A method for restoring missing sampling points in an array spectrometer

Abstract

A method for restoring missing sampling points in an array spectrometer leverages the advantages of Fourier interpolation. By adding high-frequency zero values ​​in the frequency domain, it reduces the sampling interval of spectra without missing points, thus increasing the amount of sampled data. In principle, if the original data has sufficient sampling density, Fourier interpolation offers higher accuracy compared to local interpolation. This invention proposes utilizing the distribution characteristics of spectral peaks to reset the sampling density of the original data. After meeting the interpolation prerequisites, it extracts higher-density Fourier interpolations to compensate for the sampling deficiencies in the original data, obtaining estimates with higher accuracy than linear interpolation and spline interpolation. The benefits of this invention are twofold: firstly, it obtains higher-accuracy completed values; secondly, because it does not alter the frequency distribution characteristics of the spectrum, it ensures the processing accuracy of the derived data.

Description

Technical Field

[0001] This invention relates to the field of array spectrometer research, and in particular to a method for restoring missing sampling points in an array spectrometer. Background Technology

[0002] Spectroscopic measurements often produce outliers due to instrument defects and environmental factors, such as hot spots in the photosensitive array or random sharp lines caused by cosmic rays. The usual procedure is to remove these outliers and then fill in the missing points using interpolation. The most common interpolation methods are linear interpolation and spline interpolation. Linear interpolation uses nearest neighbor points to estimate missing points with a straight line; it is the simplest but also has the largest error. Spline interpolation uses high-order polynomial regression to expand the range of data points, reducing the error somewhat. However, due to the Runge phenomenon, the expansion range is limited, and it cannot fully utilize the continuity of spectral peaks, making it difficult to further reduce the error of the estimated value.

[0003] Fourier interpolation is another type of interpolation method that increases the number of samples by padding with zeros in the frequency domain to achieve the interpolation purpose. However, if some data points in the original samples are missing, the frequency distribution of the overall spectrum will be disrupted, which does not meet the prerequisites for the application of Fourier interpolation. Therefore, although Fourier interpolation can make full use of the overall distribution of spectral peaks and provide more accurate sample estimates, it cannot be used to fill in missing sample points.

[0004] Interpolation essentially uses the similarity of neighboring data to estimate missing data. According to the Nyquist-Shannon sampling theorem, if the sampling frequency is greater than twice the required signal frequency, the signal can be accurately reconstructed; that is, if the peak width of the spectral peak obtained by array sampling is greater than twice the number of missing points, the spectral peak can be completely reconstructed, and the missing sampling points can be reconstructed using the information redundancy of the spectral peak in the frequency domain. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to provide a method for restoring missing sampling points in an array spectrometer.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A method for restoring missing sampling points in an array spectrometer comprises the following steps.

[0008] Step 1: Collect the spectrum and label each data point with its serial number; the measured value is SY, and the corresponding serial number is SX;

[0009] Step 2: Due to the poor usability of the first and last values ​​of the spectral measurement, if the number of data points in SY and SX is odd, the last point will be discarded to keep the number of sampling points in SY and SX even.

[0010] Step 3: Find the outlier SYF in SY, mark the corresponding value SXF in SX, and define SYF as a null value in SY;

[0011] Step 4: If there is more than one empty value in SY, fill in these empty values ​​with spline interpolation to obtain a new spectral sequence SYS;

[0012] Step 5: Divide SYS into two sequences according to the odd and even positions of the data points, with odd positions being SYO and even positions being SYE;

[0013] Step 6: Use Fourier interpolation to restore the number of sampling points of SYO and SYE to be consistent with the number of data points of SX;

[0014] Step 7: Based on the parity of SXF, find the corresponding points from SYO and SYE respectively to form the restored value YR;

[0015] Step 8: Fill YR back into SY to restore the missing data and obtain the supplemented spectrum SYR.

[0016] Furthermore, in step three, the abnormal point SYF is determined based on hotspots or cosmic rays; a hotspot is an abnormal point existing on the array detector; each measurement of this position is either too low or too high compared to the adjacent points, while a cosmic ray is a sudden instantaneous response value that is significantly higher than the adjacent points during measurement.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0018] This invention leverages the advantages of Fourier interpolation by adding high-frequency zero values ​​to the frequency domain to reduce the sampling interval of the missing sample spectrum (i.e., the time or spatial domain of the signal), thereby increasing the amount of sampled data. In principle, if the original data has sufficient sampling density, Fourier interpolation offers higher accuracy compared to local interpolation methods (linear, polynomial, spline).

[0019] This invention proposes to utilize the distribution characteristics of spectral peaks to reset the sampling density of the original data. After satisfying the interpolation prerequisites, higher-density Fourier interpolation is extracted to compensate for the sampling deficiencies of the original data, obtaining estimates with higher accuracy than linear interpolation and spline interpolation. The benefits of this invention are twofold: firstly, it obtains higher-precision complement values; secondly, because it does not alter the frequency distribution characteristics of the spectrum, it ensures the processing accuracy of derived data (such as derivative values). Attached Figure Description

[0020] Figure 1 This is a simulated measurement spectral signal diagram;

[0021] Figure 2 To supplement the missing spectrum (a) and a magnified view (b);

[0022] Figure 3 This invention provides a comparison of the results obtained using the method of the present invention with those obtained using linear interpolation and spline interpolation.

[0023] Figure 4 The images show the restored spectrum of the derivative lines (a) and magnified views of the outlier locations (b1, b2, b3). Detailed Implementation

[0024] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0025] Example:

[0026] like Figure 1-4 As shown, a method for restoring missing sampling points in an array spectrometer;

[0027] In this example, a digital signal consisting of 101 sampled values ​​with two Gaussian peaks is used. Three points among the 101 true values ​​are set as defect points, and the present invention is used to restore them to the original true values.

[0028] Step 1, such as Figure 1 As shown, where SY is the measured value. Figure 1 (solid line in the middle), corresponding to the serial number SX ( Figure 1 The horizontal axis is the midline. The presence of outliers causes the spectral lines to deviate from the true value. Figure 1 (Middle dashed line). Mark the sequence number of each data point in SY.

[0029] Step 2: Keep the number of sampling points for SY and SX an even number, that is, select the number of data points as 100.

[0030] Step 3: Identify the outliers in the spectrum SY, including 3 points, namely SXF = [26, 47, 60], and define these points as null values ​​in SY.

[0031] Step 4: Fill in these missing values ​​with spline interpolation to obtain the new sequence SYS.

[0032] Step 5: Divide SYS into two sequences according to the odd and even positions of the data points. The sequence for odd positions is sequence SYO, and the sequence for even positions is sequence SYE.

[0033] Step 6: Use Fourier interpolation to restore the number of sampling points of SYO and SYE to two sequences, SYOR and SYER, which are consistent with the number of data points of SX.

[0034] Step 7: Based on the parity of SXF, find the corresponding points from SYOR and SYER respectively to form the restored value YR.

[0035] Step 8: Fill in the missing data back into SY using YR to restore the missing data and obtain the supplemented spectrum SYR, as shown below. Figure 2 As shown.

[0036] In step three, the abnormal point SYF is determined based on hot spots or cosmic rays; hot spots are abnormal points existing on the array detector; each measurement of this position is either too low or too high compared to the adjacent points, while cosmic rays are sudden instantaneous response values ​​that are significantly higher than those of the adjacent points during measurement.

[0037] Figure 3 This is a comparison of the difference between the restored value and the true value after processing by the method of the present invention and linear interpolation and spline interpolation.

[0038] from Figure 2 , 3 The effect of this invention is clearly visible. Compared with commonly used linear and spline interpolation, missing points are perfectly restored to true values.

[0039] Furthermore, the derivative of the reduced spectral line is taken, and the result is as follows: Figure 4 As shown in (a). A local magnification of the anomaly point location is shown below. Figure 4 (b1) Figure 4 (b2) Figure 4 (b3) shows the restoration effect of the present invention more clearly. After the first derivative is processed, it still coincides well with the true value.

[0040] The results show that the precision and accuracy of the present invention are significantly better than the currently used spectral missing value compensation methods, without increasing the computational and operational difficulty. It is an effective method to improve the performance of spectrometers.

[0041] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions conceived without inventive effort should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope defined in the claims.

Claims

1. A method for restoring missing sampling points in an array spectrometer, characterized in that: It consists of the following steps, Step 1: Collect the spectrum and label each data point with its serial number; the measured value is SY, and the corresponding serial number is SX; Step 2: If the number of data points in SY and SX is odd, then discard the last point to keep the number of sampling points in SY and SX even. Step 3: Find the outlier SYF in SY, mark the corresponding value SXF in SX, and define SYF as a null value in SY; Step 4: If there is more than one empty value in SY, fill in these empty values ​​with spline interpolation to obtain a new spectral sequence SYS; Step 5: Divide SYS into two sequences according to the odd and even positions of the data points, with odd positions being SYO and even positions being SYE; Step 6: Use Fourier interpolation to restore the number of sampling points of SYO and SYE to be consistent with the number of data points of SX; Step 7: Based on the parity of SXF, find the corresponding points from SYO and SYE respectively to form the restored value YR; Step 8: Fill YR back into SY to restore the missing data and obtain the supplemented spectrum SYR.

2. The method according to claim 1, characterized in that: In step three, the abnormal point SYF is determined based on hot spots or cosmic rays; hot spots are abnormal points existing on the array detector; each measurement of this position is either too low or too high compared to the adjacent points, while cosmic rays are sudden instantaneous response values ​​that are significantly higher than those of the adjacent points during measurement.

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