# Application of Image Denoising Algorithm and Data Mining in Psychological Teaching Quality Evaluation

Authors: Lingling Li
Journal: Security and Communication Networks
 (2022)

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## Abstract

In order to improve the psychological teaching quality of college students, this paper combines image denoising algorithm and data mining algorithm to construct a psychological teaching quality evaluation system. The denoising algorithm is mainly used to identify the behavior and expressions of the students so as to explore the psychological state of the students. Moreover, this paper combines the data mining algorithm to carry out the quantitative analysis of students’ psychological state and analyzes and introduces the calibration principle of Dirckx method in detail to improve it and then forms a new calibration method. In addition, based on the arctangent function, this paper proposes a new two-frame random phase-shift fringe image phase shift extraction algorithm. The research results show that the image denoising algorithm and data mining proposed in this paper have a good effect in the evaluation method of psychological teaching quality and can play a good role in the improvement of students’ mental health.


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## Body

## 1. Introduction

Traditional education focuses on indoctrination and information and technology training, while disregarding students’ life experiences. This is represented in traditional education techniques that overlook the development of human personality, thereby ignoring creativity and the perfection of human nature. Learning is emphasised in terms of mastering book information, memory, and skill training, but genuine knowledge and personal practise are ignored. Individual features and values are ignored in the teaching paradigm, which stresses compliance and obeys the norms. The evaluation paradigm stresses a single summative assessment, which validates the test winners while ignoring the majority of losers and so on. In reality, traditional education has played a significant role in the historical arena of social progress. However, now that the bell of reform in China’s modern education is ringing anew, we must think thoroughly, and seeking breakthroughs and transcendence of conventional education has become a requirement for social progress. When the whole world laments the loss of human nature and lack of emotion in education, we should recognise that the absence of human nature, emotion, will, and experience has become a mystery and dilemma that the entire world is grappling with. Furthermore, the quest of experience is no longer only a slogan, and it is eager to put it into action. As a result, one of the most important concerns in school education study and investigation is paying attention to students’ educational experiences.The psychological expansion training has a certain foundation in the school physical education curriculum. For example, in the implementation process, it is favored by students and recognized by the school, and some basic problems in the curriculum have been solved (the theoretical basis of psychological expansion, curriculum and resource development, implementation of some basic conditions, etc.); feasibility demonstration and local experiments in practice have achieved good results. However, due to the short time of introduction to the school, the lack of comprehensive understanding, insufficient systematic theoretical preparation, and insufficient authority for feasibility demonstrations, the implementation of psychological development training courses is still in the simple imitation stage of “following gourds and drawing scoops.” There are many problems in the current teaching mode of psychological expansion training in schools, such as the nihilization of guiding ideology, the representation of operating procedures, and the formalization of operating procedures. There are still many problems that need to be clarified through research on how the school’s psychological development training courses can stand up to the scrutiny of pedagogy, psychology, curriculum theory, and so on, to form a real curriculum of healthy and sustainable development.Schools and other organisations are increasingly paying attention to students’ mental health difficulties. Many colleges and universities have made mental health education a requirement for freshman as a quality education course. However, several issues remain in the development of mental health education courses at this time, such as huge class teaching, where instructors are unable to take into consideration every student. Furthermore, the substance of this topic is not directly related to students’ psychological requirements. Simultaneously, it lacks a structured and functional course assessment mechanism, and the professors themselves are of low professional and personal quality. Various researchers have conducted relevant research in the areas of teaching techniques, teaching goals, teaching material, and teaching instructors in order to address the many challenges that modern college students encounter in their mental health education and have offered some recommendations. For example, instead of fixing students’ psychological issues as the daily aim, they focus on their physical and mental health growth, and they employ the flipped classroom teaching technique.This paper combines image denoising algorithm and data mining algorithm to construct a psychological teaching quality evaluation system and improves the effect of contemporary students’ mental health education through an intelligent system.


## 2. Related Work

Scholars who hold the teaching concept of solving students’ psychological development problems believe that college students’ mental health education courses should actively pay attention to students’ internal needs and help students better cope with difficulties in study and life. Scholars who attach importance to the development of students’ potential think that mental health education courses should pay more attention to the development of students’ potential [1]. Pay attention to the positive and unique qualities of each student, and believe that mental health education courses oriented to solve students’ psychological problems, neglecting the more important and better aspects of individual development, ignoring positive psychological experience and the development of positive psychological potential, putting the cart before the horse in the teaching goal of mental health education, and weakening the effectiveness of school mental health teaching [2]. Literature [3] believes that the ultimate goal of college students’ mental health education course should be to fully develop students’ potential, focusing on the positive side of students rather than focusing on students’ existing psychological problems to carry out teaching. These two completely different teaching philosophies seem to be contradictory, but in fact, they both share the same purpose, that is, to help students grow better. The two teaching concepts have their own advantages, and the single use of any one concept in teaching cannot maximize the effectiveness of mental health education. In the process of teaching practice, these two teaching concepts can be used in combination. For some common and negative psychological problems, teachers of mental health education have the responsibility to guide students to have a correct understanding [4]. Teachers should also pay attention to students’ positive and unique personalities and maximize their potential. Therefore, proper guidance and correction should be given to negative and general psychological problems, and attention and support should be given to the positive and unique advantages of individuals. Not only are these two directions not contradictory, but if they can be taken into account at the same time, it will be beneficial to students and teachers alike. It is of great benefit to oneself [5].In colleges and universities, the substance of mental health classroom training is slightly lacking. One of the metrics used to assess the success of mental health education is the classroom teaching impact [6]. Classroom teaching success may be measured in three ways: if it is staffed with qualified instructors, whether the material is scientific and rational, and whether the teaching format suits the requirements of students. Many psychology professors, according to the professional staff, do not have a firm psychological base and lack professional psychological counselling abilities [7]. Some are ideological and political education professors in colleges and universities, others are senior school administrators who, due to their age and health, are unable to meet the demands of administrative work, and still others are family members of teachers who are unable to be “properly placed” [8]. Although most instructors can grasp the real requirements of students via surveys, visits, and other means and provide focused explanations, the transfer of this information often occurs only at the level of awareness. The “subconsciousness” of mental health education necessitates that mental health education classroom instruction reach the subconscious level in order to successfully combine with the conscious level and profoundly address students’ difficulties [9]. Most colleges and universities provide conventional face-to-face mental health education courses, based on the teaching format. Teachers talk and pupils listen in conventional classrooms. It is uncommon for kids to be able to ask inquiries concerning their own concerns. They may only look for stuff that is useful to them among the information offered by professors. Learning is not only ineffective, but also inactive [10].The teaching goal of the mental health education course is to improve the mental health awareness and psychological quality of college students and to improve the ability of psychological adjustment. The ultimate goal of the course is to apply the knowledge of mental health learned in the classroom to daily life, which requires the integration of “classroom teaching, psychological experience and behavioral training” [11]. Specifically, it is required to focus on practicality and operability in teaching content and in teaching methods from focusing on teaching methods to learning methods. Unify, learn to effectively apply psychological knowledge to solve psychological confusion and psychological problems in real life, improve psychological quality, and effectively solve and deal with practical problems [12]. Project-based teaching can better meet the above requirements. The main feature of project-based teaching is to decompose the course content into a number of specific and implementable teaching tasks and combine the themes closely related to social practice to form time- and resource-limited projects with clear goals, which are highlighted through the implementation of projects [13].For a long time, students have paid little attention to mental health education as a public mandatory subject at higher vocational institutions. Traditional teaching approaches are often used in mental health education and teaching, stressing theory while disregarding practise. The prevalent psychological attitude of professors and students for this subject is a hatred of teaching and pupils [14]. Or, on the other hand, the teaching method places too much emphasis on activities and employs a variety of games to carry them out, incorrectly equating games with group tutoring and failing to encourage students to consider the meaning of games. The impact is relatively little after the exercise, and the teaching effect is not perfect. This humiliating situation may be successfully changed by implementing project-based education reform and including psychological practise activities. Practical, real-life exercises will totally pique students’ attention, activate their passion, encourage them to engage, and teach them something [15].


## 3. Application of Image Denoising Algorithm in Students’ Psychological Exploration

The image denoising algorithm in this paper is mainly used to identify students’ behaviors and expressions, which is convenient for exploring students’ psychological state. It combines data mining algorithm for quantitative analysis of students’ psychological state. Therefore, the image algorithm in this paper needs to be studied first.By analyzing the measurement principle of the shadow Moiré of phase shift, it can be known that when the conditionh≫z is satisfied, the introduced phase shift increment can be simplified to δ=2πdΔh/ph. At this time, if the measurement phase is known, the height value of the object can be obtained, and the calculation formula is as follows:(1)zx,y=p⋅h2πdϕx,y=s2πϕx,y.In formula (1), s is defined as the measurement sensitivity, and compared with formula δ=2πdΔh/ph, we can get(2)s=2πΔhδ.Formula (2) shows that as long as the phase shift introduced by the measurement field of view is determined, the measurement sensitivity is also determined.The angular frequency of its change can be known from the expression of light intensity [16]:(3)ω=2πdph+z≈2πdph.Then, the change period of light intensity is(4)T=2πω=phd.It can be seen from formula (4) that the light intensity variation period is only related to three system parameters. Therefore, the overall calibration of the light intensity period can be used to replace the individual calibration of the three parameters of the measurement system. This is the basic idea of Dirckx method calibration, and its calibration principle is as follows:(1)
The theoretical light intensity variation periodT is calculated by the theoretical given value(2)
The actual change periodTr is calculated by continuously collecting the multiframe fringe images(3)
The difference valueΔT between T and Tr is obtainedΔT reflects the approximation degree of T and Tr, and the smaller the value, the higher the positioning accuracy of the system. On the contrary, the positioning accuracy is lower.The calibration of the measurement system can be achieved by adjusting the relative positions of the components in the measurement device to reduceΔT to a reasonable range.


### 3.1. Principle of Sensitivity Calibration

The precision displacement stage drives the grating to move twice in the direction perpendicular to the grating surface, and the distance between each time isΔh. We can get(5)Inx,y=ax,y+bx,ycosϕx,y+nΔx,y,n=0,1,2.In formula (5), ϕx,y is the phase, and Δx,y is the introduced phase shift increment.To determine the measurement sensitivity, formula (5) is rewritten as(6)In=a+bcosϕ+nδn=0,1,2.For the convenience of expression, the coordinates (x, y) are omitted. Formula (6) is calculated as(7)In1=I0−I12=Bsinδ2sinϕ+δ2=B′sinφ,In2=I0−I12=Bsinδ2sinϕ+3δ2=B′sinφ+δ.We further get(8)Is=In2−In12=B′sinδ2⋅cosϕ+δ2,Ia=In2−In12=B′cosδ2⋅sinϕ+δ2.Since the number of fringes in the collected fringe image is greater than 1, the following formula is approximately established:(9)B⋅sinϕ+δ2−B⋅cosϕ+δ2=∑∑B2sin2ϕ+δ2−B2cos2ϕ+δ2=∑∑B2sinϕ+δ2+cosϕ+δ2sinϕ+δ2−cosϕ+δ2=∑∑B2sin2ϕ+δ−π2≈0.In formula (9), M=∑x=1m∑y=1nMx,y2 is the matrix norm operation; m, n reflect the size of the matrix. Formulas (8) and (9) are combined; we can get [17](10)k=IsIa=sinδ/2Bcosϕ+δ/2cosδ/2Bsinϕ+δ/2=tanδ2.Therefore, we can get(11)δ=2arctank.It should be pointed out that formula (11) indicates that the phase shift extraction method based on the matrix norm is the result of the calculation of the spatial fringe pattern data, not the calculation result of a fixed data point, so it has an average meaning.The two-step phase shift method can obtain the phase to be measured by using only two fringe images without knowing the amount of phase shift, which is fast and accurate.In the two-step phase shift method, the light intensityI1^I2^ of the two frames of fringe images after filtering out the background item can be expressed as follows:(12)I^1,k=bkcosφk,(13)I^2,k=bkcosφk+δ,where k is the coordinate of the pixel point. From formulas (12) and (13), we can get(14)φk=arctanI^1,kcosδ−I^2,kI^1,ksinδ.After the phase shift is determined, the phase to be measured can be obtained from formula (14).Many two-step phase shift algorithms have been used in the past. The interference extremum approach and the two-step phase shift algorithm based on the ratio of inner products are the key topics covered in the following sections. The following are the guidelines.


#### 3.1.1. Extreme Interference Value

The phase shift between the fringe patterns is determined by using the pixel spots with the greatest or lowest value of light intensity in the fringe pattern and then calculating the phase to be measured according to formula (14). Method. The basic idea is as follows:We can derive the following from formulas (12) and (13):(15)I^2,kI^1,k=cosφk+δcosφk.The interference extremum point in the fringe patternI^1,k of the first frame is denoted as I^1,KVI, and the interference extremum point of the corresponding pixel in the fringe pattern I^2,KVI of the second frame is denoted as I^2,k. The phase of the pixel point at the extreme value of the light intensity is φEVI=2mπ or 2m+1π. Then, the phase shift can be obtained by the following formula [18]:(16)θ=arccosI^2,EVII^1,EVI.After the phase shift is obtained from formula (5), the phase to be measured can be recovered by bringing its value into formula (14).By examining the idea of the interference extremum technique, it is clear that this approach calculates the phase shift by using the interference extremum points in the collected fringe pattern, therefore recovering the phase to be measured. The fringe pattern gathered in practise, however, will be influenced by the ambient noise. As a result, only one interference extreme value is used in the calculation, resulting in a large error in the calculated result, lowering measurement accuracy. (2) Another method is a two-step phase shift algorithm based on inner product ratio.This method first uses Gaussian high-pass filtering to filter out the background items contained in the fringe image. The light-intensity expressions after filtering out the background term are obtained as follows:(17)I^1=bcosφ,I^2=bcosφ+δ.Second, the inner product of the filtered fringe image is calculated; we get(18)P1=I^1,I^1=∑x=1M∑y=1Nb2cos2φ,(19)P2=I^1,I^2=∑x=1M∑y=1Nb2cosφcosφ+δ,=∑x=1M∑y=1Nb2cos2φcosδ−b2cosφsinφsinδ.If the fringe number of the fringe pattern is greater than 1, that is, the period of the trigonometric function in the light-intensity expression of the fringe pattern is greater than 1, therefore there are approximate conditions:(20)∑x=1M∑y=1Ncos2φcosδ≫∑x=1M∑y=1Ncosφsinφsinδ.Combined with the approximate conditions, formula (19) is simplified to [19](21)P2=∑x=1M∑y=1Nb2cos2φcosδ.From formulas (18) and (19), the phase shift can be calculated by the arc cosine function:(22)δ=arccosP2P1=arccosI^1,I^2I^1,I^1.In order to obtain the phase to be measured, the extracted value is converted into the arctangent function of formula (14).The arc cosine function is used in both the interferometric extremum method and the two-step phase shift algorithm based on the ratio of the inner product, as shown in the above analysis. The ratio in the aforementioned formulas (16) and (22) for determining the phase shift may exceed the value range of the arc cosine function in real measurement owing to physical device variables. In this context, this work proposes a two-frame arctangent function-based random phase shift extraction approach.Generally, the intensity of the fringe pattern observed by the camera can be expressed as(23)In=ax,y+bx,ycosϕx,y+Δn,n=0,1,2….Here,ax,yandbx,y has the same meaning as the formula:ϕx,y—measure phaseΔn—introduced phase shiftWithout loss of generality,Δ0=0 and Δn≠π are assumed in this paper. The fringe pattern background item in the formula is easy to remove, so we can get(24)Ifnx,y=bx,ycosϕx,y+Δn,n=0,1,2….For the sake of clarity, the coordinates (x, y) will be omitted in the text below, and the fringe pattern If0,Ifn will be used to solve the phase shift between fringe patterns. First, If0 is regularized to give(25)IN^1=If0If0=bcosϕbcosϕ.Here, the symbol || || represents the matrix norm operation, and there isM=∑x=1X∑y=1YMx,y. Among them, X,Y reflects the size of the fringe map. Ifn is projected to the space formed by If0; we can get(26)IN∼n=Ifn−Ifn,IN^1⋅IN^1=bcosϕ+Δn−∑X∑Yb2cosϕ+Δncosϕbcosϕbcosϕ2.<,> represents the inner product operation. Usually, in order to perform high-precision measurement, the number of fringes in the collected fringe images is often greater than 1. Therefore, according to the literature, the following approximate relationship can be obtained:(27)IN∼n≈−bsinϕsinΔn,n=1,2.There is an approximate relationbsinϕ≈bcosϕ, and then, we can get(28)kn1=sinΔn=IN˜nIf0.Formula (24) is rewritten as(29)Ifu=bcosϕcosΔn−bsinϕsinΔn.Meanwhile, it is substituted into formula (27) to get(30)IN˜n≈Ifn−bcosϕcosΔn,n=1,2.From formula (24) and assumption Δ0=0, we can get(31)If0=bcosϕ.Formulas (30) and (31) are simultaneously obtained:(32)cosΔn=Ifn−IN˜nIf0.Thus, there are(33)kn2=cosΔn=Ifn−IN∼nIf0.Then, there are(34)ϕ=arctanIf0cosΔn−IfnIf0sinΔn.If the introduced phase shift is assumed to be within the range of0,2π, we combine formulas (28) and (33) and the MATLAB four-quadrant arctangent function to obtain(35)Δn=atankn1,kn2.Phase function:ϕx,y=6peaks (peaks is a MATLAB function)Phase shift function:0.3+0.3irad,i=1,2⋯20Modulation term:b=10−4exp−0.5x2+y2 (in the formula, there is 0.1≤x≤3.1mm,0.1≤y≤3.1mm)Therefore, the simulated light intensity distribution isIn=bcosϕ+δ. Meanwhile, the noise was set to an additive Gaussian distribution with a signal-to-noise ratio of 5%. Figure 1 shows the simulated two-frame fringe image.Figure 1
Simulated phase shift fringe diagram. (a) Simulation diagram 1. (b) Simulation diagram 2.
(a)(b)Figure2 shows the phase shift (which is shown in Figure 2(a)) and its error (which is shown in Figure 2(b)) obtained using the method in this paper. In order to further illustrate the performance of the method in this paper, the processing results of the method in this paper are compared with the TGS algorithm. Because the measurement range of the TGS algorithm is small, the introduced phase shift is set to be 0.1+0.1irad,i=1,2,⋯,10. The demodulation results of Figures 2(c) and 2(d) depict the TGS algorithm (d). When comparing Figures 2(a) and 2(b), we can observe that the range of demodulation results is narrowed down owing to the TGS algorithm’s usage of the arc cosine function. Furthermore, the TGS algorithm has a greater inaccuracy within the same demodulation range as the approach in this study.Figure 2
Simulation results. (a) Phase shift obtained by our method. (b) The error of our method. (c) Phase shift obtained by the TGS method. (d) Error of the TGS method. (e) Phase shift obtained by the method in this paper, TEE, and TGS. (f) Root mean square error.
(a)(b)(c)(d)(e)(f)Due of the random nature of the preceding comparison, this research conducts 30 separate simulation trials to evaluate the performance of the approach with the TEE and TGS algorithms. When a phase shift of 0.6 rad is implemented, the results of the three methods are shown in Figure2(e). When the phase shift is modified from 0.1 rad to 1.1 rad, Figure 2(f) shows the root mean square error achieved by the three techniques. Obviously, the method in this work produces superior processing results.Description. The above simulation results are obtained based on the complete removal of the striped background, and only Gaussian noise is added. However, the actual collected fringe pattern data is more complex than the simulated data. The background frequency band, the noise frequency band, and the contour term frequency band all have a certain degree of aliasing, so it is difficult to achieve complete separation from each other. Moreover, the two-frame algorithm uses a small number of fringe images and contains less measurement information, so it has a large measurement uncertainty. For the above separation error sensitive, the proposed method should carefully analyze the effective separation of background items, contour items, and noise items in fringe images in the application to reduce the loss of measurement accuracy as much as possible. In addition, although the method proposed in this paper has a larger phase shift extraction range than the classical method. However, according to the application characteristics of general phase shift technology, the recommended phase shift extraction range is [π/4, π], and its accuracy is within 0.02 rad, which is better than the classical phase shift extraction algorithm.


## 3.1. Principle of Sensitivity Calibration

The precision displacement stage drives the grating to move twice in the direction perpendicular to the grating surface, and the distance between each time isΔh. We can get(5)Inx,y=ax,y+bx,ycosϕx,y+nΔx,y,n=0,1,2.In formula (5), ϕx,y is the phase, and Δx,y is the introduced phase shift increment.To determine the measurement sensitivity, formula (5) is rewritten as(6)In=a+bcosϕ+nδn=0,1,2.For the convenience of expression, the coordinates (x, y) are omitted. Formula (6) is calculated as(7)In1=I0−I12=Bsinδ2sinϕ+δ2=B′sinφ,In2=I0−I12=Bsinδ2sinϕ+3δ2=B′sinφ+δ.We further get(8)Is=In2−In12=B′sinδ2⋅cosϕ+δ2,Ia=In2−In12=B′cosδ2⋅sinϕ+δ2.Since the number of fringes in the collected fringe image is greater than 1, the following formula is approximately established:(9)B⋅sinϕ+δ2−B⋅cosϕ+δ2=∑∑B2sin2ϕ+δ2−B2cos2ϕ+δ2=∑∑B2sinϕ+δ2+cosϕ+δ2sinϕ+δ2−cosϕ+δ2=∑∑B2sin2ϕ+δ−π2≈0.In formula (9), M=∑x=1m∑y=1nMx,y2 is the matrix norm operation; m, n reflect the size of the matrix. Formulas (8) and (9) are combined; we can get [17](10)k=IsIa=sinδ/2Bcosϕ+δ/2cosδ/2Bsinϕ+δ/2=tanδ2.Therefore, we can get(11)δ=2arctank.It should be pointed out that formula (11) indicates that the phase shift extraction method based on the matrix norm is the result of the calculation of the spatial fringe pattern data, not the calculation result of a fixed data point, so it has an average meaning.The two-step phase shift method can obtain the phase to be measured by using only two fringe images without knowing the amount of phase shift, which is fast and accurate.In the two-step phase shift method, the light intensityI1^I2^ of the two frames of fringe images after filtering out the background item can be expressed as follows:(12)I^1,k=bkcosφk,(13)I^2,k=bkcosφk+δ,where k is the coordinate of the pixel point. From formulas (12) and (13), we can get(14)φk=arctanI^1,kcosδ−I^2,kI^1,ksinδ.After the phase shift is determined, the phase to be measured can be obtained from formula (14).Many two-step phase shift algorithms have been used in the past. The interference extremum approach and the two-step phase shift algorithm based on the ratio of inner products are the key topics covered in the following sections. The following are the guidelines.


### 3.1.1. Extreme Interference Value

The phase shift between the fringe patterns is determined by using the pixel spots with the greatest or lowest value of light intensity in the fringe pattern and then calculating the phase to be measured according to formula (14). Method. The basic idea is as follows:We can derive the following from formulas (12) and (13):(15)I^2,kI^1,k=cosφk+δcosφk.The interference extremum point in the fringe patternI^1,k of the first frame is denoted as I^1,KVI, and the interference extremum point of the corresponding pixel in the fringe pattern I^2,KVI of the second frame is denoted as I^2,k. The phase of the pixel point at the extreme value of the light intensity is φEVI=2mπ or 2m+1π. Then, the phase shift can be obtained by the following formula [18]:(16)θ=arccosI^2,EVII^1,EVI.After the phase shift is obtained from formula (5), the phase to be measured can be recovered by bringing its value into formula (14).By examining the idea of the interference extremum technique, it is clear that this approach calculates the phase shift by using the interference extremum points in the collected fringe pattern, therefore recovering the phase to be measured. The fringe pattern gathered in practise, however, will be influenced by the ambient noise. As a result, only one interference extreme value is used in the calculation, resulting in a large error in the calculated result, lowering measurement accuracy. (2) Another method is a two-step phase shift algorithm based on inner product ratio.This method first uses Gaussian high-pass filtering to filter out the background items contained in the fringe image. The light-intensity expressions after filtering out the background term are obtained as follows:(17)I^1=bcosφ,I^2=bcosφ+δ.Second, the inner product of the filtered fringe image is calculated; we get(18)P1=I^1,I^1=∑x=1M∑y=1Nb2cos2φ,(19)P2=I^1,I^2=∑x=1M∑y=1Nb2cosφcosφ+δ,=∑x=1M∑y=1Nb2cos2φcosδ−b2cosφsinφsinδ.If the fringe number of the fringe pattern is greater than 1, that is, the period of the trigonometric function in the light-intensity expression of the fringe pattern is greater than 1, therefore there are approximate conditions:(20)∑x=1M∑y=1Ncos2φcosδ≫∑x=1M∑y=1Ncosφsinφsinδ.Combined with the approximate conditions, formula (19) is simplified to [19](21)P2=∑x=1M∑y=1Nb2cos2φcosδ.From formulas (18) and (19), the phase shift can be calculated by the arc cosine function:(22)δ=arccosP2P1=arccosI^1,I^2I^1,I^1.In order to obtain the phase to be measured, the extracted value is converted into the arctangent function of formula (14).The arc cosine function is used in both the interferometric extremum method and the two-step phase shift algorithm based on the ratio of the inner product, as shown in the above analysis. The ratio in the aforementioned formulas (16) and (22) for determining the phase shift may exceed the value range of the arc cosine function in real measurement owing to physical device variables. In this context, this work proposes a two-frame arctangent function-based random phase shift extraction approach.Generally, the intensity of the fringe pattern observed by the camera can be expressed as(23)In=ax,y+bx,ycosϕx,y+Δn,n=0,1,2….Here,ax,yandbx,y has the same meaning as the formula:ϕx,y—measure phaseΔn—introduced phase shiftWithout loss of generality,Δ0=0 and Δn≠π are assumed in this paper. The fringe pattern background item in the formula is easy to remove, so we can get(24)Ifnx,y=bx,ycosϕx,y+Δn,n=0,1,2….For the sake of clarity, the coordinates (x, y) will be omitted in the text below, and the fringe pattern If0,Ifn will be used to solve the phase shift between fringe patterns. First, If0 is regularized to give(25)IN^1=If0If0=bcosϕbcosϕ.Here, the symbol || || represents the matrix norm operation, and there isM=∑x=1X∑y=1YMx,y. Among them, X,Y reflects the size of the fringe map. Ifn is projected to the space formed by If0; we can get(26)IN∼n=Ifn−Ifn,IN^1⋅IN^1=bcosϕ+Δn−∑X∑Yb2cosϕ+Δncosϕbcosϕbcosϕ2.<,> represents the inner product operation. Usually, in order to perform high-precision measurement, the number of fringes in the collected fringe images is often greater than 1. Therefore, according to the literature, the following approximate relationship can be obtained:(27)IN∼n≈−bsinϕsinΔn,n=1,2.There is an approximate relationbsinϕ≈bcosϕ, and then, we can get(28)kn1=sinΔn=IN˜nIf0.Formula (24) is rewritten as(29)Ifu=bcosϕcosΔn−bsinϕsinΔn.Meanwhile, it is substituted into formula (27) to get(30)IN˜n≈Ifn−bcosϕcosΔn,n=1,2.From formula (24) and assumption Δ0=0, we can get(31)If0=bcosϕ.Formulas (30) and (31) are simultaneously obtained:(32)cosΔn=Ifn−IN˜nIf0.Thus, there are(33)kn2=cosΔn=Ifn−IN∼nIf0.Then, there are(34)ϕ=arctanIf0cosΔn−IfnIf0sinΔn.If the introduced phase shift is assumed to be within the range of0,2π, we combine formulas (28) and (33) and the MATLAB four-quadrant arctangent function to obtain(35)Δn=atankn1,kn2.Phase function:ϕx,y=6peaks (peaks is a MATLAB function)Phase shift function:0.3+0.3irad,i=1,2⋯20Modulation term:b=10−4exp−0.5x2+y2 (in the formula, there is 0.1≤x≤3.1mm,0.1≤y≤3.1mm)Therefore, the simulated light intensity distribution isIn=bcosϕ+δ. Meanwhile, the noise was set to an additive Gaussian distribution with a signal-to-noise ratio of 5%. Figure 1 shows the simulated two-frame fringe image.Figure 1
Simulated phase shift fringe diagram. (a) Simulation diagram 1. (b) Simulation diagram 2.
(a)(b)Figure2 shows the phase shift (which is shown in Figure 2(a)) and its error (which is shown in Figure 2(b)) obtained using the method in this paper. In order to further illustrate the performance of the method in this paper, the processing results of the method in this paper are compared with the TGS algorithm. Because the measurement range of the TGS algorithm is small, the introduced phase shift is set to be 0.1+0.1irad,i=1,2,⋯,10. The demodulation results of Figures 2(c) and 2(d) depict the TGS algorithm (d). When comparing Figures 2(a) and 2(b), we can observe that the range of demodulation results is narrowed down owing to the TGS algorithm’s usage of the arc cosine function. Furthermore, the TGS algorithm has a greater inaccuracy within the same demodulation range as the approach in this study.Figure 2
Simulation results. (a) Phase shift obtained by our method. (b) The error of our method. (c) Phase shift obtained by the TGS method. (d) Error of the TGS method. (e) Phase shift obtained by the method in this paper, TEE, and TGS. (f) Root mean square error.
(a)(b)(c)(d)(e)(f)Due of the random nature of the preceding comparison, this research conducts 30 separate simulation trials to evaluate the performance of the approach with the TEE and TGS algorithms. When a phase shift of 0.6 rad is implemented, the results of the three methods are shown in Figure2(e). When the phase shift is modified from 0.1 rad to 1.1 rad, Figure 2(f) shows the root mean square error achieved by the three techniques. Obviously, the method in this work produces superior processing results.Description. The above simulation results are obtained based on the complete removal of the striped background, and only Gaussian noise is added. However, the actual collected fringe pattern data is more complex than the simulated data. The background frequency band, the noise frequency band, and the contour term frequency band all have a certain degree of aliasing, so it is difficult to achieve complete separation from each other. Moreover, the two-frame algorithm uses a small number of fringe images and contains less measurement information, so it has a large measurement uncertainty. For the above separation error sensitive, the proposed method should carefully analyze the effective separation of background items, contour items, and noise items in fringe images in the application to reduce the loss of measurement accuracy as much as possible. In addition, although the method proposed in this paper has a larger phase shift extraction range than the classical method. However, according to the application characteristics of general phase shift technology, the recommended phase shift extraction range is [π/4, π], and its accuracy is within 0.02 rad, which is better than the classical phase shift extraction algorithm.


## 3.1.1. Extreme Interference Value

The phase shift between the fringe patterns is determined by using the pixel spots with the greatest or lowest value of light intensity in the fringe pattern and then calculating the phase to be measured according to formula (14). Method. The basic idea is as follows:We can derive the following from formulas (12) and (13):(15)I^2,kI^1,k=cosφk+δcosφk.The interference extremum point in the fringe patternI^1,k of the first frame is denoted as I^1,KVI, and the interference extremum point of the corresponding pixel in the fringe pattern I^2,KVI of the second frame is denoted as I^2,k. The phase of the pixel point at the extreme value of the light intensity is φEVI=2mπ or 2m+1π. Then, the phase shift can be obtained by the following formula [18]:(16)θ=arccosI^2,EVII^1,EVI.After the phase shift is obtained from formula (5), the phase to be measured can be recovered by bringing its value into formula (14).By examining the idea of the interference extremum technique, it is clear that this approach calculates the phase shift by using the interference extremum points in the collected fringe pattern, therefore recovering the phase to be measured. The fringe pattern gathered in practise, however, will be influenced by the ambient noise. As a result, only one interference extreme value is used in the calculation, resulting in a large error in the calculated result, lowering measurement accuracy. (2) Another method is a two-step phase shift algorithm based on inner product ratio.This method first uses Gaussian high-pass filtering to filter out the background items contained in the fringe image. The light-intensity expressions after filtering out the background term are obtained as follows:(17)I^1=bcosφ,I^2=bcosφ+δ.Second, the inner product of the filtered fringe image is calculated; we get(18)P1=I^1,I^1=∑x=1M∑y=1Nb2cos2φ,(19)P2=I^1,I^2=∑x=1M∑y=1Nb2cosφcosφ+δ,=∑x=1M∑y=1Nb2cos2φcosδ−b2cosφsinφsinδ.If the fringe number of the fringe pattern is greater than 1, that is, the period of the trigonometric function in the light-intensity expression of the fringe pattern is greater than 1, therefore there are approximate conditions:(20)∑x=1M∑y=1Ncos2φcosδ≫∑x=1M∑y=1Ncosφsinφsinδ.Combined with the approximate conditions, formula (19) is simplified to [19](21)P2=∑x=1M∑y=1Nb2cos2φcosδ.From formulas (18) and (19), the phase shift can be calculated by the arc cosine function:(22)δ=arccosP2P1=arccosI^1,I^2I^1,I^1.In order to obtain the phase to be measured, the extracted value is converted into the arctangent function of formula (14).The arc cosine function is used in both the interferometric extremum method and the two-step phase shift algorithm based on the ratio of the inner product, as shown in the above analysis. The ratio in the aforementioned formulas (16) and (22) for determining the phase shift may exceed the value range of the arc cosine function in real measurement owing to physical device variables. In this context, this work proposes a two-frame arctangent function-based random phase shift extraction approach.Generally, the intensity of the fringe pattern observed by the camera can be expressed as(23)In=ax,y+bx,ycosϕx,y+Δn,n=0,1,2….Here,ax,yandbx,y has the same meaning as the formula:ϕx,y—measure phaseΔn—introduced phase shiftWithout loss of generality,Δ0=0 and Δn≠π are assumed in this paper. The fringe pattern background item in the formula is easy to remove, so we can get(24)Ifnx,y=bx,ycosϕx,y+Δn,n=0,1,2….For the sake of clarity, the coordinates (x, y) will be omitted in the text below, and the fringe pattern If0,Ifn will be used to solve the phase shift between fringe patterns. First, If0 is regularized to give(25)IN^1=If0If0=bcosϕbcosϕ.Here, the symbol || || represents the matrix norm operation, and there isM=∑x=1X∑y=1YMx,y. Among them, X,Y reflects the size of the fringe map. Ifn is projected to the space formed by If0; we can get(26)IN∼n=Ifn−Ifn,IN^1⋅IN^1=bcosϕ+Δn−∑X∑Yb2cosϕ+Δncosϕbcosϕbcosϕ2.<,> represents the inner product operation. Usually, in order to perform high-precision measurement, the number of fringes in the collected fringe images is often greater than 1. Therefore, according to the literature, the following approximate relationship can be obtained:(27)IN∼n≈−bsinϕsinΔn,n=1,2.There is an approximate relationbsinϕ≈bcosϕ, and then, we can get(28)kn1=sinΔn=IN˜nIf0.Formula (24) is rewritten as(29)Ifu=bcosϕcosΔn−bsinϕsinΔn.Meanwhile, it is substituted into formula (27) to get(30)IN˜n≈Ifn−bcosϕcosΔn,n=1,2.From formula (24) and assumption Δ0=0, we can get(31)If0=bcosϕ.Formulas (30) and (31) are simultaneously obtained:(32)cosΔn=Ifn−IN˜nIf0.Thus, there are(33)kn2=cosΔn=Ifn−IN∼nIf0.Then, there are(34)ϕ=arctanIf0cosΔn−IfnIf0sinΔn.If the introduced phase shift is assumed to be within the range of0,2π, we combine formulas (28) and (33) and the MATLAB four-quadrant arctangent function to obtain(35)Δn=atankn1,kn2.Phase function:ϕx,y=6peaks (peaks is a MATLAB function)Phase shift function:0.3+0.3irad,i=1,2⋯20Modulation term:b=10−4exp−0.5x2+y2 (in the formula, there is 0.1≤x≤3.1mm,0.1≤y≤3.1mm)Therefore, the simulated light intensity distribution isIn=bcosϕ+δ. Meanwhile, the noise was set to an additive Gaussian distribution with a signal-to-noise ratio of 5%. Figure 1 shows the simulated two-frame fringe image.Figure 1
Simulated phase shift fringe diagram. (a) Simulation diagram 1. (b) Simulation diagram 2.
(a)(b)Figure2 shows the phase shift (which is shown in Figure 2(a)) and its error (which is shown in Figure 2(b)) obtained using the method in this paper. In order to further illustrate the performance of the method in this paper, the processing results of the method in this paper are compared with the TGS algorithm. Because the measurement range of the TGS algorithm is small, the introduced phase shift is set to be 0.1+0.1irad,i=1,2,⋯,10. The demodulation results of Figures 2(c) and 2(d) depict the TGS algorithm (d). When comparing Figures 2(a) and 2(b), we can observe that the range of demodulation results is narrowed down owing to the TGS algorithm’s usage of the arc cosine function. Furthermore, the TGS algorithm has a greater inaccuracy within the same demodulation range as the approach in this study.Figure 2
Simulation results. (a) Phase shift obtained by our method. (b) The error of our method. (c) Phase shift obtained by the TGS method. (d) Error of the TGS method. (e) Phase shift obtained by the method in this paper, TEE, and TGS. (f) Root mean square error.
(a)(b)(c)(d)(e)(f)Due of the random nature of the preceding comparison, this research conducts 30 separate simulation trials to evaluate the performance of the approach with the TEE and TGS algorithms. When a phase shift of 0.6 rad is implemented, the results of the three methods are shown in Figure2(e). When the phase shift is modified from 0.1 rad to 1.1 rad, Figure 2(f) shows the root mean square error achieved by the three techniques. Obviously, the method in this work produces superior processing results.Description. The above simulation results are obtained based on the complete removal of the striped background, and only Gaussian noise is added. However, the actual collected fringe pattern data is more complex than the simulated data. The background frequency band, the noise frequency band, and the contour term frequency band all have a certain degree of aliasing, so it is difficult to achieve complete separation from each other. Moreover, the two-frame algorithm uses a small number of fringe images and contains less measurement information, so it has a large measurement uncertainty. For the above separation error sensitive, the proposed method should carefully analyze the effective separation of background items, contour items, and noise items in fringe images in the application to reduce the loss of measurement accuracy as much as possible. In addition, although the method proposed in this paper has a larger phase shift extraction range than the classical method. However, according to the application characteristics of general phase shift technology, the recommended phase shift extraction range is [π/4, π], and its accuracy is within 0.02 rad, which is better than the classical phase shift extraction algorithm.


## 4. Application of Image Denoising Algorithm and Data Mining in Psychological Teaching Quality Evaluation

This paper designs a friendly interactive interface for the system to increase the practicability and convenience of the system. The overall frame design of the system is shown in Figure3.Figure 3
Student’s mental image recognition.Figure4 depicts the facial recognition module's design and implementation process. The camera captures the current real-time video stream once the system is switched on, and when the student’s identification information is recognized, the student’s name is marked just below the framed face. The phrase “unknow” is shown if the student is not registered or recognized.Figure 4
The implementation process of face recognition.The face detection module is a key link of automatic face recognition and smile recognition in the system and is responsible for detecting faces from real-time video. Moreover, face detection is mainly implemented by face classifiers. In the current real-time video stream, multiple candidate frames are generated for each frame and corresponding scores are given. The probability that the frame is a face is judged by the score, and the highest the score, the greater the probability of being judged as a face. The face recognition module firstly asks students to register and fill in their personal information and at the same time takes pictures from the camera to collect face images and stores the information and photos into the database at the same time to complete the registration. During face recognition, real-time video images are obtained through the camera, and the collected faces are retrieved and compared with the face information in the database. After that, it confirms the student’s identity, frames the face, displays the name on the screen, and broadcasts the voice.Image denoising and data mining-based interactive learning stresses communication and interaction between professors and students. Learners take the initiative to investigate, guided by instructors, via constant conversation with teachers and classmates, in order to develop their comprehension, update their perspectives, increase exchanges, and deepen their understanding. Individual students, study groups, learning material, instructors, and the learning environment of image denoising and data mining platforms, as depicted in Figure4, are the major aspects of interactive learning. The link between the primary parts in Figure 5 shows that the course design should build the activity elements and activity flow on the basis of picture denoising and data mining as the intermediate platform. This work implements activities to share learning outcomes, offer learning evaluations, and establish a learning environment via interactive learning among individual students, study groups, learning material, and instructors, all based on theoretical direction. This work builds an interactive learning model based on picture denoising and data mining on this foundation. Furthermore, this paper suggests that the key point of this model is to effectively combine image denoising and data mining platform-assisted learning with classroom teaching, enrich teaching resources, support the development of various teaching activities, improve students’ interest, promote communication between teachers and students and students and students, and improve the learning effect and students’ interpersonal skills.Figure 5
Analysis of classroom teaching mode of psychological interactive learning based on image denoising and data mining.The operation flow of psychological course teaching interaction is shown in Figure6.Figure 6
Psychological teaching interactive operation process.On the basis of the above research, the effect of the psychological feature recognition method based on image denoising algorithm and data mining proposed in this paper is verified, as shown in Figure7.Figure 7
An example of the application of image denoising algorithm and data mining in psychological teaching quality evaluation. (a) Original image. (b) Marked identification objects. (c) Background removal and denoising. (d) Recognition of facial expressions and mental states.
(a)(b)(c)(d)Figure7 shows the quantitative identification of mental states of designated students in psychological teaching. Among them, Figure 7(a) is the actual teaching image, and Figure 7(b) is the identification object. In Figure 7(c), except for the recognized objects, the rest of the students and the background are eliminated, and the image is denoised. Figure 7(d) is the recognition of facial expressions and mental states. Figure 7 verifies that the method proposed in this paper has certain reliability and can realize psychological teaching quality evaluation on the basis of data mining. In this paper, the image denoising algorithm and data mining are verified in the psychological teaching quality evaluation system combined with simulation experiments, and Table 1 is obtained.Table 1
Application effect of image denoising algorithm and data mining in psychological teaching quality evaluation.
NumEvaluating the effectNumEvaluating the effectNumEvaluating the effectNumEvaluating the effect184.421987.333786.165587.65286.422086.993887.095690.48391.532191.663983.105785.25487.832282.374081.095891.40590.812385.064183.785981.64691.512488.454283.836091.48781.902588.184389.446187.19887.692690.494482.376291.11989.502783.364581.066382.191088.382888.364681.896491.921181.232982.624783.336591.961288.443088.444883.246691.011381.243182.444990.506783.311482.543286.445082.136891.041585.823387.045184.446984.791684.433483.135288.777081.011781.713581.355382.597182.501884.353690.465488.097285.78From the above research, it can be seen that the image denoising algorithm and data mining proposed in this paper have a good effect in the evaluation of psychological teaching quality and can play a good role in the improvement of students’ mental health.


## 5. Conclusion

This study investigates the teaching method of a psychological expansion training course based on the teaching mode, with the goal of comprehending the key qualities of psychological expansion training. The goal is to build a teaching mode that is consistent with the psychological expansion training that takes place on campus in order to increase the quality of teaching and the impact of education. On the one hand, the purpose of this study is to sort out and construct the teaching mode of psychological expansion training in schools, and on the other hand, to provide a reference for the teaching of psychological expansion training in schools. However, it promotes the healthy growth of school psychological expansion training and serves as a teaching resource for instructors. This work builds a psychological teaching quality rating system using an image denoising technique and a data mining approach. The findings demonstrate that the picture denoising algorithm and data mining described in this work have a positive impact on the way of evaluating psychological education quality and may help students improve their mental health.



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*Source: 4172887-2022-05-11.xml*