Retrospection of Nonlinear Adaptive Algorithm-Based Intelligent Plane Image Interaction System

This paper introduces the application and classification of an adaptive filtering algorithm in the image enhancement algorithm. And the filtering noise reduction impact is compared using MATLAB software for programming, image processing, LMS algorithm, RLS algorithm, histogram equalisation algorithm, and Wiener filtering method filtering noise reduction effect. To optimize the intelligent graphic image interaction system, the proposed nonlinear adaptive algorithm of intelligent graphic image interaction system research is based on the digital filter and adaptive filtering algorithm for simulation experiment. The experimental results of several noise index data filtering algorithms show that the fuzzy coefficient k of LMS index is 0.86, RLS index is 0.91, the histogram equalization index is 0.53, and the Wiener filtering index is 0.62. LMS index of quality index Q is 0.90, RLS index is 0.95, histogram equalization index is 0.58, Wiener filtering index is 0.65. According to the above results, comparing LMS with the RLS method and according to SNR, k, and Q values in the simulation results in the process of processing, it is found that the convergence speed of the RLS algorithm is obviously better than that of the LMS algorithm, and the stability is also good. Additionally, the differential imaging data can provide a strong reference for the clinical diagnosis and qualitative differentiation of TBP and CP, and MSCT is worthy of extensive application in the clinical diagnosis of peritonitis. The processing effect of the image with high similarity to the original image is greatly improved compared with the histogram equalization and Wiener filtering methods used in the simulation.


Introduction
Rapid breakthroughs in scientific knowledge have created a vast amount of picture data in a variety of industries, including entertainment, art galleries, fashion design, education, medical, and industry. We frequently need to efficiently store and retrieve visual data in order to complete given jobs and make decisions. As a result, establishing appropriate tools for picture retrieval from big image libraries is difficult. In picture retrieval, two methodologies are often used: textbased methodology and content-based methodology. e photos in the text-based system are manually labeled with text descriptors before being employed by a database management system to do image retrieval [1,2]. With the progress of science and technology and the development of social productivity, the control objects in the actual industrial process are more and more complex, and there are many strong nonlinearity, uncertainty, and time variations, so people's requirements for the control of the actual production process are increasingly accurate. erefore, the classical linear feedback control has been difficult to adapt to the needs [3].
e nonlinear system is approximately linearized through the transformation of input and state variables. Although it is convenient for people to understand the characteristics of the system more conveniently and simply, it is difficult to describe the nonlinear characteristics of the original system, and the linearized system cannot well reflect the nonlinear characteristics of the actual system [4]. e nonlinear control theory, in the late twentieth century based on the original control theory, became the dominant trend in the 21 th century. Adaptive control theory has gained importance as a subset of nonlinear control theory and has become a research priority [5]. When the parameters of the controlled system are uncertain or vary little, the traditional adaptive control shows good control effect. It is based on the input and output of the control system and the online identification of system parameters. In the process of control, a more accurate model of the system is gradually obtained, and the design of the controller is combined with the system identification. Because the model of the system gradually approximates the actual model, the interference caused by the uncertainty of the model is greatly reduced, and the utility of the designed controller is also getting better and better [6]. Conceptually, the controller is designed to be adaptable. e adaptive controller's advantages and disadvantages are determined by the controller's design method on the one hand and the system identification algorithm's calculation speed on the other. e algorithm converges quickly and has a good control effect if the chosen initial value is close to the real value. As a result, the adaptive controller assumes that the operating environment is either constant or slowly changing over time. e controller can then be built using either a model with constant parameters or one with slow changes. If the system parameters have a large jump, for example, in display industrial control, boundary condition changes, subsystem failure, external interference, and other problems often make the system jump from the original working point to the new working point, the transient error at the jump time is often very large and the convergence rate of identification algorithm is reduced. e control effect is greatly reduced, so another new control method is needed [7]. To better solve the previous problems, a multimodel adaptive control method can be adopted to control the controlled system. An and Liu proposed an algorithm for a specific quadratic index and obtained the corresponding explicit feedback control law. e theory of the nonlinear control system method mainly includes Lyapunov method synthesis of asymptotically stable system, variable structure control, global linearization, and regularization [8]. Comprehensive surveys exist on content-based image retrieval (CBIR) [9]. CBIR is a technique that helps to organize digital image archives based on their visual content. CBIR covers anything from an image similarity tool to a comprehensive image annotation engine, according to this definition. CBIR's classification as a field of research places it in an unusual position within the scientific world. We see people from various fields, such as computer vision, human-computer interaction, database systems, information retrieval, machine learning, web and data mining, information theory, statistics, and psychology, contributing and becoming part of the CBIR community. Surveys also exist on closely related topics such as relevance feedback [10], applications to art and cultural imaging [11], and face recognition [12].
Liu found defects in their existing theories, which are actually universal in nonlinear systems. e defects are mainly reflected in two aspects: the reversible problem of the nonlinear system and the structural problem under dynamic feedback. Both have long been the focus and difficulty of research. e problem of the nonlinear system has not been clearly understood, and the design of dynamic feedback is also stuck in the initial stage [6]. Liu et al. used a linear algebra method to study the structural characteristics of nonlinear systems from a new perspective [7]. erefore, in this case, the control of nonlinear systems has a completely new development. On the basis of the current research, this paper mainly introduces the application and classification of the adaptive filtering algorithm in the image enhancement algorithm and uses MATLAB software for programming and image processing. e LMS algorithm, RLS algorithm, histogram equalization algorithm and Wiener filtering method filtering noise reduction effect is compared. According to the experimental results of the noise reduction index data of several filtering algorithms, the LMS index of fuzzy coefficient k is 0.86, the RLS index is 0.91, the histogram equilibrium index is 0.53, and the Wiener filtering index is 0.62. e LMS index of quality index Q is 0.90, RLS index is 0.95, histogram equalization index is 0.58, Wiener filtering index is 0.65. It is proved that the processing effect of the image with high similarity to the original image is greatly improved compared with the histogram equalization and Wiener filtering methods used in the simulation in this paper. Comparing LMS with the RLS method, according to SNR, k, and Q values in the simulation results, it can be seen that both methods have better image processing effects, among which RLS is better. Moreover, in the process of processing, it is found that the convergence speed of the RLS algorithm is obviously better than that of the LMS algorithm, and the stability is also good [13].

Concept of Adaptive Filtering.
Adaptive filters are commonly employed in image processing to enhance or restore data by decreasing noise without significantly distorting the image's features. e literature on adaptive filtering is vast, and it is difficult to cover it all in a single chapter. However, much of the study has been concentrated on one-dimensional (1D) signals. Such techniques are not immediately applicable to image processing, and there are no easy ways to extend 1D technique to higher dimensions, owing to the fact that data points in dimensions more than one do not have a unique ordering. Because higher-dimensional medical imaging data are common, we choose to focus this study on adaptive filtering techniques that can be applied to multiple signals (2D pictures, 3D volumes, and 4D time volumes) [14,15]. Adaptive filtering methods mainly include digital filters and adaptive algorithms. ere are two kinds of digital filters commonly used for adaptive filtering; one is FIR (two-dimensional finite impulse response) digital filter; the other is IIR (two-dimensional infinite impulse response) digital filter. e commonly used adaptive filtering algorithms mainly include the following categories: least mean square algorithm (LMS), recursive least square algorithm (RLS), adaptive filtering algorithm based on neural network, adaptive filtering algorithm based on QR decomposition, adaptive filtering algorithm based on the unified model, and adaptive algorithm based on high order simulant. Among them, the LMS algorithm is divided into two types: variable step size algorithm and transform domain algorithm. Due to its wide applicability, the adaptive filtering algorithm has been applied in many fields such as image enhancement and echo cancellation [16]. When passed through a nonlinear function, for any nonlinear function, UKF is the Gaussian filters such that the posterior mean and covariance can be accurate to the second order, but EKF can only obtain the accuracy of the first order. Moreover, the calculation of mean and variance only involves standard vector and matrix operations, which makes the algorithm of UKF suitable for any dynamic model. At the same time, because there is no need to calculate the Jacobian matrix of the nonlinear function, the UKF algorithm is faster than EKF. However, UKF still approximates the posterior probability density of the system state by Gaussian distribution, so in the case of non-Gaussian PDF of the system state, the filtering result will have a great error. e study of nonlinear control theory and linear control theory is almost simultaneous. However, due to the complexity and diversity of the nonlinear system, each part of the system influences each other and produces the equilibrium. Until now, it has not been accurately described and understood. For example, there are many kinds of stability that describe the zero point of a nonlinear system. Any singular equilibrium point leads to a more complex convergence of the system. In addition, there is no good mathematical description tool for nonlinear control systems. erefore, linear control methods still occupy the main position in practical application, and most nonlinear control theories need to be developed.

Adaptive Filter and Digital
Filter. Two-dimensional finite impulse response digital filter, also known as an FIR digital filter, is a kind of digital filters, which is more commonly seen in two-dimensional digital signal processing, in the application of adaptive filtering in image processing. Given that medical images are mostly twodimensional gray images and FIR digital filters have a certain length in both dimensions, a stable filtering function can be achieved. e extended Kalman filter (EKF) is a classical method to deal with nonlinear systems [17]. e idea of EKF is to linearize the nonlinear vector functions φ and H of the stochastic nonlinear system model to get the linearized system model and then apply the basic equation of Kalman filter to solve the nonlinear filtering problem. e EKF algorithm is simple and easy to implement. It is one of the most commonly used nonlinear filtering methods. However, due to the linearization processing method of Taylor expansion, the filtering result of EKF can be close to the true value only when the state equation and observation equation of the system are close to linear and continuous [18]. When the state equation and observation equation are seriously nonlinear, the filtering result of EKF will be very bad. e filtering results of EKF are also related to the statistical characteristics of state noise and observation noise. In the recursive filtering process of EKF, the covariance matrix of state noise and observation noise remains unchanged. If the estimation of the two noise covariance matrices is not accurate enough, it is easy to produce error accumulation, leading to the divergence of filtering. Another disadvantage is that it is not easy to determine the initial state, which causes the state estimation accuracy to be sometimes low in application, and the divergence of filtering is easy to occur [19].
In this paper, the digital filter adopts the FIR digital filter. In the design process, the size of the two-dimensional matrix is set as N 1 × N 2 , and the order of the two dimensions is N 1 − 1, N 2 − 1, respectively. e frequency response function of the filter is shown in the formula as follows: Here, ω 1 , ω 2 is the frequency of the two dimensions, and its value range is [−π, π].

Adaptive Filtering
Algorithm. An adaptive algorithm is one that adjusts its behaviour as it runs, based on the information available and a reward structure that has been designed in advance (or criterion). e tale of recently received data, information on available computational capabilities, or other run-time acquired (or a priori known) knowledge about the environment in which it operates are examples of such information. e adaptive filtering algorithm mainly includes the LMS method and the RLS method. In this paper, in the process of research on the adaptive filtering algorithm, first of all, the governing equation of two kinds of adaptive filtering algorithm is analyzed and deduced, and the two algorithms are simulated by the programming software MATLAB, and the effect of the two algorithms in the actual application process is compared: (1) LMS method is a least mean square algorithm; the algorithm of time early is developed on the basis of the Wiener filtering method; with Wiener filtering solution as the initial value, by using the steepest descent method as a recurrence formula and iterative calculation, the optimal solution is finally obtained, as shown in the formula as follows:.
where X(n) is the input reference vector value; μ represents the space (time) step factor of the weighted vector of the input signal after filtering; Computational Intelligence and Neuroscience y(n) is the output value of the filter; e(n) is output simultaneously as the error signal; W(n) represents both the weighted vector of the digital signal of the input image and the coefficient vector of the filter itself, and W(n) is expressed in the formula as follows: where N represents the length of the selected filter. During the calculation of the LMS algorithm, the following steps should be followed: initialization: determine the initial value of the image to be processed and determine W(0) at the initial time; iteration calculation (iteration): iteration step n � 0.1, . . . ,; output y(n); estimate the calculation error: output e(n); update the input image signal: output W(n + 1) � W(n) + 2μX(n)e(n) in the process of the LMS algorithm design and calculation, attention should be paid to the setting of µ value, which has a great impact on the convergence and robustness of the algorithm. To ensure the stability of the iterative process, the value is generally selected as 0 < μ < 2MPin, and Pin is the input power in the calculation process. e adaptive algorithm process is shown in Figure 1. (2) RLS algorithm, namely, recursive least squares algorithm, is based on the LMS algorithm. e difference is that in the process of filtering, the calculation of mean square error takes the variable length image input signal as the object and adds the weighted factor that changes with time. Compared with the LMS method, the error representation in this algorithm is shown in the formula as follows: where n � 1, 2, . . ., k in the above equation; θ(k, n) is the added weighting factor 0 ≤ θ ≤ 1 that changes with time.
In the above equation, a ⟶ 1 − sorted the two equations to obtain the mean square error equation of the RLS algorithm, as shown in the following formula:.
In the calculation process of the RLS algorithm, when ζ(k) obtains the minimum value, it can be understood that the following equivalence relationship exists, as shown in the following formula: In this formula, the first term on the left side and the term on the right side of the equation are defined as follows: e weight coefficient ω * (k) is the minimum value of ζ(k), and the calculation formula of ω * (k) is derived; that is, the calculation of the weight vector is shown as follows: where some orthogonal vector is the value in the inverse of the target matrix Q(k).

Results and Analysis
In this paper, MATLAB software is used to program the above two algorithms, which are used to process the image in this paper. e processing method is as follows: firstly, the original image (510 × 400 × 3) is processed with noise, and Gaussian noise (E � 0.25) is added to the original image. en, the algorithm designed in this paper is used to process the image and compared with the histogram equalizer and Wiener filtering methods. e software implementation process is shown in Figure 2. An adaptive filter is a system with a linear filter and a transfer function controlled by variable parameters that may be adjusted using an optimization technique. Almost all adaptive filters are electronic filters due to the complicated of the optimization techniques. For some applications, adaptive filters are required because some variables of the required production process (for example, the positions of reflected surfaces in a reverberant space) are unknown or changeable. e closed loop adaptive filter streamlines its transfer function with feedback in the form of an error signal. e time domain of its input signal is shown in Figure 3. Time domain analysis is particularly useful for circuit designs with antennas where a designer may encounter stray signals and reflections. Time domain signal processing enables an engineer to separate extraneous signals in time from the desired signal, thereby identifying the contaminated signals. e mathematical form of SNR is PSNR, and at PSNR � 10, 1g(255 2 /MSE), where MSE is the root mean square value of the corresponding point before and after filtering,

Open loop adaptive system
Adaptive algorithms Import Output Figure 1: Flowchart of adaptive algorithm.

MSE
e larger the PSNR value is, the greater the proportion of the effective signal in the total signal is. e fuzzy coefficient mainly represents the comparison between the edge energy of the processed image and the original image, and its mathematical expression is shown as follows: e closer the score on the right is to 1, the better the treatment quality is. e quality index Q is the most obvious index that represents the image processing effect. ere is a big gap between the image processed by histogram equalization and the original image. Several methods in the simulation were quantitatively compared, with signal-tonoise ratio (SNR), fuzzy coefficient, and quality index as the main indicators.
e comparison results are shown in Table 1.

Discussion
Based on the digital filter and adaptive filtering algorithm for the simulation and experimental results of several noise index data filtering algorithms, the fuzzy coefficient k of LMS index is 0.86, RLS index is 0.91, histogram equalization index is 0.53, and the Wiener filtering index is 0.62. LMS index of quality index Q is 0.90, RLS index is 0.95, histogram equalization index is 0.58, and Wiener filtering index is 0.65. According to the above results, comparing LMS with the RLS method and according to SNR, K, and Q values in the simulation results, it can be seen that both methods have better image processing effects, among which RLS is better. In the process of processing, it is found that the convergence speed of the RLS algorithm is obviously better than that of the LMS algorithm, and the stability is also good. roughout this study, there were significant differences between patients with TBP and patients with CP in abdominal asitoneal fluid, parietal peritoneal changes, omentum changes, and mesentery changes, indicating that MSCT can achieve the acquisition of many image data related to pathological changes in patients with TBP and CP. e difference between the adaptive filtering algorithm and other filtering algorithms, such as Wiener filtering and Kalman filtering, lies in that the filtering coefficient of this algorithm is not fixed but changes correspondingly with the change of image signal and noise. Wiener filter and Kalman filter are the traditional simple linear filters, which have great limitations in image noise processing. In the adaptive filtering algorithm, the adaptive filter parameters determine its obvious advantages in image noise processing and image signal enhancement.

Conclusions
In the present work, based on the nonlinear adaptive algorithm that projected intelligent graphic image interaction system research and based on the digital filter and adaptive filtering algorithm for the simulation and experimental  Computational Intelligence and Neuroscience findings of different noise index data filtering algorithms, the fuzzy coefficient k of LMS index is 0.86, RLS index is 0.91, histogram equalization index is 0.53, and the Wiener filtering index is 0.62. e LMS index of quality index Q is 0.90, RLS index is 0.95, histogram equalization index is 0.58, and Wiener filtering index is 0.65. According to the above results, comparing LMS with the RLS method and according to SNR, K, and Q values in the simulation results, it can be seen that both methods have better image processing effects, among which RLS is better. In the process of processing, it is found that the convergence speed of the RLS algorithm is obviously better than that of the LMS algorithm, and the stability is also good. roughout this study, there were significant differences between patients with TBP and patients with CP in abdominal asitoneal fluid, parietal peritoneal changes, omentum changes, and mesentery changes, indicating that MSCT can achieve the acquisition of many image data related to pathological changes in patients with TBP and CP. e adaptive filtering algorithm differs from other filtering algorithms such as Wiener and Kalman filtering in that the filtering coefficient of this algorithm is not set but evolves in response to changes in picture signal and noise. Traditional simple linear filters such as the Wiener and Kalman filters have significant limitations in image noise processing. e adaptive filtering algorithm's obvious advantages in image noise processing and image signal enhancement are ascertained by the adaptive filter parameters.

Data Availability
All the data used to support the findings of this study are included within the article.