## Use The Coiflets and Daubechies Wavelet Transform To Reduce Data Noise For a Simple Experiment | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

IRAQI JOURNAL OF STATISTICAL SCIENCES | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Article 9, Volume 19, Issue 2, December 2022, Pages 91-103 PDF (1.31 M)
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Document Type: Research Paper | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

DOI: 10.33899/iqjoss.2022.176225 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Authors | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Mahmood M Taher^{*} ^{1}; Sabah Manfi Redha^{2}
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^{1}Department of Informatics & Statistic, College of Computer & Mathematical Science, University of Mosul, Mosul, Iraq | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

^{2}Department of Statistics, College of Administration And Economics , Baghdad University, Iraq. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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In this research, a simple experiment in the field of agriculture was studied, in terms of the effect of out-of-control noise as a result of several reasons, including the effect of environmental conditions on the observations of agricultural experiments, through the use of Discrete Wavelet transformation, specifically (The Coiflets transform of wavelength 1 to 2 and the Daubechies transform of wavelength 2 To 3) based on two levels of transform (J-4) and (J-5), and applying the hard threshold rules, soft and non-negative, and comparing the wavelet transformation methods using real data for an experiment with a size of 2^{6} observations. The application was carried out through a program in the language of MATLAB. The researcher concluded that using the wavelet transform with the Suggested threshold reduced the noise of observations through the comparison criteria. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Highlights | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

2- Obtaining the best results when applying the hard threshold rule with the Universal and suggested threshold according to standards. 3-When processing the observations noise (wheat crop 2 4-When processing the observations noise (wheat crop 2 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Keywords | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

Data Noise; Wavelet; Coiflets; Daubechies; Random Complete Blocks Design | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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The Discrete Wavelet transformation is one of the very important topics used in several application fields, especially in data noise processing. In general, noise represents an unexplained variance within the data (Reid & Reading,2010); that is, it cannot be eliminated. But it can be reduced in several ways according to the study or its field of application. In agricultural experiments, the experiment is divided into blocks. It replicates according to the different experimental units, which directly or indirectly affect the observation value, resulting from the mathematical model according to the applied design. The method or procedure cannot be controlled in most experiments due to out-of-control conditions during the application of the experiment. The wavelet transform has been discussed in addressing pollution and heterogeneity (Ali & Mawlood,2010) for the complete randomized design using wavelet filters and some types of threshold rules. In addition, a threshold was Suggested to reduce the observations noise for a factorial experiment by (Taher&Sabah,2022) compared with the Universal Threshold. In this research, the application of different levels of analysis, through the use of the Daubechies transform of wavelengths from 2 to 3 and the transformation of Coiflets of wavelengths from 1 to 2 with hard, soft, and non-negative threshold rules, and comparison of the results.
The Discrete wave transform is one of the most Transfers used in the wavelet due to its multiple applications in various practical fields and its theoretical uses in various sciences. The researcher will give a comprehensive idea of this transformation and focus on its use in designing experiments Through the application of a simple experiment. The work of the discrete wavelet transform depends on the Mallat pyramidal algorithm, which is an efficient algorithm proposed by the researcher Mallat (1989) (Nason, 2008) to calculate the wavelet coefficients for a set of data containing noise The principle of The work of this algorithm is to create filters for smoothing and heterogeneity from the wavelet coefficients, and these filters are used frequently to obtain data for all scales, meaning that the wavelet transform splits the data into two components, the first component is called detail, which includes high frequencies and can be calculated from the mother wavelet by the following formula ( In & Kim, 2013)
Whereas Represents a high-pass filter (In & Kim, 2013) he Second component is called Approximate, which includes low frequencies (noise) or (anomalous) values according to the nature of the study and its application, and it can be calculated from the father wavelet by the following formula: (In, F., & Kim, S 2013)
Whereas Represents a low-pass filter, (In & Kim, 2013).and it is related to through
The following figure shows the division of data into two components
In general, the discrete wavelet transform is used with data that contain discrete variables and have discrete outputs.
We will give a brief overview of the key concepts of multiscale analysis before attempting formal definitions of wavelets and the wavelet transform and How we extract multiscale "information" from the vector y . We identify the "detail" in the sequence at various scales and places as the essential information. Transform levels are determined from the design observation, and through the application side, we will have a simple experiment containing sixteen treatments and four blocks represented by the following vector.
Through the observations vector, the levels of analysis for this experiment will be (Nason, 2008). The next stage is how to extract information from vector , where the information extracted from vector It is called (detail), which can be obtained from different locations and levels, and in general, the word "detail" means "degree of difference" or "variance" in the observations of the vector. This information is calculated based on the following two equations (Nason,2008).
The next step is calculating the elaboration and measurement coefficients for the other levels (Nason,2008).
This process is called the multiscale transform algorithm, Through the simple experiment applied, we will have the following levels { (j) , (j-1) , (j-2) , (j-3) , (j-4) , (j-5)}.
Whereas observation value (j) from treatment (i), The general arithmetic mean, The effect of the i-treatment for this observation, The amount of random error , number of treatments number of blocks
The vector x contains all the observations of the experiment. One of the critical conditions in the wavelet transformation is The size of the observations fulfills the following condition.
whereas The wavelet coefficients vector Orthogonal matrix Vector observation From the formula (9), we get a vector coefficient of a discrete wavelet which can be represented in the following form.
Whereas, Represents the first component of the transform, which is the detail coefficients computed from the rate of the difference of the data at each measurement and is symbolized by CD. As for Represents the second component of the transform, which is the approximation coefficients and represents the rate of The measurement is symbolized by CA.
To clarify what was mentioned above, we take the following figure, which shows the discrete wavelet transformation coefficients for the data for four levels .
Several types of Wavelets exist through the above offer About Discrete Wavelet transformation and orthogonality. In this research, we will address: Daubechies Wavelet, Coiflets Wavelet
Equation (7) represents the Universal Threshold (UT) value (Gençay et al.,2001) (Zhang et al., 2021), while equation (8) represents the Suggested Threshold (ST) (Taher & Ridha, 2022).
The name came in relation to the researcher Ingrid Daubechies (Tammireddy & Tammu, 2014). It has made a boom in the wavelet theory, as it is generated from a group of intermittent wavelets. The most crucial characteristic of this family of wavelets is their smoothness. It is abbreviated as follows. where's Db: Abbreviation for the name of the researcher Daubechies N: Wavelet rank considered wavelet haar of one the members of this family of wavelets and is symbolized by the symbol db1 or The wavelet is called Daubechies the first order Because built from the function of the father (father wave), the function of the mother (mother wave), as follows (Tammireddy & Tammu, 2014).
Where Daubechies scaling function coefficients
Where Daubechies wavelet function coefficients
Figure Next represents a Daubechies Wavelet of several lengths
They are discrete wavelets designed by Ingrid Daubechies, at the request of Ronald Coifman (Tammireddy & Tammu, 2014). where's : Abbreviation for the name of the researcher Ronald Coifman : Wavelet rank This family of wavelets is characterized by the presence of a relationship that relates the length of the filter with its rank
It is also built from the father function (father wavelet) and mother function (mother wavelet), in the following formula (Tammireddy & Tammu, 2014)
Where Coiflets scaling function coefficients
Where Coiflets wavelet function coefficients ,
This family of wavelets is considered orthogonal and is close to symmetry, as it connects the mother and father function through the high-pass filter and the low-pass filter by obtaining the vanishing torque, unlike each filter separately.
Three types of threshold rules will be applied in this research, namely:
One of the types of threshold rules, it is applied in discrete wavelet transform and takes the following form (Dehda & Melkemi, 2017),( Zaeni et al.,2018).
Through the formula (9) where the coefficients whose values are greater and equal to the threshold do not change, and the coefficients whose values are less than the threshold are replaced by the value zero
It is another type of threshold rule and can be written as (Bruce & Gao , 1995).
And It is considered one of the standard techniques for processing observational noise (Tang et al., 2013) (Han & Xu, 2016).
Through the above formulas (10) and (11), we note that if the coefficients of the wavelet are less than the threshold value, it goes to zero, but in the case of being greater than the threshold value, it preserves its value. Using a Shrinking wavelet based on a soft-threshold rule tends to bias because all large coefficients Shrink towards zero.
This threshold is characterized by the small samples. It is less sensitive to observation than the hard threshold, especially in small fluctuations, and it is less biased than the soft threshold and can be written as follows (Gao,1997).
It is also the base of wavelet Shrink introduced by Gao
For the purpose of comparing the results between the Coiflets Wavelet Transformation and the Daubechies Wavelet Transformation, several criteria were applied,
1- Where total sum of squares , treatments Sum of squares , blocks Sum of squares
,
8.4.
Where’s: , and The following diagram shows the steps of the wavelet transform, with the comparison criteria
Figure (5):
The field experiment on wheat cultivation was conducted in one of the stations of the National Program for the Development of Wheat Cultivation in Iraq, and sixteen wheat varieties were included.(al sds (12) A1, al sahel (1)A2 , al sds (1)A3 , Egypt (1)A4 .Egypt (2) A5, Sakha (93)A6, al Geza (11)A7, al Geza (168)A8, Apaa (99)A9, Italia(1)A10, Italia (2)A11, Caronia A12, gold kernels A13, aom al rabee A14, Smitto A15, Waha A16). According to the complete random blocks design (CRBD) of four blocks, each block contained 16 experimental units. Then the characteristics of the field yield were taken, which are (number of branches, plant height cm, dry weight of g, number of spikes / m By applying equations (10-19) on experiment observations, The results are shown in table (1), Which represents a summary of wavelet transformation when the level of analysis is (J-4)
By applying equations (10-19) on experiment observations, The results are shown in table (2), Which represents a summary of wavelet transformation when the level of analysis is (J-5)
Table (1) represents a summary of the wavelet transform results for all cases when the transform level is (J-4), where led to decline in the MSe value of the used design and a significant improvement in the CV criterion. In addition to obtaining low values for the standard .with an increase in the SNR criterion value, Especially for ( Table(2) represents a summary of the wavelet transform results for all cases when the transform level is (J-5), where led to decline in the MSe value of the used design and a significant improvement in the CV criterion. In addition to obtaining low values for the standard .with an increase in the SNR criterion value, Especially for( Where
2- Obtaining the best results when applying the hard threshold rule with the Universal and suggested threshold according to standards. 3-When processing the observations noise (wheat crop 2 4-When processing the observations noise (wheat crop 2 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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[1] Ali, Taha, Husean & Mawlod , Kurdestan ,Ibrahem (2010)." Addressing the problem of contamination and variance heterogeneity in a complete random design using a small wave filter",Iraqi Journal of Statistical Science,No.18,Issue.10. [2]. Bruce, A. G., & Gao, H. Y. (1995, September). WaveShrink: Shrinkage functions and thresholds. In [3]. Dehda, B., & Melkemi, K. (2017). Image denoising using new wavelet thresholding , Function. [4]. Gao, H. Y. (1997). [5]. Gençay, R., Selçuk, F., & Whitcher, B. J. (2001). An introduction to wavelets and other Filtering methods in finance and economics. Elsevier. [6]. Han, G., & Xu, Z. (2016). Electrocardiogram signal denoising based on a new improved, Wavelet thresholding. [7]. He, C., Xing, J. C., & Yang, Q. L. (2014). Optimal wavelet basis selection for wavelet denoising of structural vibration signal. In Applied Mechanics and Materials (Vol. 578, pp. 1059-1063). Trans Tech Publications Ltd. [8]. In, F., & Kim, S. (2013). An introduction to wavelet theory in finance: a wavelet multiscale Approach. World Scientific. [9]. Montgomery, D. C. (2020). Design and analysis of experiments. John Wiley & sons. [10]. Nason, G. P. (Ed.). (2008). Wavelet methods in statistics with R. New York, NY: Springer New York. [11]. Taher, M. M., & Ridha, S. M. (2022). The suggested threshold to reduce data noise for A factorial experiment. [12]. Tammireddy, P. R., & Tammu, R. (2014). Image reconstruction using wavelet Transform with extended fractional Fourier transform. [13]. Tang, H., Liu, Z. L., Chen, L., & Chen, Z. Y. (2013). Wavelet image denoising based the new threshold function. In [14]. Zaeni, A., Kasnalestari, T., & Khayam, U. (2018, October). Application of wavelet Transformation symlet type and coiflet type for partial discharge signals denoising. In [15]. Zhang, Y., Zhou, H., Dong, Y., & Wang, L. (2021). Restraining EMI of Displacement Sensors Based on Wavelet Fuzzy Threshold Denoising. In Signal and Information Processing, Networking, and Computers (pp. 543-551). Springer, Singapore.
The Discrete Wavelet transformation is one of the very important topics used in several application fields, especially in data noise processing. In general, noise represents an unexplained variance within the data (Reid & Reading,2010); that is, it cannot be eliminated. But it can be reduced in several ways according to the study or its field of application. In agricultural experiments, the experiment is divided into blocks. It replicates according to the different experimental units, which directly or indirectly affect the observation value, resulting from the mathematical model according to the applied design. The method or procedure cannot be controlled in most experiments due to out-of-control conditions during the application of the experiment. The wavelet transform has been discussed in addressing pollution and heterogeneity (Ali & Mawlood,2010)for the complete randomized design using wavelet filters and some types of threshold rules. In addition, a threshold was Suggested to reduce the observations noise for a factorial experiment by (Taher&Sabah,2022) compared with the Universal Threshold. In this research, the application of different levels of analysis, through the use of the Daubechies transform of wavelengths from 2 to 3 and the transformation of Coiflets of wavelengths from 1 to 2 with hard, soft, and non-negative threshold rules, and comparison of the results.
The Discrete wave transform is one of the most Transfers used in the wavelet due to its multiple applications in various practical fields and its theoretical uses in various sciences. The researcher will give a comprehensive idea of this transformation and focus on its use in designing experiments Through the application of a simple experiment. The work of the discrete wavelet transform depends on the Mallat pyramidal algorithm, which is an efficient algorithm proposed by the researcher Mallat (1989) (Nason, 2008) to calculate the wavelet coefficients for a set of data containing noise The principle of The work of this algorithm is to create filters for smoothing and heterogeneity from the wavelet coefficients, and these filters are used frequently to obtain data for all scales, meaning that the wavelet transform splits the data into two components, the first component is called detail, which includes high frequencies and can be calculated from the mother wavelet by the following formula ( In & Kim, 2013) Whereas Represents a high-pass filter (In & Kim, 2013) he Second component is called Approximate, which includes low frequencies (noise) or (anomalous) values according to the nature of the study and its application, and it can be calculated from the father wavelet by the following formula: (In, F., & Kim, S 2013) Whereas Represents a low-pass filter, (In & Kim, 2013).and it is related to through
The following figure shows the division of data into two components
In general, the discrete wavelet transform is used with data that contain discrete variables and have discrete outputs.
We will give a brief overview of the key concepts of multiscale analysis before attempting formal definitions of wavelets and the wavelet transform and How we extract multiscale "information" from the vector y . We identify the "detail" in the sequence at various scales and places as the essential information. Transform levels are determined from the design observation, and through the application side, we will have a simple experiment containing sixteen treatments and four blocks represented by the following vector. Through the observations vector, the levels of analysis for this experiment will be (Nason, 2008). The next stage is how to extract information from vector , where the information extracted from vector It is called (detail), which can be obtained from different locations and levels, and in general, the word "detail" means "degree of difference" or "variance" in the observations of the vector. This information is calculated based on the following two equations (Nason,2008). The next step is calculating the elaboration and measurement coefficients for the other levels (Nason,2008). This process is called the multiscale transform algorithm, Through the simple experiment applied, we will have the following levels { (j) , (j-1) , (j-2) , (j-3) , (j-4) , (j-5)}.
Whereas observation value (j) from treatment (i), The general arithmetic mean, The effect of the i-treatment for this observation, The amount of random error , number of treatments number of blocks The vector x contains all the observations of the experiment. One of the critical conditions in the wavelet transformation is The size of the observations fulfills the following condition.
whereas The wavelet coefficients vector Orthogonal matrix Vector observation From the formula (9), we get a vector coefficient of a discrete wavelet which can be represented in the following form.
Whereas, Represents the first component of the transform, which is the detail coefficients computed from the rate of the difference of the data at each measurement and is symbolized by CD. As for Represents the second component of the transform, which is the approximation coefficients and represents the rate of The measurement is symbolized by CA.
To clarify what was mentioned above, we take the following figure, which shows the discrete wavelet transformation coefficients for the data for four levels .
Several types of Wavelets exist through the above offer About Discrete Wavelet transformation and orthogonality. In this research, we will address: Daubechies Wavelet, Coiflets Wavelet
Equation (7) represents the Universal Threshold (UT) value (Gençay et al.,2001)(Zhang et al., 2021), while equation (8) represents the Suggested Threshold (ST) (Taher & Ridha, 2022).
The name came in relation to the researcher Ingrid Daubechies (Tammireddy & Tammu, 2014). It has made a boom in the wavelet theory, as it is generated from a group of intermittent wavelets. The most crucial characteristic of this family of wavelets is their smoothness. It is abbreviated as follows. where's Db: Abbreviation for the name of the researcher Daubechies N: Wavelet rank considered wavelet haar of one the members of this family of wavelets and is symbolized by the symbol db1 or The wavelet is called Daubechies the first order Because built from the function of the father (father wave), the function of the mother (mother wave), as follows (Tammireddy & Tammu, 2014).
Where Daubechies scaling function coefficients
Where Daubechies wavelet function coefficients
Figure Next represents a Daubechies Wavelet of several lengths
They are discrete wavelets designed by Ingrid Daubechies, at the request of Ronald Coifman (Tammireddy & Tammu, 2014). where's : Abbreviation for the name of the researcher Ronald Coifman : Wavelet rank This family of wavelets is characterized by the presence of a relationship that relates the length of the filter with its rank It is also built from the father function (father wavelet) and mother function (mother wavelet), in the following formula (Tammireddy & Tammu, 2014)
Where Coiflets scaling function coefficients
Where Coiflets wavelet function coefficients ,
This family of wavelets is considered orthogonal and is close to symmetry, as it connects the mother and father function through the high-pass filter and the low-pass filter by obtaining the vanishing torque, unlike each filter separately.
Three types of threshold rules will be applied in this research, namely:
One of the types of threshold rules, it is applied in discrete wavelet transform and takes the following form (Dehda & Melkemi, 2017),( Zaeni et al.,2018). Through the formula (9) where the coefficients whose values are greater and equal to the threshold do not change, and the coefficients whose values are less than the threshold are replaced by the value zero
It is another type of threshold rule and can be written as (Bruce & Gao , 1995). And It is considered one of the standard techniques for processing observational noise (Tang et al., 2013) (Han & Xu, 2016). Through the above formulas (10) and (11), we note that if the coefficients of the wavelet are less than the threshold value, it goes to zero, but in the case of being greater than the threshold value, it preserves its value. Using a Shrinking wavelet based on a soft-threshold rule tends to bias because all large coefficients Shrink towards zero.
This threshold is characterized by the small samples. It is less sensitive to observation than the hard threshold, especially in small fluctuations, and it is less biased than the soft threshold and can be written as follows (Gao,1997). It is also the base of wavelet Shrink introduced by Gao
For the purpose of comparing the results between the Coiflets Wavelet Transformation and the Daubechies Wavelet Transformation, several criteria were applied,
1- Where total sum of squares , treatments Sum of squares , blocks Sum of squares
,
8.4. Where’s: , and The following diagram shows the steps of the wavelet transform, with the comparison criteria
Figure (5):
The field experiment on wheat cultivation was conducted in one of the stations of the National Program for the Development of Wheat Cultivation in Iraq, and sixteen wheat varieties were included.(al sds (12) A1, al sahel (1)A2 , al sds (1)A3 , Egypt (1)A4 .Egypt (2) A5, Sakha (93)A6, al Geza (11)A7, al Geza (168)A8, Apaa (99)A9, Italia(1)A10, Italia (2)A11, Caronia A12, gold kernels A13, aom al rabee A14, Smitto A15, Waha A16). According to the complete random blocks design (CRBD) of four blocks, each block contained 16 experimental units. Then the characteristics of the field yield were taken, which are (number of branches, plant height cm, dry weight of g, number of spikes / m By applying equations (10-19) on experiment observations, The results are shown in table (1), Which represents a summary of wavelet transformation when the level of analysis is (J-4)
By applying equations (10-19) on experiment observations, The results are shown in table (2), Which represents a summary of wavelet transformation when the level of analysis is (J-5)
Table (1) represents a summary of the wavelet transform results for all cases when the transform level is (J-4), where led to decline in the MSe value of the used design and a significant improvement in the CV criterion. In addition to obtaining low values for the standard .with an increase in the SNR criterion value, Especially for ( Table(2) represents a summary of the wavelet transform results for all cases when the transform level is (J-5), where led to decline in the MSe value of the used design and a significant improvement in the CV criterion. In addition to obtaining low values for the standard .with an increase in the SNR criterion value, Especially for( Where
2-Obtaining the best results when applying the hard threshold rule with the Universal and suggested threshold according to standards. 3-When processing the observations noise (wheat crop 2 4-When processing the observations noise (wheat crop 2 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||

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