Landslide monitoring data processing method based on edge calculation

Abstract

The invention relates to the field of data processing, in particular to a landslide monitoring data processing method based on edge calculation. Comprising the following steps: acquiring original monitoring data, and transmitting the original monitoring data to an edge computing node for preprocessing to obtain monitoring data; fusing the monitoring data by adopting a dynamic weighted collaborative fusion mechanism to obtain fused data; performing feature extraction on the fused data by using an adaptive weighted wavelet transform algorithm to obtain a wavelet transform coefficient, and taking the wavelet transform coefficient as a multi-dimensional feature; calculating the amplitude of wavelet transform based on the wavelet transform coefficient; and performing weighted reconstruction on the multi-dimensional features to obtain comprehensive features after weighted reconstruction, and uploading the comprehensive features after weighted reconstruction to a data center. The technical problems that due to the fact that landslide monitoring depends on a centralized data processing mode, delay and network load are too heavy in the data transmission process, and the real-time performance and accuracy of data processing are difficult to guarantee when large-scale real-time data is faced are solved.

Description

Technical Field

[0001] The present invention relates to the field of data processing, and in particular to a landslide monitoring data processing method based on edge computing. Background Art

[0002] With the continuous development of landslide monitoring technology, more and more monitoring systems have adopted various types of sensors, such as displacement sensors, meteorological sensors, and soil moisture sensors, which can collect environmental data in the landslide area in real time and transmit the information to the central platform for analysis and processing through the data transmission network. In recent years, with the advancement of sensor technology, Internet of Things technology, and data processing algorithms, the accuracy and efficiency of landslide monitoring have been significantly improved. In particular, advanced data analysis methods such as wavelet transform and machine learning are widely used in landslide monitoring to extract meaningful features, analyze the potential risks of landslides, and provide support for timely warning and emergency response.

[0003] However, the existing landslide monitoring data processing methods have the following technical problems: landslide monitoring generally relies on centralized data processing methods, which leads to delays in data transmission and excessive network load, especially when facing large-scale real-time data, it is difficult to ensure the real-time and accuracy of data processing; traditional sensor data fusion methods use fixed weights for data fusion, lack of dynamic adjustment of the real-time status, reliability and stability of sensors, resulting in inaccurate fusion results, making it difficult to accurately reflect the actual changes in the landslide area, reducing the effectiveness and accuracy of landslide monitoring; existing wavelet transform methods fail to fully consider the dynamic change characteristics of data when processing landslide monitoring data, lack of adaptive adjustment mechanism for time and space dimensions, making it impossible to effectively capture small changes in data during landslide monitoring, especially the slow response to instantaneous changes, thus affecting the accuracy and sensitivity in practical applications. Summary of the invention

[0004] The present invention provides a landslide monitoring data processing method based on edge computing to solve the problem that landslide monitoring relies on a centralized data processing method, resulting in delays in the data transmission process and excessive network load. When facing large-scale real-time data, it is difficult to ensure the real-time and accuracy of data processing; the traditional sensor data fusion method uses fixed weights for data fusion, lacks dynamic adjustment of the real-time status, reliability and stability of the sensor, resulting in inaccurate fusion results, and it is difficult to accurately reflect the actual changes in the landslide area, thereby reducing the effectiveness and accuracy of landslide monitoring; the existing wavelet transform method fails to fully consider the dynamic change characteristics of the data when processing landslide monitoring data, lacks an adaptive adjustment mechanism for time and space dimensions, making it impossible to effectively capture small changes in the data during the landslide monitoring process, especially the slow response to instantaneous changes, thereby affecting the accuracy and sensitivity in practical applications.

[0005] The present invention provides a landslide monitoring data processing method based on edge computing, which specifically includes the following technical solutions: A landslide monitoring data processing method based on edge computing includes the following steps: S1: Collect the original monitoring data, transmit the original monitoring data to the edge computing node for preprocessing, and obtain the monitoring data; use the dynamic weighted collaborative fusion mechanism to fuse the monitoring data to obtain the fused data. The data fusion formula is as follows: , in, It's at the time The fusion data of is a time variable; is the number of sensors; is the sensor index variable; It is Dynamic weights of sensors; It is The variance of each sensor; It is The average value of the sensors; It is The square of the mean of the sensors; Is the sensor index variable, indicating the sensor, which is expressed in the data fusion formula as Other sensors for correlation analysis of sensors; It is The sensor and The covariance between the sensors is used to measure the The sensor and The linear relationship between the monitoring data series of the sensors reflects the The sensor and The mutual influence of sensors in landslide monitoring; It is The standard deviation of each sensor; It is The standard deviation of each sensor; and They are The sensor and The monitoring data sequence of each sensor; It is Sensors at time Reliability factor; After preprocessing, Monitoring data of sensors; S2: Use the adaptive weighted wavelet transform algorithm to extract features from the fused data to obtain wavelet transform coefficients. The adaptive weighted wavelet transform algorithm is a dynamic data processing method based on wavelet transform. By introducing an adaptive scale factor, the scale of the wavelet transform is dynamically adjusted according to the changes in the fused data. The adaptive scale factor calculation formula is as follows: , in, is the adaptive scale factor; It's at the time The fusion data of is the time interval; is the standard deviation of the fused data; In the implementation process of the adaptive weighted wavelet transform algorithm, based on the adaptive scale factor, combined with the specific scale and scale shift parameters, the wavelet transform coefficients are obtained to form multi-dimensional features. The calculation formula of the wavelet transform coefficients is: , in, It's at the time Wavelet transform coefficients; It is a specific scale; It is scale translation parameters; is a time variable; is the time window of the wavelet transform; is the time-integrated variable; It's at the time The fusion data of It's at the time The fusion data of is the mother wavelet function; is the standard deviation of the fused data; is the weighted term of the fusion data change; And the wavelet transform coefficients are used as multi-dimensional features; S3: Based on the wavelet transform coefficients, the amplitude of the wavelet transform is calculated; based on the amplitude of the wavelet transform, the multi-dimensional features are weighted reconstructed to obtain the weighted reconstructed comprehensive features, and the weighted reconstructed comprehensive features are uploaded to the data center for visualization.

[0006] Preferably, the S1 specifically includes: A dynamic weighted collaborative fusion mechanism is introduced to fuse the monitoring data from different sensors through the weighted average method to form landslide monitoring data, namely, fused data.

[0007] Preferably, the S1 specifically includes: The dynamic weighted collaborative fusion mechanism performs collaborative fusion among different sensor data by dynamically adjusting the weight of each sensor. The core of the dynamic weighted collaborative fusion mechanism is to determine the dynamic weight of each sensor. The dynamic weight reflects the reliability and stability of each sensor in landslide monitoring and adjusts the contribution of each sensor in data fusion in real time.

[0008] Preferably, the S3 specifically includes: By introducing the time variation of the wavelet transform coefficients and combining them with the exponential decay weighting function, the amplitude of the wavelet transform is calculated to measure the time variation of the wavelet coefficients. The specific calculation formula is as follows: , in, It's time point , at a specific scale , scale shift parameters and the amplitude of the wavelet transform under the adaptive scaling factor; It's at the time The wavelet transform coefficients of Indicates that within a specific time frame, based on a specific scale and scale shift parameters The standard deviation of the wavelet transform coefficients.

[0009] Preferably, the S3 specifically includes: Based on the amplitude of wavelet transform, multi-dimensional features are weighted reconstructed to obtain the comprehensive features after weighted reconstruction. The specific calculation formula is as follows: , in, It is a comprehensive feature after weighted reconstruction and is used to monitor the landslide area at a certain time point. The overall trend of change; is a time variable; is a quantity of a particular scale; is an index variable of a specific scale; is the number of scale-translation parameters; is the index variable of the scale translation parameter; Represents the relative degree of change and is used to weight the wavelet transform coefficients.

[0010] The beneficial effects of the technical solution of the present invention are: 1. The present invention provides a landslide monitoring data processing method based on edge computing. By preprocessing the monitoring data at the edge computing node, the real-time and accuracy of the monitoring data processing are effectively improved. The edge computing node can perform fast calculations at a location close to the data source, avoiding the delay of traditional centralized data processing and improving the response speed of landslide monitoring.

[0011] 2. The present invention adopts a dynamic weighted collaborative fusion mechanism to enable various types of sensor monitoring data to be dynamically weighted according to their respective reliability, stability and health status, effectively overcoming the problem of poor fusion effect of different sensor data in traditional technology. By adjusting the weight of each sensor in real time, it can more accurately reflect the actual changes in the landslide area, significantly improve the fusion accuracy and data processing capabilities of the monitoring data, not only ensure the scientific nature of data fusion, but also enhance the adaptability and stability of landslide monitoring in complex environments.

[0012] 3. The present invention combines an adaptive weighted wavelet transform algorithm to extract features from the fused data, obtain wavelet transform coefficients, and use them as multi-dimensional features; weighted reconstruction is performed on the multi-dimensional features, which effectively improves the multi-dimensional expression capability of landslide monitoring data. The adaptive weighted wavelet transform algorithm can capture the slight changes in the data on a time scale, and combined with the weighted reconstruction method, the comprehensive features after weighted reconstruction are obtained, which can not only accurately reflect the overall change trend of the landslide area at a specific time point, but also provide a scientific basis for subsequent landslide warning, risk assessment and emergency response. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is a flow chart of a landslide monitoring data processing method based on edge computing described in the present invention. DETAILED DESCRIPTION

[0014] In order to further explain the technical means and effects adopted by the present invention to achieve the predetermined purpose of the invention, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0015] Unless defined otherwise, 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 belongs.

[0016] The following is a detailed description of a landslide monitoring data processing method based on edge computing provided by the present invention in conjunction with the accompanying drawings.

[0017] Refer to the attached Figure 1 , which shows a flow chart of a landslide monitoring data processing method based on edge computing provided by an embodiment of the present invention, the method comprising the following steps: S1: Collect original monitoring data, transmit the original monitoring data to the edge computing node for preprocessing, and obtain monitoring data; use the dynamic weighted collaborative fusion mechanism to fuse the monitoring data and obtain fused data; First, by deploying various types of sensors, including displacement sensors, meteorological sensors, and humidity sensors, real-time data collection is performed on the landslide area. The sensors are used to monitor and record the displacement data, rainfall data, temperature data, and humidity data of the landslide area, and the monitored data is used as the original monitoring data. The original monitoring data not only reflects the changes in environmental conditions in the landslide area, but also provides early warning information on the occurrence of landslides. The collected original monitoring data is transmitted to the edge computing node in real time for subsequent processing.

[0018] After real-time data collection, the original monitoring data is obtained, and the original monitoring data is transmitted to the edge computing node for preprocessing to improve data quality and accuracy. The main steps of preprocessing include denoising, outlier detection and data normalization. Specifically, the denoising process uses a low-pass filter to filter out the high-frequency noise in the sensor signal, making the signal smoother and more stable, and reducing the impact of environmental noise on data analysis; the outlier detection process, according to the specific implementation scenario, sets a threshold or a statistical method based on the original monitoring data, such as using the z-value normalization method to calculate the standard deviation of the original monitoring data, identify outliers that deviate too far from the mean, identify and eliminate abnormal data caused by sensor failure or external factors, and ensure the reliability of subsequent analysis data; the data normalization process standardizes the multidimensional data from different sensors to the same dimensional range, for example, through linear transformation, so that the values ​​of all data fall within the range of [0, 1], which is convenient for subsequent fusion and analysis. The above preprocessing process is a prior art and will not be described here.

[0019] The original monitoring data are preprocessed to obtain monitoring data. The dynamic weighted collaborative fusion mechanism is introduced to fuse the monitoring data from different sensors through the weighted average method to form a comprehensive landslide monitoring data, namely, fused data, which is convenient for subsequent analysis and processing.

[0020] The dynamic weighted collaborative fusion mechanism achieves collaborative fusion between different sensor data by dynamically adjusting the weight of each sensor. The core of the dynamic weighted collaborative fusion mechanism is to determine the dynamic weight of each sensor. The dynamic weight reflects the reliability and stability of each sensor in landslide monitoring. The calculation of the dynamic weight not only considers the mean and variance of the sensor, but also combines the correlation and health status between the sensors. It can adjust the contribution of each sensor in data fusion in real time and provide more accurate and reliable landslide monitoring results.

[0021] The data fusion formula is as follows: , in, It's at the time The fused data represents the time point Comprehensive landslide monitoring results; is a time variable, indicating the specific time point of landslide monitoring; is the number of sensors, which is set according to the specific implementation scenario; Is the sensor index variable, indicating the Sensors; It is Dynamic weights of sensors; It is The variance of the sensor, The fluctuation range of the monitoring data of each sensor is calculated based on the monitoring data sequence, and the time range of the monitoring data sequence is set based on the expert experience method to capture the changes in the monitoring data; It is The average value of sensors, indicating The average value of the monitoring data output by the sensors is used to measure the The baseline output of each sensor is calculated based on the monitoring data series; Is the sensor index variable, indicating the sensor, which is expressed in the fusion data formula as Other sensors for correlation analysis of sensors; It is The sensor and The covariance between the sensors is used to measure the The sensor and The linear relationship between the monitoring data series of the sensors reflects the The sensor and The mutual influence of sensors in landslide monitoring; It is The standard deviation of each sensor; It is The standard deviation of each sensor; and They are The sensor and The monitoring data sequence of each sensor; It is Sensors at time The reliability factor is calculated by using the expert experience method according to Adjust the health status of each sensor (such as failure rate, usage time, signal stability, etc.); After preprocessing, Monitoring data of sensors; Through the dynamic weighted collaborative fusion mechanism, the weights of each sensor can be reasonably allocated, and the final fusion data can more accurately reflect the actual changes in the landslide area, ensuring the accuracy of the monitoring results; S2: Use the adaptive weighted wavelet transform algorithm to extract features from the fused data, obtain wavelet transform coefficients, and use the wavelet transform coefficients as multi-dimensional features; The adaptive weighted wavelet transform algorithm is used to extract features from the fused data. The adaptive weighted wavelet transform algorithm is a dynamic data processing method based on wavelet transform. The adaptability of wavelet transform is improved by introducing an adaptive scale factor. The adaptive scale factor dynamically adjusts the scale of wavelet transform according to the changes in fused data, thereby increasing the ability to capture instantaneous changes in landslide areas. A weighted term is introduced into the wavelet transform formula to adjust the change amplitude of the fused data, enhance the response ability of the wavelet transform to data changes, and further enhance the adaptability to dynamic changes.

[0022] The adaptive scale factor calculation formula is as follows: , in, It is an adaptive scale factor, which is a wavelet scale factor dynamically adjusted according to the changes of fused data, so that the wavelet transform can automatically adjust the scale of the wavelet transform according to the actual dynamic change process of the landslide; It's at the time The fusion data of It's at the time The fusion data of is the time interval, which is set according to the specific implementation scenario; It is the standard deviation of the fused data, which is used to standardize the fused data. The time range required to calculate the standard deviation of the fused data is set according to the needs of the specific implementation scenario; The calculation formula of wavelet transform coefficients is: , in, is the wavelet transform coefficient, reflecting the fusion data at the time point , based on the adaptive scale factor , specific scale and scale shift parameters The following features; It is A specific scale is used to control the degree of expansion and contraction of the wavelet transform. The value and number of the specific scale are set according to the specific implementation scenario. It is A scale shift parameter indicates the position of the wavelet transform on the time axis. The value and quantity of the scale shift parameter are set according to the specific implementation scenario. It is an adaptive scale factor, which is a wavelet scale factor dynamically adjusted according to the changes of fused data, so that the wavelet transform can automatically adjust the scale of the wavelet transform according to the actual dynamic change process of the landslide; is a time variable; is the time window of the wavelet transform, which is set according to the specific implementation scenario; is the time-integrated variable; It's at the time The fusion data of It's at the time The fusion data of It is the mother wavelet function, which represents the basis function used by wavelet transform, and is used to analyze the changes of signals at different times and scales. It is set according to the specific implementation scenario, such as Gaussian wavelet and Morley wavelet. is the standard deviation of the fused data; It is a weighted term for fusion data changes, which adjusts the influence of time points in wavelet transform according to the magnitude of data changes; After the adaptive weighted wavelet transform algorithm, wavelet transform coefficients containing multiple specific scales and scale shift parameters are obtained to form multi-dimensional features; S3: Based on the wavelet transform coefficients, the amplitude of the wavelet transform is calculated; based on the amplitude of the wavelet transform, the multi-dimensional features are weighted reconstructed to obtain the weighted reconstructed comprehensive features, and the weighted reconstructed comprehensive features are uploaded to the data center for visualization.

[0023] Based on each wavelet transform coefficient, the amplitude of the wavelet transform is calculated. By introducing the time variation of the wavelet transform coefficient and combining it with the exponential decay weighting function, the amplitude of the wavelet transform is calculated to reflect the variation of the wavelet transform coefficient under a specific scale and scale translation parameter, measure the variation of the wavelet transform coefficient over time, and thus evaluate the relative importance of the wavelet transform coefficient under a specific scale and scale translation parameter.

[0024] The specific calculation formula of the amplitude of wavelet transform is as follows: , in, It's time point , at a specific scale , scale shift parameters and the amplitude of the wavelet transform under the adaptive scaling factor; is the wavelet transform coefficient, reflecting the fusion data at the time point , based on the adaptive scale factor , specific scale and scale shift parameters The following features; is the wavelet transform coefficient, reflecting the fusion data at the time point , based on the adaptive scale factor , specific scale and scale shift parameters The following features; is the time interval; Indicates that within a specific time frame, based on a specific scale and scale shift parameters The standard deviation of the wavelet transform coefficients reflects the specific scale and scale shift parameters The fluctuation degree of the wavelet transform coefficients, wherein the time range is set according to the specific implementation scenario; is the time variation of the wavelet transform coefficients; is an exponentially decaying weighting function.

[0025] Based on the amplitude of wavelet transform, multi-dimensional features are weighted reconstructed to obtain the comprehensive features after weighted reconstruction. The specific calculation formula is as follows: , in, It is a comprehensive feature after weighted reconstruction and is used to monitor the landslide area at a certain time point. The overall trend of change; is a time variable; is a quantity of a particular scale; is an index variable of a specific scale; is the number of scale-translation parameters; is the index variable of the scale translation parameter; is the wavelet transform coefficient, reflecting the fusion data at the time point , based on the adaptive scale factor , specific scale and scale shift parameters The following features; It's time point , at a specific scale , scale shift parameters and the amplitude of the wavelet transform under the adaptive scaling factor; Represents the relative degree of change and is used to weight the wavelet transform coefficients.

[0026] The weighted reconstructed comprehensive features reflect the overall change trend of the landslide monitoring area at a specific time point, and can reflect the dynamic changes in the landslide area. Various processing can be performed according to the specific implementation scenario. For example, by analyzing the long-term change trend of the landslide monitoring area, the stability or potential risk of the landslide area can be evaluated, thereby providing a basis for risk assessment and early warning. During the landslide monitoring process, if the change amplitude of the weighted reconstructed comprehensive features exceeds the preset threshold, a real-time alarm can be triggered to remind relevant personnel to take preventive measures in time.

[0027] Finally, the weighted reconstructed comprehensive features are uploaded to the cloud or data center by edge computing nodes for visualization, allowing monitoring personnel to view the dynamic changes of landslide activities in real time, thereby providing support for emergency response and disaster prevention and mitigation.

[0028] In summary, a landslide monitoring data processing method based on edge computing was completed.

[0029] The order of the embodiments of the invention is for description only and does not represent the advantages and disadvantages of the embodiments. The processes depicted in the drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0030] The various embodiments in this specification are described in a progressive manner, and the same or similar parts between the various embodiments can be referenced to each other, and each embodiment focuses on the differences from other embodiments.

[0031] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions described in the above embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be included in the protection scope of the present invention.

Claims

1. A landslide monitoring data processing method based on edge computing, characterized in that: The following steps are involved: S1: Collect the original monitoring data, transmit the original monitoring data to the edge computing node for preprocessing, and obtain the monitoring data; use the dynamic weighted collaborative fusion mechanism to fuse the monitoring data to obtain the fused data. The data fusion formula is as follows: ， in, It's at the time The fusion data of is a time variable; is the number of sensors; is the sensor index variable; It is Dynamic weights of sensors; It is The variance of each sensor; It is The average value of the sensors; It is The square of the mean of the sensors; Is the sensor index variable, indicating the sensor, which is expressed in the data fusion formula as Other sensors for correlation analysis of sensors; It is The sensor and The covariance between the sensors is used to measure the The sensor and The linear relationship between the monitoring data series of the sensors reflects the The sensor and The mutual influence of sensors in landslide monitoring; It is The standard deviation of each sensor; It is The standard deviation of each sensor; and They are The sensor and The monitoring data sequence of each sensor; It is Sensors at time Reliability factor; After preprocessing, Monitoring data of sensors; S2: Use the adaptive weighted wavelet transform algorithm to extract features from the fused data to obtain wavelet transform coefficients. The adaptive weighted wavelet transform algorithm is a dynamic data processing method based on wavelet transform. By introducing an adaptive scale factor, the scale of the wavelet transform is dynamically adjusted according to the changes in the fused data. The adaptive scale factor calculation formula is as follows: ， in, is the adaptive scale factor; It's at the time The fusion data of is the time interval; is the standard deviation of the fused data; In the implementation process of the adaptive weighted wavelet transform algorithm, based on the adaptive scale factor, combined with the specific scale and scale shift parameters, the wavelet transform coefficients are obtained to form multi-dimensional features. The calculation formula of the wavelet transform coefficients is: ， in, It's at the time Wavelet transform coefficients; It is a specific scale; It is scale translation parameters; is a time variable; is the time window of the wavelet transform; is the time-integrated variable; It's at the time The fusion data of It's at the time The fusion data of is the mother wavelet function; is the standard deviation of the fused data; is the weighted term of the fusion data change; And the wavelet transform coefficients are used as multi-dimensional features; S3: Based on the wavelet transform coefficients, the amplitude of the wavelet transform is calculated; based on the amplitude of the wavelet transform, the multi-dimensional features are weighted reconstructed to obtain the weighted reconstructed comprehensive features, and the weighted reconstructed comprehensive features are uploaded to the data center for visualization.

2. A landslide monitoring data processing method based on edge computing according to claim 1, characterized in that: The S1 specifically includes: A dynamic weighted collaborative fusion mechanism is introduced to fuse the monitoring data from different sensors through the weighted average method to form landslide monitoring data, namely, fused data.

3. A landslide monitoring data processing method based on edge computing according to claim 2, characterized in that: The S1 specifically includes: The dynamic weighted collaborative fusion mechanism performs collaborative fusion among different sensor data by dynamically adjusting the weight of each sensor. The core of the dynamic weighted collaborative fusion mechanism is to determine the dynamic weight of each sensor. The dynamic weight reflects the reliability and stability of each sensor in landslide monitoring and adjusts the contribution of each sensor in data fusion in real time.

4. The landslide monitoring data processing method based on edge computing according to claim 1 is characterized in that: The S3 specifically includes: By introducing the time variation of the wavelet transform coefficients and combining them with the exponential decay weighting function, the amplitude of the wavelet transform is calculated to measure the time variation of the wavelet coefficients. The specific calculation formula is as follows: ， in, It's time point , at a specific scale , scale shift parameters and the amplitude of the wavelet transform under the adaptive scaling factor; It's at the time The wavelet transform coefficients of Indicates that within a specific time frame, based on a specific scale and scale shift parameters The standard deviation of the wavelet transform coefficients.

5. A landslide monitoring data processing method based on edge computing according to claim 4, characterized in that: The S3 specifically includes: Based on the amplitude of wavelet transform, multi-dimensional features are weighted reconstructed to obtain the comprehensive features after weighted reconstruction. The specific calculation formula is as follows: ， in, It is a comprehensive feature after weighted reconstruction and is used to monitor the landslide area at a certain time point. The overall trend of change; is a time variable; is a quantity of a particular scale; is an index variable of a specific scale; is the number of scale-translation parameters; is the index variable of the scale translation parameter; Represents the relative degree of change and is used to weight the wavelet transform coefficients.

Images