Image Enhancement Method Based on Optimizing Array Stochastic Resonance Parameters by Improved Whale Algorithm

Abstract

The present invention discloses an image enhancement method for optimizing the parameters of array stochastic resonance based on an improved whale algorithm, which is specifically implemented according to the following steps: Step 1, image dimensionality reduction and encoding to obtain a binary sequence; Step 2, performing binary amplitude pulse modulation on the sequence obtained in Step 1 to obtain a one-dimensional bipolar aperiodic BPAM signal; Step 3, establishing a parameter adaptive array model of IWOA; Step 4, demodulation and decoding; Step 5, restoring the image; The parameter adaptive array stochastic resonance strategy based on the improved whale optimization algorithm has more excellent performance than the array stochastic resonance method with fixed parameters and the classical image denoising method, both in terms of visual effect and PSNR index; and as the number of arrays increases, both the visual effect and PSNR of the denoised image are improved; This further proves the good application of the method of the present invention in weak signal detection and extraction.

Description

Technical Field

[0001] The present invention belongs to the technical field of image data processing, and relates to an image enhancement method for optimizing array stochastic resonance parameters based on an improved whale algorithm. Background Art

[0002] With the development of computer technology, images have increasingly become an important source for people to obtain information. During the generation, acquisition, and transmission of digital images, they are often affected by external environmental noise. This will seriously damage the image quality, reduce the visual effect of the image, and bring certain difficulties to further image processing such as target detection and image segmentation. Therefore, reducing the impact of noise on the original image and obtaining a denoised image with better visual effect and closer to the original image is a research topic with certain difficulties. Currently, the interference of noise on images is mainly eliminated through the following two methods: one is to obtain an original image with less noise content by improving the quality of imaging equipment; the other is to remove the noise in the original image through advanced image denoising algorithms. Compared with the former, the latter has the advantages of low hardware cost and good reliability. Therefore, continuously improving the performance of image denoising algorithms has become one of the main research directions for researchers to conduct image enhancement and restoration research.

[0003] In recent decades, scholars have conducted multi-faceted research on image denoising methods. Currently, classical denoising methods mainly include mean filtering, Wiener filtering, median filtering, Gaussian filtering, etc. Some of these methods have good smoothing effects but cannot well protect image details; some have good overall denoising effects but require the original image and noise to be stationary and random, and it is difficult for classical image denoising methods to completely filter out noise in a strong noise background. The application of stochastic resonance theory in the field of image enhancement provides another idea for image denoising. The stochastic resonance theory improves the output of a nonlinear system by transferring noise energy to a weak input signal, and does not damage the original image while filtering out noise. Therefore, in recent years, methods for removing image noise using the stochastic resonance principle have been widely studied by domestic and foreign scholars.

[0004] The adaption of stochastic resonance parameters has always been a research hotspot in this field. Currently, many research scholars use intelligent optimization algorithms to select the structural parameters of stochastic resonance, but there are problems such as the optimization results being prone to falling into local optima and low computational efficiency. Therefore, when optimizing stochastic resonance parameters, selecting a suitable intelligent optimization algorithm is crucial for the enhancement effect of images. At the same time, although the image is enhanced to a certain extent after denoising by a single nonlinear stochastic resonance system, there are still some deficiencies in the processing of images by a single nonlinear system, especially in a strong noise environment, the processing effect is not good. Therefore, it is of great significance to propose a research method that can obtain better image enhancement effects.

[0005] In view of the above background, the present invention proposes a method for enhancing images by parameter adaptive array stochastic resonance based on an improved whale optimization algorithm. Based on the bistable array stochastic resonance model, the method performs dimensionality reduction scanning, encoding, and modulation processing on the noisy grayscale image to make it a one-dimensional aperiodic BPAM signal suitable for input to the stochastic resonance processing module. Then, the traditional whale optimization algorithm is improved in terms of initial solution distribution, global search ability, and population diversity generalization, and the algorithm is applied to select the structural parameters a, b, and h of the stochastic resonance processing module, effectively improving the adaptive ability of the array stochastic resonance model parameters. Finally, the output of the processing module is demodulated, decoded, and inverse scanned to obtain the restored image after denoising, further improving the enhancement effect of weak image signals. Practical applications show that the method of this patent has better image denoising effects and image enhancement capabilities in a strong noise environment. Summary of the Invention

[0006] The object of the present invention is to provide an image enhancement method for optimizing array stochastic resonance parameters based on an improved whale algorithm, which solves the problems of easy entrapment in local optima of the optimization results, low computational efficiency, distortion of the restored image, and high bit error rate.

[0007] The technical solution adopted by the present invention is an image enhancement method for optimizing array stochastic resonance parameters based on an improved whale algorithm, which is specifically implemented according to the following steps:

[0008] Step 1: Image dimensionality reduction and encoding to obtain a binary sequence;

[0009] Step 2: Perform binary amplitude pulse modulation on the sequence obtained in Step 1 to obtain a one-dimensional bipolar aperiodic BPAM signal;

[0010] Step 3: Establish a parameter adaptive array model of IWOA;

[0011] Step 4: Demodulation and decoding;

[0012] Step 5: Restore the image.

[0013] The characteristics of the present invention also lie in:

[0014] Among them, Step 1 is specifically as follows:

[0015] Adopt the Hilbert scanning method to perform dimensionality reduction scanning on the original grayscale image T m×n ; The original two-dimensional image matrix T m×n is dimensionally reduced and scanned into a one-dimensional image sequence J 1×mn ; Encode the one-dimensional image sequence J 1×mn to obtain an 8-bit binary symbol sequence H composed of 0s and 1s 1×8mn ;

[0016] Among them, step 2 is specifically as follows: For the binary sequence H 1×8mn Perform binary pulse amplitude modulation (BPAM) processing to obtain a one-dimensional bipolar aperiodic BPAM signal r(t), as shown in the following formula:

[0017]

[0018] In the formula, A is the amplitude of the signal r(t), m and n are the rows and columns of the original grayscale image, G(t) is a rectangular pulse with a period of T, that is, when t∈(0,T), G(t) is 1, and when When, G(t) is 0; S i (i = 1, 2,..., 8mn) is a one-dimensional sequence composed of -1 and 1 obtained by performing polarity conversion on the binary sequence H 1×8mn (0→-1, 1→1); Through image dimensionality reduction scanning, binary symbol coding, and polarity conversion of image symbols, a one-dimensional sequence S i is obtained, that is, all the information on S i are independent random variables;

[0019] Among them, step 3 is specifically as follows: First, perform noise addition processing on the one-dimensional bipolar aperiodic BPAM signal r(t) to obtain the input signal g of each independent sub-array in the array stochastic resonance system k (t) = r(t) + ξ k (t). The one-dimensional noise-added signal g k (t) is processed by N saturation system units to obtain x k (t). The obtained x k (t) is averaged by summation to obtain the output response x(t) of the array model. Then, initialize the parameters of the improved whale optimization system, run the improved whale optimization algorithm, find the system parameters that induce stochastic resonance, perform stochastic resonance processing on the noisy image, and use the evaluation index of peak signal-to-noise ratio to consider the results;

[0020] Among them, the output response x(t) of the array model in step 3 is specifically calculated according to the following steps:

[0021] Each non-linear system unit in the array saturation system is:

[0022]

[0023] In the formula, a and b are the system parameters of the array saturation stochastic resonance processing model, k = 1, 2,..., N, N is the size of the system array unit, r(t) = s(t) + η(t) is the input signal of the array model, x k (t) is the output of the array unit, ξ k (t) is the mean of 0 and the variance is Independent and identically distributed Gaussian white noise;

[0024] Take the one-dimensional noisy signal g in formula (2) k (t) = r(t) + ξ k (t) as the input of each array saturation unit. The one-dimensional noisy signal g k (t) is processed by N saturation system units to obtain x k (t). After taking the mean by summation of x k (t), the output response x(t) of the array model is obtained. The formula is as follows:

[0025]

[0026] In the array stochastic resonance system, the fourth-order Runge-Kutta method is used for calculation. The principle is as follows:

[0027] For the differential equation

[0028]

[0029] The calculation formula using the fourth-order Runge-Kutta method is:

[0030]

[0031] where h is the solution step size;

[0032] The improved whale optimization algorithm in step 3 is specifically as follows: First, initialize the whale population using the chaotic Iterative map to obtain a solution space with a more uniform initial solution distribution; then, balance and improve the global exploration and local development capabilities of the algorithm through the non-linear time-varying factor and the adaptive weight strategy; finally, increase the population diversity by combining the random learning strategy to improve the global optimization ability of the algorithm, and introduce the Cauchy mutation operator to enhance the ability of the algorithm to jump out of the local optimum. Specifically as follows:

[0033] Initialization of the Iterative map, specifically as the following formula:

[0034] x k+1 = sin(dπ / x k ) (6)

[0035] In the formula, d ∈ (0, 1);

[0036] Non-linear convergence factor and variable weight:

[0037] The non-linear change strategy of the convergence factor v' with the increase of the evolutionary iteration times, that is:

[0038]

[0039] The value of the non-linear time-varying factor v' changes dynamically as the number of iterations increases;

[0040] Variable weight strategy, namely:

[0041]

[0042] The improved position update formula is as follows:

[0043] X(t + 1) = X rand × w - A · D rand , p < 0.5, |A| > 1 (9)

[0044] X(t + 1) = X * (t) × w - A · D, p < 0.5, |A| ≤ 1 (10)

[0045] X(t + 1) = D'(t)e ml cos(2πl) + X * (t) × (1 - w), p ≥ 0.5 (11)

[0046] As the number of iterations increases, the weights in the variable weight strategy increase non-linearly;

[0047] Stochastic learning strategy:

[0048] Introduce the learning stage of the teaching-learning based optimization algorithm, propose a stochastic learning strategy, simulate the learning mode of whales discussing and communicating with each other, optimize their own positions by learning from excellent individuals, increase the social learning ability of the whale population, thereby increasing the diversity of the whale population and improving the quality of the whale population to improve the global search performance of the algorithm; as shown in formula (12), for whale individual x, randomly select different individuals x p from the whale population and learn from them to adjust its own position;

[0049]

[0050] where the learning factor rand(0, 1) is a random number between (0, 1), which reflects the differences in the learning abilities of whale individuals; after learning, compare the fitness values to select a more excellent individual. If f(x new ) < f(x), then the population accepts the new individual x new and replaces the individual x, otherwise the population rejects the inferior individual x new ;

[0051] Cauchy mutation strategy:

[0052] Adopt the following Cauchy mutation formula to update the position of the current optimal individual, namely:

[0053]

[0054] In the formula, is the new value obtained from the current optimal value after Cauchy perturbation, cauchy(0,1) is the Cauchy operator, and the formula for the standard Cauchy distribution function is:

[0055]

[0056] Since the Cauchy probability density function has a wide distribution range and can generate random numbers far from the origin, it can impose a strong perturbation on the whale individuals, enabling the perturbed whales to quickly avoid the local optimum. At the same time, due to the low peak value of the Cauchy distribution, the individual search time is greatly shortened, thus enabling the algorithm to converge faster.

[0057] Among them, step 4 is specifically as follows:

[0058] Set the start time of each symbol to t i = iT, and the duration is T; the demodulation method for the output response x(t) of the array saturated stochastic resonance system is as follows:

[0059]

[0060] Demodulate the one-dimensional binary signal P 1×8mn Decode it into a decimal symbol to obtain a one-dimensional sequence V 1×mn ;

[0061] Among them, step 5 is specifically as follows:

[0062] According to the anti-scanning method, perform anti-scanning for image dimensionality reduction on the one-dimensional sequence V 1×mn to obtain the restored grayscale image Q m×n .

[0063] The beneficial effects of the present invention are

[0064] An image enhancement method based on an improved whale algorithm for optimizing the parameters of array stochastic resonance. Experimental results show that the parameter adaptive array stochastic resonance strategy based on the improved whale optimization algorithm has better performance than the array stochastic resonance method with fixed parameters and the classical image denoising method in terms of both visual effects and PSNR metrics; and as the number of arrays increases, the visual effects and PSNR of the denoised images are improved; this further proves the good application of the method of the present invention in weak signal detection and extraction. Description of the Drawings

[0065] Figure 1 It is a flowchart of the parameter adaptive array stochastic resonance strategy based on the improved whale optimization algorithm;

[0066] Figure 2It is a model of bistable stochastic resonance for N parallel arrays;

[0067] Figure 3 They are the original Lena image and the image after adding noise;

[0068] Figure 4 They are the restoration effect display diagrams of the Lena image under four classic filtering methods;

[0069] Figure 5 They are the enhancement effect display diagrams of the Lena image under different array saturation model methods;

[0070] Figure 6 They are the enhancement effect display diagrams of the Baboon image under four classic filtering methods;

[0071] Figure 7 They are the enhancement effect display diagrams of the Baboon image under different array saturation model methods;

[0072] Figure 8 They are the enhancement effect display diagrams of the Brain image under four classic filtering methods;

[0073] Figure 9 They are the enhancement effect display diagrams of the Brain image under different array saturation model methods. Specific implementation manner

[0074] The present invention will be described in detail below in conjunction with the accompanying drawings and specific implementation manners.

[0075] The present invention provides an image enhancement method based on an improved whale algorithm for optimizing array stochastic resonance parameters, as Figure 1 shown, and is specifically implemented according to the following steps:

[0076] Step 1, image dimensionality reduction and encoding; the specific process is as follows:

[0077] The size of the two-dimensional image is 2 k ×2 k ; In this application experiment, the Hilbert scanning method is used to perform dimensionality reduction scanning on the original grayscale image T m×n ; The original two-dimensional image matrix T m×n is dimensionally reduced and scanned into a one-dimensional image sequence J 1×mn ; Therefore, the one-dimensional image sequence J 1×mn is encoded to obtain an 8-bit binary symbol sequence H 1×8mn consisting of 0 and 1;

[0078] Step 2, binary amplitude pulse modulation; the specific process is as follows:

[0079] After the original grayscale image undergoes dimensionality reduction and binary encoding, a binary sequence is obtained, and further for H1×8mn Perform binary pulse amplitude modulation (BPAM) processing to obtain a one-dimensional bipolar aperiodic BPAM signal r(t); the formula for r(t) is as follows:

[0080]

[0081] In the formula, A is the amplitude of the signal r(t), m and n are the rows and columns of the original grayscale image. G(t) is a rectangular pulse with a period of T, that is, when t ∈ (0, T), G(t) is 1, and when G(t) is 0. S i (i = 1, 2,..., 8mn) is a one-dimensional sequence composed of -1 and 1 obtained by performing polarity conversion through the binary sequence H 1×8mn (0 → -1, 1 → 1); through image dimensionality reduction scanning, binary symbol encoding, and polarity conversion of image symbols, a one-dimensional sequence S i is obtained, that is, all the information on S i are independent random variables;

[0082] Step 3, the parameter adaptive array model based on IWOA; the specific process is as follows:

[0083] First, perform noise addition processing on the one-dimensional bipolar aperiodic BPAM signal r(t) to obtain the input signal g k (t) = r(t) + ξ k (t) of each independent sub-array in the array stochastic resonance system. The one-dimensional noisy signal g k (t) is processed by N saturation system units to obtain x k (t). The obtained x k (t) is averaged by summation to obtain the output response x(t) of the array model. Then, combined with the IWOA optimization algorithm, the system parameters a, b, h that induce stochastic resonance are found, and stochastic resonance processing is performed on the noisy image, and the peak signal-to-noise ratio evaluation index is used to consider the results;

[0084] Each non-linear system unit in the array saturation system can be expressed as:

[0085]

[0086] In the formula, a and b are the system parameters of the array saturation stochastic resonance processing model. k = 1, 2,..., N, N is the size of the system array unit, r(t) = s(t) + η(t) is the input signal of the array model, x k (t) is the output of the array unit, ξ k (t) is independent and identically distributed Gaussian white noise with a mean of 0 and a variance of ;

[0087] The one-dimensional noisy signal g in formula (2) k (t) = r(t) + ξ k (t) is used as the input of each array saturation unit. The model of N parallel array bistable stochastic resonance is as Figure 2 shown; therefore, after the one-dimensional noisy signal g k (t) is processed by N saturation system units, x k (t) is obtained. After taking the mean by summing x k (t), the output response x(t) of the array model is obtained, and the formula is as follows:

[0088]

[0089] In the array stochastic resonance system, the fourth-order Runge-Kutta method is used for calculation, and its principle is as follows:

[0090] For the differential equation

[0091]

[0092] The calculation formula using the fourth-order Runge-Kutta method is:

[0093]

[0094] where h is the solution step size;

[0095] Aiming at the problems of slow convergence speed and easy to fall into local optimum existing in the traditional whale optimization algorithm, the present invention first uses the chaotic Iterative mapping to initialize the whale population to obtain a solution space with a more uniform initial solution distribution; then balances and improves the global exploration and local development capabilities of the algorithm through a non-linear time-varying factor and an adaptive weight strategy; finally, combines a random learning strategy to increase the population diversity to improve the global optimization ability of the algorithm, and introduces a Cauchy mutation operator to enhance the ability of the algorithm to jump out of the local optimum. Based on the above improvements, an improved whale optimization algorithm is proposed;

[0096] 1. Initialization by Iterative mapping:

[0097] The traditional WOA initializes the population randomly, resulting in a relatively non-uniform distribution of the initial population; research shows that chaotic sequences have good randomness and ergodicity. Therefore, in this paper, the Iterative mapping method is used to initialize the population, and its equation is as follows:

[0098] x k+1 = sin(dπ / x k ) (6)

[0099] where d ∈ (0, 1), and in this paper, d = 0.5 is taken;

[0100] 2. Nonlinear Convergence Factor and Variable Weight:

[0101] The global search ability and local search ability of the whale optimization algorithm largely depend on the value of parameter A, and parameter A changes continuously with the change of the convergence factor v; in the traditional whale optimization algorithm, the convergence factor v linearly decreases from 2 to 0 as the number of evolutionary iterations increases, but the WOA algorithm is nonlinearly changing during the evolutionary search process, and the linear decreasing strategy of the convergence factor v cannot fully reflect the actual optimization search process of the algorithm; to address this problem, this paper proposes a nonlinear change strategy for the convergence factor v' as the number of evolutionary iterations increases, that is:

[0102]

[0103] The value of the non - linear time - varying factor v' changes dynamically as the number of iterations increases. At the initial stage of the algorithm, the value of v' is larger, increasing the probability that |A| is greater than 1, thereby increasing the step size in the global optimization stage of the algorithm, effectively expanding the scope of the algorithm's global search, and enhancing the global performance of the algorithm; in the middle stage of the algorithm, after determining the suspected target, local development is carried out. At this time, the larger value of v' enables the algorithm to have a larger step size, effectively enhancing the algorithm's ability to jump out of local extrema and avoiding the algorithm falling into local optimization; in the later stage of the algorithm, approaching the optimal solution, the convergence speed of the v' value slows down. At this time, the fluctuation range of the |A| value is significantly weakened, so that the algorithm has a smaller step size, which helps to perform local fine - search, and at the same time can stably optimize, effectively improving the convergence speed of the algorithm; therefore, the non - linear time - varying factor v' can more reasonably balance the global exploration ability in the early stage of the algorithm and the local exploitation ability in the middle and later stages without changing the segmentation point between global exploration and local exploitation.

[0104] In the traditional whale optimization algorithm, the position of the new individual generated in each iteration only depends on the current target individual position and the global optimal individual position; therefore, it is easy for the algorithm to fall into local optimum; for this, the present invention designs a variable weight strategy, that is:

[0105]

[0106] The improved position update formula is as follows:

[0107] X(t + 1) = X rand × w - A · D rand , p < 0.5, |A| > 1 (9)

[0108] X(t + 1) = X * (t) × w - A · D, p < 0.5, |A| ≤ 1 (10)

[0109] X(t + 1) = D'(t)e mlcos(2πl)+X * (t)×(1 - w), p≥0.5 (11)

[0110] As the number of iterations increases, the weights in the variable weight strategy increase non - linearly; since the target of whale individuals is fuzzy in the initial stage of search, a smaller weight is used to perturb the current optimal solution position; in the middle and late stages of iteration, the target of whales becomes gradually clear, and at this time, a larger weight is used to perturb the current optimal position to achieve the purpose of fine search and fast convergence in the neighborhood of the optimal solution;

[0111] 3. Stochastic learning strategy

[0112] The quality of the whale population has a great impact on the performance of the traditional whale optimization algorithm. A high - quality whale population can improve the algorithm's accuracy, optimization performance, and convergence speed while improving the algorithm's accuracy; since the traditional whale optimization algorithm only relies on the guidance of random individuals in the population to update the individual positions during global search, the learning stage of the teaching - learning - based optimization algorithm is introduced to propose a stochastic learning strategy, which simulates the learning mode of whales discussing and communicating with each other. By learning from excellent individuals, the position of the whale itself is optimized, the social learning ability of the whale population is increased, thereby increasing the diversity of the whale population and improving the quality of the whale population to improve the global search performance of the algorithm; as shown in formula (12), for whale individual x, different individuals x p are randomly selected from the whale population, and the whale learns from them to adjust its own position.

[0113]

[0114] In the formula, the learning factor rand(0, 1) is a random number between (0, 1), which reflects the difference in the learning ability of whale individuals; after learning, by comparing the fitness values, a more excellent individual is selected. If f(x new ) < f(x), then the population accepts the new individual x new and replaces the individual x, otherwise the population rejects the inferior individual x new ; the stochastic learning of individuals enhances the information sharing ability of the whale population, thereby increasing the population diversity and improving the global optimization performance of the algorithm;

[0115] 3. Cauchy mutation strategy:

[0116] Regarding the problem that the traditional whale optimization algorithm is prone to falling into local extrema, a Cauchy mutation strategy is introduced by combining the Cauchy distribution, and a Cauchy perturbation is given to the current optimal individual; in the later stage of the algorithm, the Cauchy operator can generate a large step size to help the algorithm jump out of the local optimum, and can also generate a small step size to accelerate the search speed for the optimal solution; therefore, the following Cauchy mutation formula is adopted in this paper to update the position of the current optimal individual, that is:

[0117]

[0118] In the formula, is the new value obtained from the current optimal value after Cauchy perturbation, cauchy(0,1) is the Cauchy operator, and the formula for the standard Cauchy distribution function is:

[0119]

[0120] Since the Cauchy probability density function has a wide distribution range and can generate random numbers far from the origin, it can impose a strong perturbation on the whale individuals, enabling the perturbed whales to quickly avoid local optima. At the same time, due to the low peak value of the Cauchy distribution, the individual search time is greatly shortened, thus enabling the algorithm to converge faster.

[0121] Step 4, demodulation and decoding; the specific process is as follows:

[0122] Set the start time of each symbol as t i = iT, and the duration is T; the demodulation method for the output response x(t) of the array saturated stochastic resonance system is as follows:

[0123]

[0124] Demodulate the one-dimensional binary signal P 1×8mn Decode it into a decimal symbol to obtain a one-dimensional sequence V 1×mn ;

[0125] Step 5, restore the image; the specific process is as follows:

[0126] According to the anti-scanning method, process the one-dimensional sequence V 1×mn to obtain the restored grayscale image Q m×n .

[0127] To verify the correctness of the method proposed in the present invention, simulation experiments were respectively carried out on three noisy images of Lena, Baboon, and Brain.

[0128] (1) Lena image

[0129] In the experiment, the actual grayscale image of Lena with a pixel size of 256×256 pixels was selected, and Gaussian white noise with a mean of 0 and an intensity of 0.3 was added to the original Lena image; the PSNR of the Lena noisy image = 8.7167 dB; the original image and the noisy image are as Figure 3 shown, and the output images of the noisy image denoised by the mean method, median method, Wiener method, and Gaussian method are as Figure 4 shown. Figure 5Describes the comparison effect of the image restoration performance of the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper;

[0130] It can be seen from Figure 4 that in a strong noise environment, the restored images obtained by the mean method, median method, Wiener method, and Gaussian method have been severely distorted, blurring the basic content of the original image; Figure 5 Gives the restored Lena images processed by the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper when the array element size is N = 1, 2, 4, 8; It can be seen from Figure 5 that the structure of the restored image obtained by the parameter adaptive array model method based on IWOA proposed in this paper is most similar to the original image, and can better show the gray level and image content of the image. When the array element is small, there are more noise points on the restored image, resulting in a poor visual effect of the image. As the array element increases, the image restoration effect is enhanced and the image becomes clearer; The above analysis shows that compared with the traditional filtering algorithm, the array saturation model has a better processing effect on the noisy signal. On the basis of the array saturation model, compared with the array model method with fixed parameters and the parameter adaptive array model method based on WOA, the parameter adaptive array model method based on IWOA has more superiority in the processing of noisy signals; The increase of the array element makes the image restoration effect better, but as the array element increases, the computational complexity of the algorithm also increases accordingly, and the processing time will also become longer;

[0131] The above analysis is based on subjective visual comparison. In order to more objectively judge the denoising effect of the image, this paper uses the peak signal-to-noise ratio PSNR as a measurement index for comparison and explanation. The PSNR of the Lena restored images under the four classic filtering algorithms is shown in Table 1, and the PSNR of the Lena restored images under different array saturation model methods is shown in Table 2;

[0132] Table 1 shows the PSNR performance comparison of the mean filtering, median filtering, Wiener filtering, and Gaussian filtering methods; Compared with the PSNR of the noisy Lena image, the PSNR of the four classic filtering methods has increased slightly, but the enhancement effect is not obvious;

[0133] Figure Name Size Noisy Image Mean Filtering Median Filtering Wiener Filtering Gaussian Filtering Lena 256×256 8.7167 16.6138 13.3217 15.9101 16.6173

[0134] Table 2 shows the PSNR of the Lena restored images under different array saturation model methods.

[0135] Table 2 shows the PSNR of the Lena restored images under different array saturation model methods.

[0136]

[0137] Table 2 shows the PSNR performance comparison of the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper; compared with the array model method with fixed parameters and the parameter adaptive array model method based on WOA, the PSNR values under the parameter adaptive array model method based on IWOA are the largest in different array elements; thus, it can be seen that the parameter adaptive array model method based on IWOA proposed in this paper has certain superiority.

[0138] (2) Baboon image

[0139] In the experiment, the actual grayscale image of the Baboon image with a pixel size of 256×256 pixels is selected, and Gaussian white noise with a mean of 0 and an intensity of 0.3 is added to the original Baboon image; the PSNR of the Baboon noisy image is 8.6783 dB. The original image, the noisy image, and the output images of the noisy image denoised by the mean method, median method, Wiener method, and Gaussian method are as Figure 6 shown, Figure 7 describes the comparison effect of the image restoration performance of the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper;

[0140] It can be seen from Figure 6 that in a strong noise environment, the images restored by mean filtering, median filtering, Wiener filtering, and Gaussian filtering are blurred and very different from the original image; Figure 7 shows the restored images obtained by the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper under different array element sizes; according to Figure 7 the comparison of the restored images, it can be seen that the restored image obtained by the parameter adaptive array model method based on IWOA proposed in this paper is the most similar to the original image, and as the array element increases, the noise points on the restored Baboon image are significantly reduced until finally almost none, indicating that the restoration method in this paper effectively suppresses noise;

[0141] Tables 3 and 4 show the PSNR performance after enhancing the noisy Baboon image;

[0142] Table 3 is the PSNR of the restored Baboon images under four classic filtering algorithms

[0143] Figure Name Size Noisy Image Mean Filtering Median Filtering Wiener Filtering Gaussian Filtering Baboon 256×256 8.6783 16.5892 12.9568 15.9909 16.6008

[0144] It can be seen from Table 3 that the PSNR of the restored images obtained by the four classic filtering methods is relatively small;

[0145] Table 4 shows the PSNR of the Baboon restored images under different array saturation model methods

[0146]

[0147] In Table 4, when the number of arrays is 1, the PSNR of the restored images obtained by the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper all increase, but the increase amplitude is relatively small, and the image enhancement effect is still not clear; as the number of array elements increases, the PSNR of the restored images also increases, thus making the image restoration effect clearer. And in each array element, the PSNR of the restored images obtained by the parameter adaptive array model method based on IWOA proposed in this paper is the largest, which indicates that the method proposed in this paper has significant advantages in the process of gray image restoration.

[0148] (3) Brain image

[0149] In the experiment, the actual gray image of the Brain image with a pixel size of 256×256 pixels is selected, and Gaussian white noise with a mean of 0 and an intensity of 0.3 is added to the original Brain image; the PSNR of the Brain noisy image = 8.6885 dB; the original image, the noisy image, and the output images of the noisy image denoised by the mean method, median method, Wiener method, and Gaussian method are as Figure 8 shown, Figure 9 describes the comparison effect of the image restoration performance of the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper;

[0150] From Figure 8 the comparison of the effect diagrams in, it can be seen that in a strong noise environment, the image enhancement effects of mean filtering, median filtering, Wiener filtering, and Gaussian filtering are similar. The restored Brain images obtained by these four filtering methods are blurred and the picture content cannot be recognized; Figure 9 shows the image enhancement effect based on the array model method. From Figure 9It can be seen that as the size of the array unit increases, the black and white noise points on the restored images of the array model method with fixed parameters, the parameter adaptive array model method based on WOA, and the parameter adaptive array model method based on IWOA proposed in this paper become fewer and fewer, and the restored images gradually become clearer. Among them, under different array unit sizes, the restored images obtained by the parameter adaptive array model method based on IWOA proposed in this paper are the clearest. When the array unit size is 8, the restored image obtained by the parameter adaptive array model method based on IWOA proposed in this paper is extremely similar to the original image, with only a small amount of noise points.

[0151] Table 5 and Table 6 show the comparison results of the PSNR performance of the processed Brain images.

[0152] Table 5 is the PSNR of the Brain restored images under four classical filtering algorithms.

[0153] Figure Name Size Noisy Image Mean Filtering Median Filtering Wiener Filtering Gaussian Filtering Brain 256×256 8.6885 15.6739 14.1595 14.9413 15.6747

[0154] It can be seen from Table 5 that compared with the PSNR of the noisy Brain image, after mean filtering, median filtering, Wiener filtering, and Gaussian filtering, the PSNR values of the Brain images are all smaller, the improvement effect of the PSNR value is not obvious, and the image enhancement effect is not good.

[0155] Table 6 is the PSNR of the Brain restored images under different array saturation model methods.

[0156]

[0157] It can be seen from Table 6 that when the number of arrays is 1, the PSNR values obtained by the parameter adaptive array model method based on IWOA proposed in this paper, the array model method with fixed parameters, and the parameter adaptive array model method based on WOA for image restoration are all relatively small, and the processing effect is not good. As the size of the array unit increases, the PSNR of the restored images of the above three methods also increases, resulting in a better image restoration effect. Moreover, the PSNR values of the restored images obtained by the parameter adaptive array model method based on IWOA proposed in this paper are the largest, and the image enhancement effect is the best. The experimental results show that the parameter adaptive array model method based on IWOA proposed in this paper has significant advantages in image enhancement.

Claims

1. An image enhancement method for optimizing the parameters of array stochastic resonance based on an improved whale algorithm, characterized in that The implementation is specifically carried out according to the following steps: Step 1: Image dimensionality reduction and encoding to obtain a binary sequence; Adopt the Hilbert scanning method to process the original grayscale image for dimensionality reduction scanning; reduce the dimensionality of the original two-dimensional image matrix to scan it into a one-dimensional image sequence ; encode the one-dimensional image sequence to obtain an 8-bit binary symbol sequence composed of 0s and 1s ; Step 2: Perform binary amplitude pulse modulation on the sequence obtained in Step 1 to obtain a one-dimensional bipolar aperiodic BPAM signal; Perform binary pulse amplitude modulation (BPAM) processing on the binary sequence to obtain a one-dimensional bipolar aperiodic BPAM signal , as follows: （1） In the formula, is the amplitude of the signal ; and are the row and column of the original grayscale image, is a rectangular pulse with a period of , that is, when , is 1, and when , is 0; is a one-dimensional sequence formed by performing polarity conversion on the binary sequence such that 0 becomes -1 and 1 becomes 1. In , a one-dimensional sequence is obtained through image dimensionality reduction scanning, binary symbol coding, and polarity conversion of image symbols, that is, all the information on it are mutually independent random variables; Step 3: Establish a parameter adaptive array model of IWOA; First, the one-dimensional bipolar aperiodic BPAM signal is subjected to noise addition processing to obtain the input signal of each independent sub-array in the array stochastic resonance system , the one-dimensional noise-added signal is processed by N saturated system units to obtain , and the obtained is averaged by summation to obtain the output response of the array model , then the parameters of the improved whale optimization system are initialized, the improved whale optimization algorithm is run, the system parameters that induce stochastic resonance are found, the noisy image is subjected to stochastic resonance processing, and the results are considered using the evaluation index of peak signal-to-noise ratio; Step 4: Demodulate and decode; Step 5: Restore the image.

2. The image enhancement method based on optimizing the parameters of array stochastic resonance by an improved whale algorithm according to claim 1, characterized in that, The output response of the array model in step 3 The calculation is specifically performed according to the following steps: Each non-linear system unit in the array saturation system is: （2） In the formula, and are the system parameters of the array saturation stochastic resonance processing model, , is the size of the system array unit, is the input signal of the array model, is the output of the array unit, is independent and identically distributed Gaussian white noise with a mean of 0 and a variance of ; The one-dimensional noisy signal in formula (2) is used as the input of each array saturation unit. The one-dimensional noisy signal is processed by saturation system units to obtain . is averaged by summation to obtain the output response of the array model. The formula is as follows: （3）； In the array stochastic resonance system, the fourth-order Runge-Kutta method is used for calculation, and its principle is as follows: For the differential equation （4） The calculation formula using the fourth-order Runge-Kutta method is: （5） where h is the solution step size.

3. The image enhancement method for optimizing the parameters of array stochastic resonance based on the improved whale algorithm according to claim 2, characterized in that The improved whale optimization algorithm in Step 3 is specifically as follows: First, use the chaotic Iterative mapping to initialize the whale population to obtain a solution space with a more uniform initial solution distribution; then, balance and improve the global exploration and local development capabilities of the algorithm through the non-linear time-varying factor and the adaptive weight strategy; finally, combine the stochastic learning strategy to increase the population diversity to improve the global optimization ability of the algorithm, and introduce the Cauchy mutation operator to enhance the ability of the algorithm to jump out of the local optimum; specifically as follows: Iterative mapping initialization, specifically as the following formula: （6） In the formula, ; Non-linear convergence factor and variable weight: Convergence factor A non-linear variation strategy as the number of evolutionary iterations increases, that is: （7） Nonlinear time-varying factor takes values that change dynamically as the number of iterations increases; Variable weight strategy, that is: （8） The improved position update formula is as follows: （9） （10） （11） As the number of iterations increases, the weight in the variable weight strategy increases non-linearly; Stochastic learning strategy: In the learning stage of the teaching and learning-based optimization algorithm, a stochastic learning strategy is proposed to simulate the learning mode of whales discussing and communicating with each other. By learning from excellent individuals, the position of each whale is optimized, the social learning ability of the whale population is increased, thereby increasing the diversity of the whale population and improving the quality of the whale population, so as to improve the global search performance of the algorithm. As shown in formula (12), for whale individuals , different individuals are randomly selected from the whale population , and learn from them to adjust their own positions; （12） where the learning factor is a random number between (0, 1), reflecting the differences in the learning abilities of individual whales; After learning, by comparing the fitness values to select more excellent individuals, if , the population accepts the new individual and replaces the individual , otherwise the population rejects the inferior individual ; Cauchy mutation strategy: Use the following Cauchy mutation formula to update the position of the current optimal individual, that is: （13） wherein, is the new value obtained by the current optimal value after Cauchy perturbation, is the Cauchy operator, and the formula of the standard Cauchy distribution function is: （14） Since the Cauchy probability density function has a wide distribution range and can generate random numbers far from the origin, it can impose a strong perturbation on the whale individuals, enabling the perturbed whales to quickly avoid the local optimum; at the same time, due to the low peak value of the Cauchy distribution, the individual search time is largely shortened, so that the algorithm can converge faster.

4. The image enhancement method based on optimizing the parameters of array stochastic resonance by an improved whale algorithm according to claim 1, wherein Step 4 is specifically: Set the start time of each symbol to be , and the duration to be ; the demodulation method for the output response of the array saturation stochastic resonance system is as follows: （15） Demodulated one-dimensional binary signal is decoded into decimal symbols to obtain a one-dimensional sequence .

5. The image enhancement method for optimizing the parameters of array stochastic resonance based on the improved whale algorithm according to claim 1, wherein Step 5 is specifically: According to the anti-scanning method, the one-dimensional sequence is subjected to anti-scanning for image dimensionality reduction to obtain a restored grayscale image .

Images