vector for obtaining the initial denoised signal includes: Based on the Lagrange multiplier method, an augmented Lagrange function is constructed for the loss function; The ADMM algorithm is used to optimize the augmented Lagrangian function of the loss function, and the value of the independent variable corresponding to the minimum value of the loss function is used as the optimal wavelet coefficient vector of the initial denoised signal.

9. A method for denoising isolated mechanically perfused heart detection signals based on dual-domain transform according to claim 7, characterized in that, The augmented Lagrangian function of the loss function is: By introducing auxiliary variables and replacing the independent variables used in the total variation regularization term with auxiliary variables, a total variation regularization term containing auxiliary variables is obtained. Based on the difference between the auxiliary variable and the independent variable used to indicate the wavelet coefficient vector, an augmentation term for the augmented Lagrangian function is constructed; The augmented Lagrangian function is obtained by adding the data fitting term and the non-convex sparse regularization term, which contain independent variables indicating the wavelet coefficient vector, the total variation regularization term containing auxiliary variables, and the augmented term.

10. A method for denoising detection signals of isolated mechanically perfused hearts based on dual-domain transform according to claim 1, characterized in that, The obtained denoising detection signal includes: The optimal wavelet coefficient vector is subjected to inverse wavelet transform to obtain the denoised detection signal.

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