CN104143031A - Vegetation index time series data reconstruction method based on wavelet multi-scale decomposition - Google Patents
Vegetation index time series data reconstruction method based on wavelet multi-scale decomposition Download PDFInfo
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Abstract
The invention relates to a vegetation index time series data reconstruction method based on wavelet multi-scale decomposition. The method is characterized by comprising the following steps: performing wavelet transformation according to the vegetation index time series data to respectively sequentially decompose the original time series data of vegetation indexes and climatic factors into corresponding half moth, month, double month, season, half a year, and time series data based on interannual scales; further selecting the climatic factor time series data under the corresponding scale according to the features of the vegetation index time series data in each scale; selecting a proper model; reconstructing time series data in different scales; finally combining the vegetation index time series data in all scales to realize the reconstruction of the original vegetation index time series data. The method has the characteristics of being high in precision and wide in applicable scope.
Description
Technical field
The present invention relates to techniques of teime series analysis field, be specifically related to a kind of vegetation index (Vegetation index, VI) time series data reconstructing method based on Multiscale Wavelet Decomposition.
Background technology
Remote sensing vegetation index time series data is widely used in forest, crops vegetation Monitoring on Dynamic Change.In remote sensing data acquiring and image processing process, due to the interference of the various factorss such as observation angle and cloud, cause generated vegetation index time series data quality not ideal enough, therefore need further original vegetation index time series data to be carried out to denoising and reconstruct.
The method of the denoising of vegetation index time series data and reconstruct has a lot, as optimum gradient index extraction method (Best slope extraction, BISE), Fourier analysis method, polynary least square method, Geostatistics, non-linear Gaussian function method and S-G (Savizky-Golay) filter method etc.These methods all have certain rationality and practical reference value, but that its weak point is that vegetation index time series data generally all has is non-stationary, are not suitable for adopting stationarity method, therefore inevitably have some limitations.
Wavelet transformation, as a kind of mathematical tool of multiscale analysis, can be decomposed into the time series data on a series of different scales by original time series data effectively.The present invention carries out wavelet transformation to vegetation index time series data, by differentiating time series data on the different scale generating after wavelet decomposition, whether meet stationarity, and according to the changing character of himself, choose suitable method, respectively the time series data on different scale is chosen to suitable method and rebuild, will provide a kind of new thinking and method for the reconstruct of vegetation index time series data.
Summary of the invention
In view of this, the object of the present invention is to provide a kind of vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition, for achieving the above object, technical scheme of the present invention is: a kind of vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition, it is characterized in that: the method is based on vegetation index time series data, utilize wavelet transformation, the original time series data of vegetation index and climatic factor is decomposed into respectively to corresponding first quarter moon successively, month, bimonthly, season, time series data on half a year and year border yardstick, further according to the vegetation index time series data feature on each yardstick, select the climatic factor time series data on corresponding yardstick, choose suitable model, the time series data carrying out on different scale is rebuild, vegetation index time series data on last comprehensive all yardsticks is realized the reconstruct of original vegetation index time series data.
Method of the present invention is taken the non-stationary feature of vegetation index into account, and generalized time and space two aspect factors, according to time series data feature on the different scale generating after wavelet decomposition, adopt respectively suitable method, carries out the reconstruct of vegetation index time series data.The present invention has the features such as precision is high, applied widely.
Accompanying drawing explanation
Fig. 1 is the realization flow figure of the embodiment of the present invention.
Embodiment
Below in conjunction with drawings and the specific embodiments, the present invention is described in detail.
The present invention is based on the vegetation index time series data reconstructing method of Multiscale Wavelet Decomposition, as shown in Figure 1, utilize wavelet transformation, vegetation index original signal is decomposed into the High-frequency and low-frequency composition on a plurality of yardsticks such as corresponding first quarter moon respectively, the moon, bimonthly, season, half a year and Nian Ji, further according to the vegetation index time series data Changing Pattern on each yardstick, choose suitable model and carry out the reconstruction of vegetation index time series data, last comprehensive different scale time series data is realized the reconstruct of vegetation index time series data.
Concrete, the vegetation index time series data reconstructing method of the present embodiment based on Multiscale Wavelet Decomposition, further comprising the steps:
Step S1: set up vegetation index time series data collection.
Based on 16 days synthetic MODIS EVI (enhancement mode vegetation index) data (MOD09Q1), set up study area 2001-2011 phase vegetation index time series data collection for many years.
Step S2: set up climatic factor time series data collection.
Based on Continuous Observation climatic factor time series data collection every day, generate corresponding with the vegetation index data 16 days synthetic temperature in 2001-2011 study area, precipitation time series data collection.
Step S3: respectively vegetation index and climatic factor time series data are carried out to wavelet transformation, obtain vegetation index and climatic factor time series data collection on different scale.
Based on the female small echo of Meyer, the study area original time series data of 2001-2011 vegetation index is carried out to wavelet transformation 1 time, generate respectively low-frequency component A
1and radio-frequency component D (Approximation)
1(Detail), then to low-frequency component A
1proceed wavelet transformation, further obtain low-frequency component A
2with radio-frequency component D
2, by that analogy, until obtain the low-frequency component A after the 5th wavelet decomposition
5with radio-frequency component D
5.According to the female wavelet center frequency of Meyer and original vegetation index time series data interval, can calculate and obtain D
1, D
2, D
3, D
4, D
5, A
5the vegetation index time series data on corresponding first quarter moon, moon, bimonthly, season, half a year and year border yardstick roughly respectively.Be specially: D
1(<24 days), D
2(24-48 days), D
3(48-95 days), D
4(95-190 days), D
5(190-380 days), A
5(>380 days).
Wavelet transformation can be expressed as:
(1)
A wherein, b is respectively frequency field and time domain parameter,
for original signal,
for wavelet coefficient.
Because the little wave energy of Meyer is guaranteed that time series data is level and smooth and have the advantage such as to be simple and easy to use, therefore adopt Meyer small echo to carry out multi-scale wavelet transformation, be expressed as:
(2)
According to said method, climatic factor time series data is carried out to wavelet transformation, obtain the climatic factor time series data D on corresponding first quarter moon respectively, moon, bimonthly, season, half a year and year border yardstick
1, D
2, D
3, D
4, D
5, A
5.
Step S4: choose suitable model form, rebuild respectively D
1(first quarter moon), D
2(moon), D
3(bimonthly), D
4(season), D
5(half a year), A
5vegetation index time series data on different scales such as (year borders).
Step S4.1 adopts autoregression method to D
1(first quarter moon), D
2(moon) time series data is rebuild.Adopt akaike information criterion (Akaike Information Criterion) method to carry out determining rank to model, set up D
1, D
2autoregressive model.Model form is as follows:
(3)
Wherein, a
1, a
2a
nfor coefficient, y (t-1), y (t-2) ... y (t-n) is respectively 1,2 ... n rank autoregression item,
for residual error.
Step S4.2 adopts autoregressive model with controlled quentity controlled variable to D
3(bimonthly) and D
5(half a year), time series data was rebuild.First adopt akaike information criterion (Akaike Information Criterion) method to determine Autoregressive, then set up time series data y(D
3or D
5) with a plurality of factor time series data (D such as temperature (T) on autoregression project and corresponding yardstick and precipitation (R)
3or D
5) quantitative model.Model form is:
(4)
Wherein, a
1, a
2a
n, b, c is coefficient, y (t-1), y (t-2) ... y (t-n) is respectively 1,2 ... n rank autoregression item, the D that T is temperature index
3or D
5time series data, R is the D of precipitation index
3or D
5time series data,
for residual error.
Step S4.3 adopts linear regression model (LRM) method to D
4(season), time series data was reconstructed.With the time series data (D on the corresponding yardstick of the climatic factors such as temperature and precipitation
4) as independent variable, set up vegetation index time series data y(D on yardstick in season
4) answer the time series data (D on yardstick with a plurality of factor pairs such as temperature (T) and precipitation (R)
4) quantitative model.Model form is:
(5)
Wherein, a, b is coefficient, C is constant, the D that T is temperature index
4time series data, R is the D of precipitation index
4time series data,
for residual error.
Step S4.4 calculates the A of each pixel
5the mean value of time series data, is called vegetation signal criterion surface layer.Spatial distribution characteristic based on vegetation signal criterion surface layer, choose respectively elevation (DEM), the gradient (slope), Land Use Degree (land use intensity, LUI), mean annual temperature (Temperature, T), mean precipitation (rainfall for many years, R) and with the distance (river) in nearest river, some factors of influence such as distance (resident) with nearest residential area, first to elevation, the gradient and the accessibility factor are (apart from river, the distance in residential area) carry out log-transformation, then all independents variable are done to normalized, finally set up the linear regression model (LRM) that obtains vegetation signal criterion surface layer (B).Its model form is as follows:
(6)
Wherein,
,
for coefficient, C is constant term, DEM, Slope, River, Resident, LUI, T and R represent respectively through pretreated absolute elevation, the gradient, with the distance in river recently, with distance, Land Use Degree and the temperature in residential area and the A of precipitation index recently
5the average of time series data,
for residual error.
Obtaining on the basis of vegetation signal criterion surface layer (Base), by the A obtaining after wavelet decomposition by pixel
5time series data subtracts each other with corresponding vegetation signal criterion surface layer, obtains A
5the difference of level and reference field, is called the A of this pixel
5trend time series data.First by ADF (Augmented Dickey-Fuller test) check, determine A
5whether trend time series data meets time stationarity.If do not meet time stationarity, by difference method, ask calculation increment sequence, until increment sequence reaches steadily, thereby obtain A stably
5trend time series data.To A stably
5trend time series data, adopts AIC method to carry out determining rank to model, sets up A
5the ARMA model of trend time series data.Model form is as follows:
(7)
Wherein
for autoregressive coefficient,
for moving average coefficient,
for white noise sequence.
Step 5: by the D after rebuilding
1, D
2, D
3, D
4, D
5, A
5signal plus, thus realize the reconstruct of vegetation index time series data.
D after comprehensive redevelopment
1, D
2, D
3, D
4, D
5, A
5signal, obtains the vegetation index time series data after reconstruct
s ':
Wherein
for the time series data after rebuilding on corresponding yardstick.
The foregoing is only preferred embodiment of the present invention, all equalizations of doing according to the present patent application the scope of the claims change and modify, and all should belong to covering scope of the present invention.
Claims (9)
1. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition, it is characterized in that: the method is based on vegetation index time series data, utilize wavelet transformation, the original time series data of vegetation index and climatic factor is decomposed into respectively to corresponding first quarter moon successively, month, bimonthly, season, time series data on half a year and year border yardstick, further according to the vegetation index time series data feature on each yardstick, select the climatic factor time series data on corresponding yardstick, choose suitable model, the time series data carrying out on different scale is rebuild, vegetation index time series data on last comprehensive all yardsticks is realized the reconstruct of original vegetation index time series data.
2. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition according to claim 1, it is characterized in that: describedly based on vegetation index time series data, comprise: first, according to N days synthetic vegetation index data, generate phase vegetation index sequential image for many years; Then generate and this temperature of phase for many years, precipitation time series data that phase vegetation index time series data is corresponding for many years, N is greater than 10 natural number.
3. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition according to claim 2, is characterized in that: described N is 16.
4. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition according to claim 1, is characterized in that: also comprise by the time series data on described first quarter moon, the moon, bimonthly, season, half a year and year border yardstick respectively correspondence be defined as D
1, D
2, D
3, D
4,, D
5, A
5; Describedly choose suitable model and comprise: D
1and D
2adopt autoregressive model, D
3and D
5employing is with the autoregressive model of controlled quentity controlled variable, D
4adopt linear regression model (LRM), A
5first adopt trend surface model to carry out overall fit, then to residual error, partly adopt difference to move autoregressive model.
5. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition according to claim 4, is characterized in that: described D
1and D
2adopt the implementation of autoregressive model to be: to adopt akaike information criterion (Akaike Information Criterion is called for short AIC) to carry out determining rank to model, set up D
1, D
2autoregressive model; Model form is as follows:
Wherein, a
1, a
2a
nfor coefficient, y (t-1), y (t-2) ... y (t-n) is respectively 1,2 ... n rank autoregression item,
for residual error.
6. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition according to claim 4, is characterized in that: described D
3and D
5employing with the implementation of the autoregressive model of controlled quentity controlled variable is: first adopt akaike information criterion (Akaike Information Criterion, being called for short AIC) method determines Autoregressive, then sets up the quantitative model of time series data y and the time series data of temperature T on autoregression item and corresponding yardstick and precipitation R; Model form is:
Wherein, a
1, a
2a
n, b, c is coefficient, y (t-1), y (t-2) ... y (t-n) is respectively 1,2 ... n rank autoregression item, the D that T is temperature index
3or D
5time series data, R is the D of precipitation index
3or D
5time series data,
for residual error.
7. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition according to claim 4, is characterized in that: described D
4adopt the implementation of linear regression model (LRM) to be: with the D on temperature and the corresponding yardstick of rainfall factor
4time series data, as independent variable, is set up vegetation index time series data y(D on yardstick in season
4) answer the D on yardstick with temperature T and precipitation R factor pair
4the quantitative model of time series data; This model form is:
Wherein, a, b is coefficient, C is constant, the D that T is temperature index
4time series data, R is the D of precipitation index
4time series data,
for residual error.
8. the vegetation index time series data reconstructing method based on Multiscale Wavelet Decomposition according to claim 4, is characterized in that: the A that calculates each pixel
5the mean value of time series data, is called vegetation signal criterion surface layer, spatial distribution characteristic based on vegetation signal criterion face, choose respectively elevation (DEM), the gradient (slope), Land Use Degree (land use intensity, LUI), mean annual temperature (temperature, T), mean precipitation (rainfall for many years, R) and with the distance (river) in nearest river, some factors of influence such as distance (resident) with nearest residential area, first to elevation, the gradient and the accessibility factor are (apart from river, the distance in residential area) carry out log-transformation, then all independents variable are done to normalized, finally set up the linear regression model (LRM) that obtains vegetation signal criterion surface layer (B), its model form is as follows:
Wherein,
,
for coefficient, C is constant term, DEM, Slope, River, Resident, LUI, T and R represent respectively through pretreated absolute elevation, the gradient, with the distance in river recently, with distance, Land Use Degree and the temperature in residential area and the A of precipitation index recently
5the average of time series data,
for residual error;
Obtaining on the basis of vegetation signal criterion surface layer (Base), by the A obtaining after wavelet decomposition by pixel
5time series data subtracts each other with corresponding vegetation signal criterion surface layer, obtains A
5the difference of level and reference field, is called the A of this pixel
5trend time series data; First by ADF (Augmented Dickey-Fuller test) check, determine A
5whether trend time series data meets time stationarity;
If do not meet time stationarity, by difference method, ask calculation increment sequence, until increment sequence reaches steadily, thereby obtain A stably
5trend time series data; To A stably
5trend time series data, adopts akaike information criterion (Akaike Information Criterion is called for short AIC) method to carry out determining rank to model, sets up A
5the ARMA model of trend time series data; Model form is as follows:
Wherein
for autoregressive coefficient,
for moving average coefficient,
for white noise sequence.
9. according to claim 1 a kind of based on the multi-level vegetation index time series data reconstructing method decomposing of small echo, it is characterized in that: the method is applied in time series data denoising, reconstruct and prediction field.
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