Method for identifying the turning point of a waveform signal
A dynamic programming-based method for identifying waveform extrema in echocardiography addresses noise and irregularity issues by introducing a penalty value, ensuring accurate detection of cardiac cycle phases like end-systole and end-diastole.
Patent Information
- Authority / Receiving Office
- JP · JP
- Patent Type
- Applications
- Current Assignee / Owner
- ALPHA INTELLIGENCE MANIFOLDS INC
- Filing Date
- 2026-01-13
- Publication Date
- 2026-07-24
AI Technical Summary
Conventional methods for identifying extreme values in waveform signals, such as those used in echocardiography, often misidentify local maxima or minima due to signal noise and irregularity, making it difficult to accurately estimate cardiac cycles like end-systole and end-diastole.
A computer-implemented method using dynamic programming to detect phase transitions in waveform signals by introducing a penalty value to suppress noise-induced errors, allowing for accurate identification of extrema without prior knowledge of the signal period.
The method achieves consistent and accurate detection of waveform extrema, even in noisy conditions, by maximizing a penalized total path and reducing the need for parameter adjustment, suitable for signals with irregular periods.
Smart Images
Figure 2026121359000001_ABST
Abstract
Description
Technical Field
[0001] 〔Related Application〕 This application claims the benefit of U.S. Provisional Application No. 63 / 744,827, filed on January 13, 2025, entitled "Video-Based Multi-Contour Learning Method for Heart Image Segmentation and Analysis", which is hereby incorporated by reference in its entirety.
[0002] The present invention relates to a computer-implemented method for identifying transition points of waveform signals, particularly waveform signals with noise.
Background Art
[0003] Discovering the positions of extreme values at peaks and troughs is a commonly used signal processing technique for waveform signals in various fields. For example, it can be used for analyzing the light curves of variable stars or respiratory signals. It can also be used in photoplethysmography (PPG), electrocardiogram (EKG), or echocardiography.
[0004] In echocardiography, to track changes in ventricular volume, it is necessary to identify the end-systole (ES) and end-diastole (ED) in each cardiac cycle. However, due to the irregularity of temporal volume changes and signal noise, conventional methods such as peak detection methods and maximum / minimum value detection methods often identify local maxima or minima instead of true extreme values in one cardiac cycle. Therefore, it is difficult to reliably estimate the cardiac cycle and ES / ED frames using these methods.
[0005] Therefore, it is desirable to develop a new method for more accurately identifying the extreme value positions of waveform signals.
Summary of the Invention
[0006] To solve the above problems, the present invention provides a computer-implemented method for identifying the extreme positions of a waveform signal, whereby the phase transition of the signal can be detected with fewer parameters by a program compared to the prior art. In other words, the new method disclosed in the present invention reduces the need for parameter adjustment and enables consistent performance across datasets. The new method is suitable for signals with irregular periods as it detects the extrema without prior knowledge of the period. It also exhibits high noise tolerance and jitter tolerance, thereby maintaining accurate detection even with small noise disturbances and ensuring the identification of correct extrema.
[0007] The computer-implemented method includes: (1) obtaining a displacement series including the displacements in each time frame of the waveform signal; (2) determining, based on the displacement series, an optimized state series of all state series that maximizes the penalized total path as the optimized state series; and (3) determining the position of the conversion point of the waveform signal based on the optimized state series. In this method, the all state series includes state values representing the rising or falling status of the waveform signal in each time frame, and the penalized total path is calculated based on the displacement series and the all state series. To suppress misidentifying local extrema caused by noise as conversion points, a penalty value is introduced into the penalized total path each time the state value changes in the all state series. In one embodiment, the optimized state series is determined by a dynamic programming algorithm.
[0008] The penalty value may be a statistical measure for measuring the spread or dispersion of signal values. In one embodiment, the penalty value is the standard deviation of the waveform signal. In one embodiment, the penalty value is the interquartile range of the waveform signal. In one embodiment, the penalty value is the mean absolute deviation of the waveform signal. In yet another embodiment, the penalty value is the median absolute deviation of the waveform signal.
[0009] In one embodiment, the identified turning point of the waveform signal is a plurality of time frames in which the state value changes in the optimized state sequence.
[0010] In a preferred embodiment, the entire penalty path is defined by the formula
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[0011] In one embodiment of the computer implementation method, the step of determining the optimized state sequence includes, in each time frame, the steps of iteratively calculating one or more penalized temporal paths and identifying one or more suboptimal temporal paths from the one or more penalized temporal paths. In one embodiment, each of the one or more penalized temporal paths is calculated by adding the individual penalized path in the current time frame to the previous temporal path in the previous time frame, and in a preferred embodiment, each of the one or more penalized temporal paths is calculated by adding the individual penalized path in the current time frame to the previous temporal path in the previous time frame.
[0012] In a preferred embodiment, the penaltyed individual path includes a current displacement and a transition penalty. In one embodiment, the one or more suboptimal temporal paths include a first current path having an ascending status in the current time frame and a second current path having a descending status in the current time frame. The first and second current paths are calculated based on a first previous path, a second previous path, and the penaltyed individual path, wherein the first previous path is the largest of the previous temporal paths having an ascending status in the previous time frame, and the second previous path is the largest of the previous temporal paths having a descending status in the previous time frame.
[0013] In one embodiment, the step of determining the optimized state sequence includes: (1) an iterative step of obtaining the first previous path, the second previous path, and the current displacement in each time frame; (2) an iterative step of calculating the first current path and the second current path based on the first previous path, the second previous path, and the current displacement; (3) an iterative step of recording a first previous state value corresponding to the first current path and a second previous state value corresponding to the second current path; and (4) an iterative step of updating the first previous path with the first current path for use in the next iteration and updating the second previous path with the second current path for use in the next iteration.
[0014] After performing an iterative step of calculating the first current path and the second current path in the final time frame, the method further includes the step of selecting the larger of the first current path and the second current path as the optimized final path. A step of obtaining the optimized state sequence by iteratively determining the previous state values from the final time frame to the first time frame, wherein the previous state value in each time frame is selected from the first previous state value and the second previous state value. The selected previous state values in all time frames are combined as the optimized state sequence.
[0015] In some embodiments, the first previous path and the second previous path described above correspond to the first previous state sequence and the second previous state sequence, respectively, and each of the first previous state sequence and the second previous state sequence includes state values representing the rising or falling status of the waveform signal in each time frame from the first time frame to the previous time frame. In one embodiment, the first previous path is equal to the previous temporal path in the previous time frame calculated based on the displacement sequence and the first previous state sequence, and the second previous path is equal to the previous temporal path in the previous time frame calculated based on the displacement sequence and the second previous state sequence.
[0016] In one embodiment, the step of determining the optimized state sequence includes: (1) an iterative step of acquiring the first previous path, the first previous state sequence, the second previous path, the second previous state sequence, and the current displacement in each time frame; (2) an iterative step of calculating the first current path and the second current path based on the first previous path, the second previous path, and the current displacement; (3) an iterative step of updating the first previous path with the first current path and updating the second previous path with the second current path; and (4) an iterative step of updating the first previous state sequence with the first current state sequence corresponding to the first current path and updating the second previous state sequence with the second current state sequence corresponding to the second current path. In a preferred embodiment, the first current path is the larger of the first upward path and the second upward path, the second current path is the larger of the first downward path and the second downward path, (1) the first upward path is the first previous path plus the current displacement, (2) the second upward path is the second previous path plus the current displacement and subtracting the penalty value, (3) the first downward path is the first previous path minus the current displacement and the penalty value, and (4) the second downward path is the second previous path minus the current displacement. In one embodiment, the first previous state sequence and the second previous state sequence are updated based on the following rules: (1) if the first current path is the first ascending path, an ascending state is added to the first previous state sequence to form the first current state sequence; (2) if the first current path is the second ascending path, an ascending state is added to the second previous state sequence to form the first current state sequence; (3) if the second current path is the first descending path, a descending state is added to the first previous state sequence to form the second current state sequence; and (4) if the second current path is the second descending path, a descending state is added to the second previous state sequence to form the second current state sequence.After performing the iterative steps described above in the final time frame, the method may further include the step of selecting the larger of the first current path and the second current path as the optimized final path. The optimized state sequence can be obtained by determining the total state sequence corresponding to the optimized final path.
[0017] In one embodiment, each of the one or more penalty-affected temporal paths is calculated based on the formula TP(t,s) = TP(t-1,s') + p(t), where TP(t,s) is the penalty-affected temporal path having the current state value s, TP(t-1,s') is the previous temporal path having the previous state value s', and P(t) = V diff (t)·s(t)-Z(t) is the aforementioned penalty-bearing individual path, where V diff (t) is the current displacement, which is the value of the displacement sequence in the current time frame t; s(t) is the current state value, which is the value of the entire state sequence in the current time frame t, where the current state value is either 1, representing an upward status, or -1, representing a downward status; Z(t) is the transition penalty in the time frame t, where Z(t) = the penalty value if s(t) ≠ s(t-1), and Z(t) = 0 if s(t) = s(t-1).
[0018] Other objectives, advantages, and novel features of the present invention will become more apparent from the following detailed description when read in conjunction with the accompanying drawings. [Brief explanation of the drawing]
[0019] [Figure 1] This is a state transition diagram showing the rising (S+) and falling (S-) states and possible transitions. A penalty σ is imposed for each state transition, from the rising state to the falling state, or from the falling state to the rising state. [Figure 2]Examples of state / phase transitions identified by a dynamic programming (DP) algorithm performing the novel method disclosed herein are shown. The top row is the original frequency-modulated (FM) signal, and in the middle row, noise is introduced into the original signal. The signal is also used for transition point detection by a DP algorithm performing an extremum identification method. The detected transition points are shown as dots on the curve in the middle row, and the phase changes (rising / falling or on / off) are shown in the bottom row. [Figure 3] Examples of state / phase transitions identified by a dynamic programming (DP) algorithm performing the novel method disclosed herein are shown. The top row is the original chirp signal, and in the middle row, noise is added to the original signal. The signal is also used for transition point detection by a DP algorithm performing an extremum identification method. The detected transition points are shown as dots on the curve in the middle row, and the phase changes (rising / falling or on / off) are shown in the bottom row. [Figure 4A] This shows the contraction and relaxation cycles of the myocardium over time, along with the extreme values tracked by the DP algorithm. [Figure 4B] This graph shows the contraction and relaxation cycles of the myocardium over time, along with the extreme values tracked by the DP algorithm. The curve represents the strain signal, and the tracked extreme values (maximum and minimum) are indicated by the symbols ▼ and ▲. [Modes for carrying out the invention]
[0020] Terms used in the following description are intended to be interpreted in their broadest and most applicable sense, even when used in connection with a detailed description of a specific example of the Technology. Certain terms may be emphasized below, but any term intended to be interpreted in a restricted sense is specifically defined in this [Modes for Carrying Out the Invention] section.
[0021] The embodiments described below may be implemented by programmable circuits programmed or configured by software and / or firmware, by entirely dedicated circuits, or by a combination of these methods. Such dedicated circuits (if any) may take the form of, for example, one or more application-specific integrated circuits (ASICs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), graphics processing units (GPUs), etc.
[0022] This invention provides a computer implementation method for identifying the extremum of a waveform signal. In this method, an objective function derived from the waveform signal is used to identify the extremum. The objective function has a "state" parameter related to different states (e.g., rising and falling) of the waveform signal in each time frame. By selecting an appropriate state parameter that maximizes the objective function and identifying the locations in the waveform signal where the state parameter changes, the extremum of the waveform signal (i.e., turning points) and the corresponding signal values can be identified.
[0023] [Objective function] The objective function aims to maximize the difference in signal values between a identified peak and its adjacent trough, while simultaneously ensuring the identification of state transitions. To achieve this objective, a transition penalty is introduced into the objective function to prevent the misidentification of noise-induced local extrema as true extrema in the wave period. The objective function resembles the cumulative path that a virtual point moves during signal recording, except that a penalty value is subtracted from the cumulative path each time a state transition occurs. Because a penalty is imposed each time a transition occurs, the transition penalty prevents the misidentification of noise-induced local extrema as transition points.
[0024] In a preferred embodiment, the objective function has the following form:
number
[0025] [Penalty Value] The penalty value (σ) may be any appropriate value to avoid unnecessary state transitions. In preferred embodiments, a statistical measure that measures the spread or variance of the signal values is used. Examples of statistical measures that may be used as the penalty value include, but are not limited to, the interquartile range (IQR), standard deviation (SD), mean absolute deviation (AAD), or median absolute deviation (MAD) of the waveform signal. The definitions and important characteristics of these statistical measures are described below.
[0026] 1. Interquartile Range (IQR) The Interpolational Quarter Value (IQR) is the range of the middle 50% of the data, i.e., the difference between the third quartile (Q3) and the first quartile (Q1), and is expressed by the formula IQR = Q3 - Q1. IQR is robust to outliers and focuses on the central portion of the data. However, it ignores the edges of the data.
[0027] 2. Standard deviation (SD) SD is the square root of variance, measuring the mean deviation from the mean in the same units as the data, and is expressed by the formula SD = √Variance. It has the same units as the data and is widely used. However, it is more sensitive to outliers.
[0028] 3. Mean Absolute Deviation (AAD) AAD refers to the average of absolute deviations from the mean, and the formula is
number
[0029] 4. Median Absolute Deviation (MAD) The median absolute deviation (MAD) is a robust measure that is the median of absolute deviations from the median of the data, and is given by the formula MAD = median(|x). i It is expressed as -median(x)|). This is very robust to outliers, but may not be sensitive enough to datasets with fine variability.
[0030] [State determination] For a given signal V, the objective function
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[0031] 〔State sequence〕
Number
[0032] Here, the penalty - attached time path is defined.
Number
[0033] According to the rules, the penaltyed temporal path in the current time frame t is equal to the penaltyed temporal path in the previous time frame t-1 (called the previous temporal path) plus the penaltyed individual path in the current time frame t. That is, TP(t-1,s')+V diff (t)·s(t)-Z(t)=TP(t,s). In the equation, s' is the state value at the previous time frame t-1, called the previous state value. Max The maximum TP value at (t-1, s') is defined as the previous path, where a path with the previous state s'=1 is called the first previous path, and a path with the previous state s'=-1 is called the second previous path. In other words, the first previous path is the largest among the previous temporal paths that have an ascending status in the previous time frame t-1, and the second previous path is the largest among the previous temporal paths that have a descending status in the previous time frame t-1. From the above equation, the following recurrence relation is obtained.
number
[0034] Based on the above analysis, TP Max TP at all t including (T,s) Max It can be shown that (t,s) can be calculated. Furthermore, the optimized final path is the largest among all possible objective values, so TP Max (T,1) and TP Max This can be determined by selecting the larger of (T, -1).
[0035] According to Equation 3, each TP Max (t,s) is TP Max (t-1,1) and TP Max TP selected from (t-1,-1) Max It can be seen that this corresponds to (t-1, s'). Therefore, the first previous route TP Max (t-1,1) and the second previous route TP Max When recording the value of (t-1,-1), TP Max The time frame t- generates (t,s). You can obtain the previous state value s' in 1. In other words, TP Max After calculating (t,s), TP Max The previous state value and TP corresponding to (t,1) Max We can determine the two previous state values corresponding to (t,-1). Starting from the optimized final path and its corresponding state value s(T), we can trace back all previous state values to t=1, resulting in the state sequence.
number
[0036] The optimized state sequence may also be obtained by another approach. Based on Equation 3, each current path TP Max (t,s) is the first previous route TP Max (t-1,1) and the second previous route TP Max The previous route TP selected from (t-1,-1) Max It is known to correspond to (t-1, s'). Therefore, the state sequence may be recorded and updated continuously from the first time frame to the last time frame. In this approach, the states calculated in the previous time frame are recorded as the first previous state sequence and the second previous state sequence, and the first previous state sequence and the second previous state sequence are updated with the newly calculated results in each time frame. In particular, the first previous state sequence corresponds to the first previous path TP Max State sequence corresponding to (t-1,1)
number
number
[0037] The optimized state sequence may be determined as follows: In each time frame, the first preceding path TP Max (t-1,1), the first previous state sequence, the second previous path TP Max (t-1,-1), the second previous state sequence, and the current displacement V diff (t) is obtained. Then, based on the first previous path, the second previous path, and the current displacement, the first current path TP is obtained. Max (t,1) and the second current route TP MaxCalculate (t,-1). As mentioned above, this is the first ascending path TP Max (t-1,1)+V diff (t) and the second ascending path TP Max (t-1,-1)+V diff The larger of (t)-σ is the first current route TP Max Select (t,1) and the first descent route TP Max (t-1,1)-V diff (t)-σ and the second descending path TP Max (t-1,-1)-V diff The larger of (t) is the second current route TP Max This may be done by selecting (t,-1). Next, the first previous path and the second previous path are replaced with the first current path and the second current path, respectively, for use in the next iteration. Finally, based on the selection to obtain the first current path and the second current path, the first current state sequence corresponding to the first current path and the second current state sequence corresponding to the second current path can be obtained. For example, if the first current path is the first ascending path, the ascending states are added to the first previous state sequence to form the first current state sequence; if the first current path is the second ascending path, the ascending states are added to the second previous state sequence to form the first current state sequence; if the second current path is the first descending path, the descending states are added to the first previous state sequence to form the second current state sequence; and if the second current path is the second descending path, the descending states are added to the second previous state sequence to form the second current state sequence. Then, for use in the next iteration, the first previous state sequence and the second previous state sequence are replaced with the first current state sequence and the second current state sequence, respectively.
[0038] Repeat the above steps until the last time frame. Then, select the larger of the first current path and the second current path in the last time frame as the optimized final path, and select the entire state sequence corresponding to the optimized final path as the optimized state sequence.
[0039] [Dynamic Programming] The tasks of calculating the target value and determining the state sequence described above can be performed using a dynamic programming algorithm. As mentioned above,
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[0040] The following is a pseudocode snippet that performs a dynamic programming (DP) method for calculating the target value and determining the state sequence. Here, the TP calculated by the dynamic programming (DP) algorithm is Max We use DP(t,s) to represent (t,s).
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[0041] [Implementation Example] The computer implementation method described above addresses the limitations of conventional methods for identifying local maximums and minimums in quasi-periodic time series, particularly in applications such as cardiac signal analysis. Figures 2 and 3 show two exemplary waveform signals for which the DP algorithm detects phase transitions.
[0042] Figure 2 shows an example of a frequency-modulated (FM) signal. The top row is the original frequency-modulated (FM) signal, and some noise is added to the original signal, as shown in the middle row. A DP algorithm, which uses the standard deviation of the waveform signal as a penalty value, is applied to the noisy signal to detect signal transition points. The transition points detected by the algorithm are shown as dots on the curve in the middle row, and phase changes (rising / falling or on / off) are shown in the bottom row.
[0043] Figure 3 shows a chirp signal, another type of quasi-periodic time series. The top row is the original chirp signal, and some noise is added to the original signal, as shown in the middle row. Similarly, a DP algorithm, which uses the standard deviation of the waveform signal as a penalty value to detect transition points in the signal, is applied to the noisy signal. The transition points detected by the algorithm are shown as dots on the curve in the middle row, and the phase changes are shown in the bottom row.
[0044] In echocardiography, the DP algorithm can be used to detect end-diastolic (ED) and end-systolic (ES) frame pairs from a time series of left ventricular (LV) endocardial length extracted from echocardiographic videos. This process is essential for tracking the phases when the heart is most dilated (ED) and contracted (ES). Figures 4A and 4B illustrate an example of how the DP algorithm is used to track the contraction and relaxation cycles of the myocardium over time. The plot shows myocardial strain against time. The curve is the strain signal, with negative values indicating muscle shortening or contraction. The algorithm identifies extreme values to pinpoint important cardiac events: ES (End of Contraction, ▼): Marks the trough representing the moment of peak contraction. ED (End Diastolas, ▲): Marks the peak representing the point of maximum relaxation just before contraction begins.
[0045] [Comparison with previously available methods] Several methods are available for detecting local extrema in quasi-periodic time series. However, all of these methods have limitations. For example, conventional approaches often rely on local comparisons, which can miss or inaccurately detect peaks in complex signals. The method of the present invention detects the globally optimal local maximum value within each period of a quasi-periodic time series, thereby ensuring the identification of all important extrema for complete data analysis. Furthermore, the method of the present invention tolerates common signal deformations such as level shifts, peak breakup, and trough shape variations. Previously available methods often fail under these conditions or require multiple parameter adjustments, while the method of the present invention maintains accuracy without requiring clean and distinct peaks.
[0046] To give a concrete example, the Scipy find_peaks function is a previously available method used by the EchoNet strain algorithm and the Unity strain algorithm. It identifies local maximum values (peaks) in a one-dimensional signal based on specified conditions. Users can filter peaks by properties such as height, threshold, distance, prominence, width, and plateau size, and obtain both peak indices and a dictionary of peak characteristics. However, it requires far more parameters than the method of this application. The following are the parameters required in the Scipy find_peaks function. (1) x: A one-dimensional array of signal data from which peaks are to be analyzed. (2) Height: Required peak height or range [min, max] (3) Threshold: The vertical distance from an adjacent point, specified as a numerical value or range [min, max]. (4) Distance: The minimum sample distance between peaks. Closer, smaller peaks are removed. (5) Prominence: The difference in height from the surrounding baseline, specified as a numerical value or range [min, max]. (6) Width: The required peak width in the sample. This can be a numerical value or a range [min, max]. (7) wlen: Window length for prominence / width calculation, if provided. (8)rel_height: The percentage of prominences used for width (default 0.5). (9) plateau_size: The required flat-top size of peaks in the sample, which can be expressed as a number or range [min, max].
[0047] In contrast, the novel method of this application requires only a single parameter σ (penalty value) for transition point detection and still exhibits good extremum detection capability. The novel method enables consistent performance across datasets by reducing the need for parameter tuning. Because the novel method does not require prior knowledge of the period, it is suitable for signals with irregular periods, such as frequency-modulated signals, chirp signals, and endocardial length time series, as exemplified. Furthermore, the novel method exhibits high noise and jitter immunity, thereby maintaining accurate detection even in the presence of small noise interferences and ensuring the correct identification of extrema.
[0048] The above description of the embodiments is provided so that those skilled in the art can manufacture and use the subject matter. Various modifications to these embodiments will be readily apparent to those skilled in the art. The new principles and subject matter disclosed herein can be applied to other embodiments without the use of innovative skills. The subject matter shown and claimed in the claims is not intended to be limited to the embodiments shown herein, but the broadest scope that corresponds to the principles and novel features disclosed herein is given. Additional embodiments are intended to be within the spirit and true scope of the disclosed subject matter. Accordingly, the present invention is intended to include modifications and variations that are within the scope of the appended claims and their equivalents.
Claims
1. A computer implementation method for identifying the turning point of a waveform signal, A step of acquiring a displacement sequence including the displacement in each time frame of the waveform signal, Based on the aforementioned displacement sequence, the step of determining the state sequence that maximizes all penalty paths as the optimized state sequence, The step includes determining the position of the transition point of the waveform signal based on the optimized state sequence, The aforementioned state sequence includes state values representing the rising or falling status of the waveform signal in each time frame. A computer implementation method wherein the penalty-bearing entire path is calculated based on the displacement sequence and the entire state sequence, and a penalty value is introduced to the penalty-bearing entire path each time the state value changes in the entire state sequence.
2. The method according to claim 1, wherein the penalty value is the standard deviation of the waveform signal.
3. The method according to claim 1, wherein the penalty value is the interquartile range of the waveform signal.
4. The method according to claim 1, wherein the penalty value is the mean absolute deviation of the waveform signal.
5. The method according to claim 1, wherein the penalty value is the central absolute deviation of the waveform signal.
6. The method according to claim 1, wherein the transition point of the waveform signal is a plurality of time frames in which the state value changes in the optimized state sequence.
7. The aforementioned penalty-inclusive route is given by: [Math 1] It is calculated by, in the formula, T is the final time frame of the waveform signal, V ｄｉｆｆ (t) is the current displacement, which is the value of the displacement sequence in time frame t. s(t) is the current state value, which is the value of the entire state sequence in time frame t, and the current state value is either 1, which represents an upward status, or -1, which represents a downward status. The method according to claim 1, wherein Z(t) is a transition penalty in time frame t, and if s(t) ≠ s(t-1), Z(t) = the penalty value, and if s(t) = s(t-1), Z(t) = 0.
8. The method according to claim 1, wherein the optimized state sequence is determined by a dynamic programming algorithm.
9. The method according to claim 1, wherein the step of determining the optimized state sequence includes, in each time frame, the steps of iteratively calculating one or more penalized temporal paths and identifying one or more suboptimal temporal paths from the one or more penalized temporal paths.
10. The method according to claim 9, wherein each of the one or more penaltyed temporal paths is calculated by adding the penaltyed individual path in the current time frame to the previous temporal path in the previous time frame.
11. The method according to claim 10, wherein the penalty-bearing individual path includes current displacement and transition penalties.
12. Each of the one or more penalty-bearing time paths is calculated based on the formula TP(t, s) = TP(t-1, s') + p(t), where, TP(t, s) is the penalty-enhanced temporal path having the current state value s, TP(t-1, s') is the previous temporal path having the previous state value s', P(t) = V ｄｉｆｆ (t)・s(t) - Z(t) is the penalty-bearing individual path, in the formula, V ｄｉｆｆ (t) is the current displacement, which is the value of the displacement series in the current time frame t. s(t) is the current state value, which is the value of the entire state sequence in the current time frame t, and the current state value is either 1, which represents an upward status, or -1, which represents a downward status. The method according to claim 11, wherein Z(t) is the transition penalty in time frame t, and when s(t) ≠ s(t-1), Z(t) = the penalty value, and when s(t) = s(t-1), Z(t) = 0.
13. The method according to claim 11, wherein the one or more suboptimal temporal paths include a first current path having an ascending status in the current time frame and a second current path having a descending status in the current time frame.
14. The first current route and the second current route are calculated based on the first previous route, the second previous route, and the penalty-bearing individual route. The first preceding path is the largest of the preceding temporal paths that have an upward status in the preceding time frame, The method according to claim 13, wherein the second previous path is the largest of the previous temporal paths having a descending status in the previous time frame.
15. The method according to claim 14, wherein the first preceding path corresponds to a first preceding state sequence including state values representing the rising or falling status of the waveform signal in each time frame from the first time frame to the preceding time frame, and the second preceding path corresponds to a second preceding state sequence including state values representing the rising or falling status of the waveform signal in each time frame from the first time frame to the preceding time frame.
16. The method according to claim 15, wherein the first previous path is equal to the previous temporal path in the previous time frame calculated based on the displacement sequence and the first previous state sequence, and the second previous path is equal to the previous temporal path in the previous time frame calculated based on the displacement sequence and the second previous state sequence.
17. The step of determining the optimized state sequence is: Each time frame, an iterative step is taken to obtain the first previous path, the first previous state sequence, the second previous path, the second previous state sequence, and the current displacement. An iterative step of calculating the first current path and the second current path based on the first previous path, the second previous path, and the current displacement, The iterative step of updating the first previous path with the first current path and updating the second previous path with the second current path, The method according to claim 15, comprising the iterative step of updating the first previous state sequence with a first current state sequence corresponding to the first current path, and updating the second previous state sequence with a second current state sequence corresponding to the second current path.
18. The first current path is the larger of the first upward path and the second upward path, and the second current path is the larger of the first downward path and the second downward path. The first upward path is obtained by adding the current displacement to the first previous path, The second upward path is obtained by adding the current displacement to the previous path and subtracting the penalty value. The first descending path is obtained by subtracting the current displacement and the penalty value from the previous path. The method according to claim 17, wherein the second descending path is obtained by subtracting the current displacement from the second preceding path.
19. If the first current path is the first ascending path, the ascending state is added to the first previous state sequence to form the first current state sequence. If the first current path is the second ascending path, the ascending state is added to the second previous state sequence to form the first current state sequence. If the second current path is the first descending path, the descending state is added to the previous state sequence of the first to form the second current state sequence. The method according to claim 18, wherein if the second current path is the second descending path, the descending state is added to the second previous state sequence to form the second current state sequence.
20. In the final time frame of the waveform signal, A step of selecting the larger of the first current path and the second current path as the optimized final path, The method according to claim 17, further comprising the step of selecting the entire sequence of states corresponding to the optimized final path as the optimized sequence of states.
21. The step of determining the optimized state sequence is: Each time frame, an iterative step of obtaining the first previous path, the second previous path, and the current displacement, An iterative step of calculating the first current path and the second current path based on the first previous path, the second previous path, and the current displacement, An iterative step of recording a first previous state value corresponding to the first current path, An iterative step of recording a second previous state value corresponding to the second current path, An iteration step of updating the first previous path with the first current path for use in the next iteration, The method according to claim 14, comprising the iteration step of updating the second previous path with the second current path for use in the next iteration.
22. After calculating the first current path and the second current path in the final time frame, A step of selecting the larger of the first current path and the second current path as the optimized final path. A step of iteratively determining the previous state value from the final time frame to the first time frame, wherein the previous state value in each time frame is selected from the first previous state value and the second previous state value, The method according to claim 21, further comprising the step of obtaining the previous state values in each time frame as the optimized state sequence.