A Signal Baseline Correction Method with Adaptive Selection of Double-Cycle Smoothing Parameters

Abstract

The present invention relates to a signal baseline correction method with adaptive selection of double-cycle smoothing parameters, including: receiving an optoelectronic sensing signal to be processed and an initial smoothing parameter value; solving the baseline for each optoelectronic sensing signal by minimizing a penalized least squares function to obtain an initial fitted baseline; successively performing iterative updates of the smoothing parameter and iterative updates of the weight value; the iterative update of the weight value is: calculating the residual signal between the optoelectronic sensing signal and the corresponding baseline, obtaining the signal mean and signal standard deviation of the negative part, so as to update the weight value; the iterative update of the smoothing parameter is: based on the final residual signal, signal mean and signal standard deviation, updating the smoothing parameter value. Compared with the prior art, the present invention has the advantages of adaptive selection of smoothing parameters and weight coefficients, can automatically, quickly and accurately fit the baseline throughout the process, correct the baseline drift problem, and further ensure the accuracy of the optoelectronic sensing signal information after correction.

Description

Technical Field

[0001] The present invention relates to the technical field of signal processing, and in particular to a signal baseline correction method for adaptively selecting double-loop smoothing parameters. Background Art

[0002] Optoelectronic sensing signals obtained by optoelectronic detection devices such as Raman spectroscopy, X-ray fluorescence spectroscopy, and electrochemical devices usually contain a lot of unnecessary information in addition to the required signal itself, such as noise and background values, which affect the accuracy of qualitative and quantitative analysis. Optoelectronic detection devices are composed of many precision optoelectronic components, and these components are prone to be affected by environmental factors such as light, stability, humidity, and vibration during long-term continuous operation. These factors can easily cause baseline drift of the measurement signal, making it impossible to further accurately analyze the peak height and peak area of useful information. Therefore, before performing qualitative and quantitative analysis of substances, it is necessary to correct the baseline of the signal.

[0003] Common baseline correction methods include derivative method, wavelet transform, polynomial fitting, automatic iterative moving average method, penalty least squares method, etc. When using the derivative method to correct the baseline of optoelectronic sensing signals, noise may be easily amplified. Once the noise is amplified, the SNR (signal-to-noise ratio) will decrease, and the spectrum may be distorted after baseline correction. Therefore, it is necessary to first smooth the signal before adopting this method, and the steps are cumbersome. Wavelet transform assumes that the baseline, noise, and spectral signal exist in different frequency bands. The baseline is a low-frequency signal, while the noise is a high-frequency signal. Therefore, high-frequency noise and low-frequency baseline can be filtered by wavelet transform and reconstruction. However, when the absorption lines of the analyte are sparse, due to the limited resolution of the spectrometer or the electrical signal detector, many peaks will appear, and the absorption peak region is considered a high-frequency signal. The wavelet transform method cannot distinguish between peak signals and noise signals, which may lead to distortion of the corrected spectrum. In addition, the selection of the optimal wavelet basis, decomposition level, and threshold of wavelet coefficients is also difficult. Although the polynomial fitting algorithm is simple and effective, it is prone to overfitting or underfitting. Appropriate parameters need to be selected. The automatic iterative moving average method is prone to overestimating the baseline in the peak region. When signal peaks overlap, it is not suitable for fitting the baseline. The baseline correction method of penalty least squares method comprehensively considers the fidelity and smoothness of the fitted baseline, has the advantages of fast correction speed and no need for peak detection, and is widely used in various optoelectronic signal preprocessing. However, this algorithm requires users to blindly select smoothing parameters according to experience, and the fitting results often have large subjectivity. The accuracy mainly depends on the operator's experience. When the smoothing parameter is assigned too large, in the non-peak region, the fitted baseline will be higher than the actual baseline, and in the peak region, the fitted baseline will be much lower than the actual baseline, and the signal after baseline correction will be lifted. When the smoothing parameter is assigned too small, the situation is opposite, and when the signal is superimposed with noise information, the fitting accuracy of the baseline will further decrease.

[0004] A variety of portable optoelectronic detection equipment (such as Raman spectroscopy, X-ray fluorescence spectroscopy, electrochemical equipment, etc.) has the advantages of fast, non-destructive, low-cost, and in-situ detection, and has played an important role in the fields of materials, food safety, environmental safety, soil and groundwater environmental protection, etc. However, in the actual use process, the existence of the baseline problem seriously affects the detection accuracy of optoelectronic detection equipment and restricts its further development. Therefore, it is of great significance to automatically correct the baseline without damaging the effective information, and there is an urgent need for an automatic baseline correction algorithm.

[0005] The invention with the publication number CN108844939A discloses a Raman spectroscopy detection baseline correction method based on asymmetric weighted least squares. This algorithm introduces a weight function. Based on the ideas of asymmetric penalty least squares and local symmetric weighting, the fitting baseline is obtained by iteratively calculating the weighted least squares, which can effectively avoid the interference of noise on the accuracy of baseline fitting. However, in the algorithm disclosed in this solution, the selection of the smoothing factor still needs to be determined by the user according to experience. The smoothing parameter is fixed and cannot solve the influence of the smoothing parameter on the baseline correction performance, which will lead to a decrease in the accuracy of the fitted baseline and fails to achieve full-parameter automation. Summary of the Invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned existing technologies and provide a signal baseline correction method with adaptive selection of double-loop smoothing parameters, which can adaptively select the optimal smoothing parameter according to the actual situation of each channel address of the signal to be corrected. Further, the baseline z is obtained by minimizing the penalty least squares function, and then the original signal data is subtracted from the baseline z to achieve baseline correction. While realizing automation, this algorithm also eliminates the influence of the smoothing parameter on the accuracy of baseline correction.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A signal baseline correction method with adaptive selection of double-loop smoothing parameters includes the following steps:

[0009] S1: Receive multiple optoelectronic sensing signals to be processed and an initial smoothing parameter value; initialize the weight value and weight matrix of the signal;

[0010] S2: Solve the baseline for each optoelectronic sensing signal by minimizing the penalty least squares function to obtain an initial fitted baseline;

[0011] S3: Determine whether the preset iteration termination condition is satisfied. If satisfied, execute step S6; otherwise, execute step S4:

[0012] S4: Calculate the residual signal of each optoelectronic sensing signal and the corresponding baseline, take the negative part of the residual signal, and calculate the signal mean and signal standard deviation;

[0013] S5: Iteratively update the weight value of the signal based on the residual signal, signal mean, and signal standard deviation, solve a new fitted baseline using the updated signal weights, and return to step S3;

[0014] S6: Output the final fitted baseline;

[0015] S7: Update the smoothing parameter value based on the final residual signal, signal mean, and signal standard deviation;

[0016] S8: Repeat steps S3 - S6 using the updated smoothing parameter value to recalculate the baseline iteratively, and then execute step S9;

[0017] S9: Subtract the fitted baseline obtained in step S8 from the multiple received optoelectronic sensing signals to be processed to obtain the signals after baseline correction.

[0018] Further, the process of solving the fitted baseline is specifically as follows:

[0019] Substitute the multiple received optoelectronic sensing signals, the smoothing parameter value, and the weight matrix into the minimized penalized least squares function, solve the minimized penalized least squares function, and make the partial derivative of the minimized penalized least squares function equal to zero, thereby obtaining the fitted baseline by solving.

[0020] Further, the expression of the minimized penalized least squares function is:

[0021] F(z) = (y - z) T (y - z) + λDz T (Dz)

[0022] In the formula, F(z) is the minimized penalized least squares function, z is the fitted baseline, y is the received optoelectronic sensing signal, λ is the smoothing parameter value, and D is the second - order difference matrix;

[0023] The solving equation of the fitted baseline is:

[0024] z = (W + λD T D) -1 Wy

[0025] In the formula, W is the weight matrix.

[0026] Further, the iteration termination condition includes that the difference between each weight value in the weight matrix in two adjacent iteration processes is less than a preset difference threshold.

[0027] Further, the iteration termination condition also includes that the number of iterations is greater than a preset maximum number of iterations.

[0028] Further, the weight value is iteratively updated using the logistic function, and the expression of the logistic function is:

[0029]

[0030]

[0031] In the formula, w i is the weight value corresponding to the i - th optoelectronic sensing signal, d iis the residual signal corresponding to the i-th electrical sensing signal, m is the signal mean of the negative part of the residual signal, σ is the signal standard deviation of the negative part of the residual signal, y i is the i-th optoelectronic sensing signal, z i is the fitting baseline corresponding to the i-th optoelectronic sensing signal.

[0032] Furthermore, the Adaptive function is used to update the smoothing parameter value.

[0033] Furthermore, the expression of the Adaptive function is:

[0034]

[0035] In the formula, is the updated smoothing parameter value corresponding to the i-th optoelectronic sensing signal, d i is the residual signal corresponding to the i-th electrical sensing signal, m is the signal mean of the negative part of the residual signal, σ is the signal standard deviation of the negative part of the residual signal.

[0036] Compared with the prior art, the present invention performs baseline correction processing on the optoelectronic sensing signals detected by the optoelectronic detection device through the method, and all the settings of the algorithm parameters are adaptively assigned by the program according to the actual situation of the signal to be processed. The assignment of the smoothing parameter and the weight value respectively adopt the Adaptive function and the logistic function, which can effectively eliminate the influence of the existence of noise information on the assignment, so as to ensure the accuracy of baseline correction, and has the following advantages:

[0037] (1) Compared with baseline correction algorithms such as the derivative method, wavelet transform, polynomial fitting, and automatic iterative moving average method, the method does not require preprocessing such as signal smoothing and noise reduction, spectral peak identification, and wavelet transform, and the calculation is simpler, more stable, and faster.

[0038] (2) Compared with the ordinary penalty least squares baseline fitting correction algorithm, the method can accurately identify the characteristic situation of the optoelectronic sensing signal to be corrected, and uses the Adaptive function to assign the smoothing parameter for each channel address, solving the following problems caused by using a fixed smoothing parameter value: "When the smoothing parameter remains unchanged, in the peak region, the fitting baseline will be higher than the true baseline, and in the non-peak region, the fitting baseline is lower than the true baseline."

[0039] (3) The Adaptive function adopted by the method is an overall local equal weighted function, and the mean and standard deviation of the residual signal are introduced as variables, which can effectively avoid the influence of noise information on the assignment, thereby improving the accuracy of the correction result.

[0040] (4) The method uses the logistic function to iteratively update the weight coefficients by combining the residual signal values, the mean and standard deviation of the assignment part as variables. By using this method, when the noise information is above and below the baseline, similar weight values can also be assigned based on these signals, thereby eliminating the influence of noise information on the assignment of weight coefficients. Moreover, the weight values of this function can also be assigned according to the numerical values of the difference signals to achieve asymmetric weighting. This further improves the accuracy of the baseline correction result, and the corrected signal information is more accurate. And constraints are imposed on the weight range to prevent the weight coefficients from being too large and causing the program to crash.

[0041] (5) All parameters of the method do not need to be set by the user. In particular, the smoothing parameter and the weight coefficient do not require the user to judge the quality of the fitting based on experience, and it has the advantage of fully automated correction in the whole process.

[0042] In summary, based on the penalty least squares baseline correction method, the present invention has the advantages of adaptive selection of smoothing parameters and weight coefficients, and can fit the baseline automatically, quickly and with high accuracy in the whole process, and correct the baseline drift problem. Furthermore, it ensures the accuracy of the corrected optoelectronic sensing signal information, providing high-quality data guarantee for subsequent qualitative and quantitative analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a schematic flow chart of a signal baseline correction method with adaptive selection of double-loop smoothing parameters provided in an embodiment of the present invention;

[0044] Figure 2 It is a schematic diagram of an original electrical signal and the fitted baseline of the method in an embodiment of the present invention;

[0045] Figure 3 It is a schematic diagram of the electrical signal after baseline correction of the method in an embodiment of the present invention;

[0046] Figure 4 It is a schematic diagram of an original LIFs optical signal and the fitted baseline of the method in an embodiment of the present invention;

[0047] Figure 5 It is a schematic diagram of the LIFs optical signal after baseline correction of the method in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Components of the embodiments of the present invention generally described and illustrated in the figures herein can be arranged and designed in a variety of different configurations.

[0049] Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0050] It should be noted that like reference numerals and letters denote like items in the following figures. Therefore, once an item is defined in one figure, it does not require further definition and explanation in subsequent figures.

[0051] Embodiment 1

[0052] The usage process of the signal baseline correction method with adaptive selection of double-cycle smoothing parameters described in this embodiment mainly includes three parts: 01 adaptive selection of smoothing parameters, 02 adaptive selection of weight coefficients, and 03 baseline correction and signal output, as Figure 1 shown. The specific steps are described as follows:

[0053] Step 1: Import the optoelectronic sensing signal y to be processed and the initial smoothing parameter value λ0;

[0054] Step 2: Initialize the weight value w0 = ones(N,1), and the weight matrix W = diag(w1, w2, w3…, w n ), where n is the number of data of the optoelectronic sensing signal;

[0055] Step 3: Minimize the penalized least squares function: F(z) = (y - z) T (y - z) + λDz T (Dz), substitute the above initialization values, and obtain the solution equation of the initial baseline by solving the partial derivative of the above function and making it equal to 0: z0 = (W0 + λD T D) -1 W0y, so as to obtain the initial baseline z0;

[0056] In the formula, F(z) is the penalized least squares function, z is the fitting baseline, y is the received optoelectronic sensing signal, λ is the smoothing parameter value, D is the second-order difference matrix, and W0 is the initial weight matrix;

[0057] Step 4: Determine whether the iteration termination condition is satisfied. If it is satisfied, jump to Step 7; if not, jump to Step 5;

[0058] Step 5: Calculate the residual signal d between the optoelectronic sensing signal y and the initial fitting baseline z i d = y i - z i Take the negative part of the residual signal i and calculate its mean value and standard deviation

[0059] Step 6: Use the logistic function to iteratively update the weights to obtain the weights W at the i-th iteration, and solve the fitting baseline z at the i-th iteration according to the baseline solution equation in Step 3: z i i = (W i + λ new D T D) -1 W i y, and return to Step 4. i Return to Step 4.

[0060] Step 7: Output the final fitting baseline z end .

[0061] Step 8: Use the Adaptive function to update the smoothing parameter value λ to obtain λ new , which is used as the smoothing parameter value of this algorithm;

[0062] Step 9: Adopt the updated smoothing parameter λ new , repeat Steps 4 to 7 to re-iteratively calculate the baseline, and then execute Step 10;

[0063] Step 10: After the calculation is completed, subtract the final baseline z obtained by this algorithm from the optoelectronic sensing signal y to be processed end to obtain the signal y after baseline correction cor , that is, y cor = y - z end , and realize the baseline adaptive correction of the optoelectronic sensing signal.

[0064] Specifically, the smoothing parameter described in Step 1 is preferably λ0 = 10 10 .

[0065] Specifically, the initial weight value w0 = ones(N,1) described in Step 2 is an identity matrix, w0 = [1, 1, 1…, 1], and the W is a sparse diagonal matrix.

[0066] Specifically, the D described in Steps 3 and 6 is a second-order difference matrix, and its basic form is as follows:

[0067]

[0068] Specifically, the basic form of the Adaptive function for adaptively updating the value of the smoothing parameter λ described in step 8 is as follows:

[0069]

[0070] In the formula, is the value of the smoothing parameter corresponding to the updated i-th optoelectronic sensing signal, d i is the residual signal corresponding to the i-th electrical sensing signal, m is the average value of the negative part of the residual signal, and σ is the standard deviation of the negative part of the residual signal.

[0071] Specifically, the Adaptive function described in step 8 also comprehensively considers the influence of signal noise on the assignment of the smoothing parameter, which can effectively avoid assigning small values to noise information below the fitting baseline, thereby affecting the accuracy of the calibration result.

[0072] Specifically, one of the iteration termination conditions in step 4 is that the difference between the respective weight values in the weight matrix in two adjacent iteration processes is less than a preset difference threshold, that is, the weights do not change significantly before and after. The discriminant formula in this embodiment is as follows:

[0073]

[0074] Specifically, the other iteration termination condition in step 4 is that the number of iterations is greater than a preset maximum number of iterations, which is 100 in this embodiment when the number of iterations t reaches the maximum number.

[0075] If either the iteration termination condition 1 or the iteration termination condition 2 is satisfied, the iteration terminates and jumps to step 7.

[0076] Specifically, the weight update function in step 6 is the logistic function, and its form is as follows:

[0077]

[0078] In the formula, w i is the weight value corresponding to the i-th optoelectronic sensing signal, d i is the residual signal, m is the average value of the negative part of the residual signal, σ is the standard deviation of the negative part of the residual signal, y i is the i-th optoelectronic sensing signal, z i is the fitting baseline corresponding to the i-th optoelectronic sensing signal, and the logistic function is specified as follows:

[0079]

[0080] Specifically, the weight is updated using the logistic function, and it is considered that the noise information is above and below the baseline, so similar weight values are assigned based on these signals. Moreover, the weight value of this function can also assign the weight value according to the value of the difference signal to achieve asymmetric weighting.

[0081] Specifically, the logistic function used has a range constraint on the weight value

[0082] The initialized smoothing parameter, iteration termination threshold, and maximum number of iterations in this embodiment are all optimal values in this embodiment and are not fixed to this value.

[0083] To further illustrate this algorithm, electrochemical electrical signals and laser-induced fluorescence spectral signals are respectively processed.

[0084] Baseline correction of electrochemical electrical signals in Example 1

[0085] Specifically, the electrochemical signal is the electrochemical signal obtained by using an electrochemical workstation as an analytical instrument to perform electrochemical analysis on a 10 nM lead ion solution as the implementation object.

[0086] Specifically, the electrochemical sampling method is differential pulse anodic stripping voltammetry.

[0087] Specifically, the three-electrode system used in the electrochemical workstation analysis is a bismuth film glassy carbon electrode as the working electrode, a saturated silver / silver chloride electrode as the reference electrode, and a platinum wire electrode as the counter electrode.

[0088] Specifically, the experimental conditions are: increment 0.005 V, amplitude 0.005 V, pulse width 0.06 s, sampling interval 0.02 s, pulse period 0.12 s, and standing time 20 s.

[0089] Perform baseline correction on this signal according to the algorithm steps in this embodiment. The original signal and the baseline fitted by the algorithm of the present invention are as Figure 2 shown, and the corrected signal is as Figure 3 shown. It can be seen from the figure that the baseline correction algorithm involved in the present invention can fit well along the direction of the actual baseline. After baseline correction, the peak shape and peak height of the signal are well preserved, and it has high baseline correction accuracy.

[0090] Baseline correction of laser-induced fluorescence spectral signals in Example 2

[0091] In the field of laser-induced fluorescence spectral analysis, due to the existence of the problem of fluorescence background interference, it will cause strong baseline drift of the signal, thus affecting subsequent qualitative and quantitative analysis.

[0092] In this embodiment, the object of implementation is the LIFs fluorescence signal collected by a spectrometer after a 50 ppb hexavalent chromium solution is combined with a sensitive material and excited by a laser with a wavelength of 405 nm.

[0093] Perform baseline correction on this signal according to the algorithm steps in this embodiment. The original signal and the baseline fitted by the algorithm of the present invention are as Figure 4 shown, and the corrected signal is as Figure 5 shown. It can be seen from the figure that the baseline correction algorithm for optical signals in the present invention can also fit well along the direction of the actual baseline. After baseline correction, the peak shape and peak height of the signal are well preserved, with high baseline correction accuracy.

[0094] The preferred specific embodiments of the present invention have been described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and variations based on the concept of the present invention without creative work. Therefore, all technical solutions that can be obtained by those skilled in the art in the technical field of the present invention based on the concept of the present invention through logical analysis, reasoning, or limited experiments should be within the protection scope determined by the claims.

Claims

1. A signal baseline correction method with adaptive selection of double-loop smoothing parameters, characterized in that It includes the following steps: S1: Receive multiple optoelectronic sensing signals to be processed and an initial smoothing parameter value; initialize the weight value and weight matrix of the signals; S2: Solve the baseline for each optoelectronic sensing signal by minimizing the penalty least squares function to obtain an initial fitted baseline; S3: Determine whether a preset iteration termination condition is satisfied. If satisfied, execute step S6; otherwise, execute step S4: S4: Calculate the residual signal of each optoelectronic sensing signal and the corresponding baseline, take the negative part of the residual signal, and calculate the signal mean and signal standard deviation; S5: Iteratively update the weight value of the signal based on the residual signal, signal mean, and signal standard deviation, solve a new fitted baseline using the updated signal weights, and return to step S3; S6: Output the final fitted baseline; S7: Update the smoothing parameter value based on the final residual signal, signal mean, and signal standard deviation; S8: Use the updated smoothing parameter value to repeat steps S3 - S6 to recalculate the baseline iteratively, and then execute step S9; S9: Subtract the fitted baseline obtained in step S8 from the multiple optoelectronic sensing signals to be processed received to obtain the baseline - corrected signal; The solving process of the fitted baseline is specifically as follows: Substitute the multiple optoelectronic sensing signals to be processed received, the smoothing parameter value, and the weight matrix into the penalty least squares function to be minimized, solve the penalty least squares function to be minimized, and make the partial derivative of the penalty least squares function to be minimized equal to zero, so as to solve and obtain the fitted baseline; The expression of the penalty least squares function to be minimized is: wherein, is to minimize the penalized least squares function, is the fitting baseline, is the received optoelectronic sensing signal, is the smoothing parameter value, is the second-order difference matrix; The solving equation of the fitted baseline is: Wherein, is a weight matrix; The iteration termination condition includes that the difference between the weight values in the weight matrix in two adjacent iteration processes is less than a preset difference threshold.

2. A signal baseline correction method with adaptive selection of double-loop smoothing parameters according to claim 1, characterized in that, The iteration termination condition also includes that the number of iterations is greater than a preset maximum number of iterations.

3. A signal baseline correction method with adaptive selection of double-loop smoothing parameters according to claim 1, characterized in that Use the logistic function to iteratively update the weight value, and the expression of the logistic function is: Wherein, is the weight value corresponding to the i-th optoelectronic sensing signal, is the residual signal corresponding to the i-th electrical sensing signal, m is the signal mean of the negative part of the residual signal, is the signal standard deviation of the negative part of the residual signal, is the i-th optoelectronic sensing signal, is the fitting baseline corresponding to the i-th optoelectronic sensing signal.

4. A signal baseline correction method with adaptive selection of double - loop smoothing parameters according to claim 1, characterized in that Use the Adaptive function to update the smoothing parameter value.

5. A signal baseline correction method with adaptive selection of double-cycle smoothing parameters according to claim 4, characterized in that, The expression of the Adaptive function is: In the formula, is the smoothed parameter value corresponding to the updated i-th optoelectronic sensing signal, is the residual signal corresponding to the i-th electrical sensing signal, m is the signal mean value of the negative part of the residual signal, is the signal standard deviation of the negative part of the residual signal.

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