A method and system for denoising sonar images based on shear wave transform of meyer window function

Abstract

The application provides a kind of based on the shear wave transformation of Meyer window function's sonar image noise reduction method and system.The method comprises: the transformation of reverberation noise model to Gaussian additive noise model is combined with shear wave transformation;In the process of shear wave transformation, considering the continuity, smoothness and compact support performance shown by wavelet function and scale function in time domain and frequency domain, Meyer window function based on the performance shown in time domain and frequency domain is proposed to construct shear wave filter;In order to avoid the influence of gray overflow in sonar image, and realize better reverberation suppression effect, noise variance estimation based on weak texture block is proposed, and the root mean square coefficient obtained by the shear wave transformation of simulated noise is combined to obtain adaptive filtering threshold in each scale and direction.Experiments show that the method proposed in the application can more effectively suppress reverberation noise, and has better edge preservation effect.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of sonar image processing, and particularly relates to a sonar image denoising method and system based on shear wave transform of a Meyer window function. BACKGROUND

[0002] With the gradual increase of people's demand for marine resources, sonar detection technology has become the current focus of research. Sonar detection technology plays a key role in seabed topography mapping, underwater search and rescue, underwater target detection and suspicious target survey of submarines. Among them, sonar imaging as a kind of current detection technology can intuitively reflect the underwater scene information, but is affected by marine noise, equipment noise, sound wave propagation scattering and the like, resulting in serious noise interference of the sonar image. The phenomenon mainly presents in the form of speckle noise on the sonar image, which leads to a serious decline in image quality and plays a strong hindrance to the accurate detection of subsequent targets. Therefore, effective denoising of the sonar image plays an important role in the preprocessing of underwater target detection.

[0003] The main noise reduction techniques of sonar images can be divided into spatial domain noise reduction (such as linear filtering and nonlinear filtering) and transform domain noise reduction (such as Fourier transform and wavelet transform). Among them, the wavelet transform has the advantages of low entropy, flexible base function selection, multi-resolution noise reduction, and simple principle, and is widely used in sonar image noise reduction technology. Among them, Kumudham compared the performance of median filter and symmetric wavelet filter, and found that symmetric wavelet filter has excellent performance in sonar image denoising. Zhang proposed a sonar image fusion method based on directional filter and morphological wavelet. The sonar images collected under different views are decomposed by morphological wavelet at multiple scales, and then the decomposed high-frequency part is input into the directional filter to provide accurate details of the image. Finally, the low-frequency and high-frequency parts of different scales and different directions are fused to reconstruct. This method has achieved good repair effect in ship detection images, but this method needs to fuse different view image sequences, and the number of directions of the directional filter is limited and cannot improve higher resolution. Priyadharsini proposed using stationary wavelet transform to denoise sonar images, using Laplace filter to sharpen low-frequency components, and calculating the difference between the sharpening result and the low-frequency to obtain the details of the low-frequency component. Add to the original image to enhance the low-frequency part. Through the result, this method has better performance than discrete wavelet transform. Sang combined morphological wavelet decomposition and hidden Markov tree model to denoise sonar images. The hidden Markov tree is trained by the noise sonar image, and the noise is removed by Bayesian estimation. It shows good performance in removing Gaussian noise of sonar images. Huang combined wavelet transform and K-SVD dictionary learning to realize adaptive learning of dictionary on each resolution component, which has good speckle suppression ability and edge detail preservation characteristics, but is affected by KSVD dictionary training. The operation speed of this method has great challenge. In summary, whether it is the application of wavelet transform or the combination with other algorithms, the current sonar image denoising method based on wavelet transform cannot better represent the sonar image and the blurred edge details in the image. The shearlet transform presents different directional characteristics from the wavelet transform, which can provide multi-scale and multi-directional detail representation, and has better edge and detail information preservation ability while suppressing noise. In the current latest research, Wang Lei applied shearlet transform to side-scan sonar image denoising and achieved certain denoising effect, but the researcher did not consider the reverberation characteristics of sonar images, and only simulated the denoising performance of shearlet transform on sonar image denoising. Liu Guangyu combined density clustering, gray scale transformation and shearlet transform to denoise sonar images. Although the characteristics of sonar images are considered, the consideration is only for the removal of simulated reverberation noise on sonar images, which is only a simulation test of the denoising performance of shearlet transform.

[0004] Based on the above analysis, current research focuses on denoising sonar images using shear wave transform. However, current researchers have not addressed the reverberation noise in actual sonar images or considered the lack of a reference image. Therefore, this invention applies shear wave transform to sonar image denoising, proposing a combination of sonar image noise transformation and shear wave transform. The shear wave filter is obtained by scaling, translating, and rotating continuous wavelets. Considering the excellent continuity, smoothness, and tight support of Meyer's wavelet function and scaling function in the time and frequency domains, a shear wave filter based on the Meyer window function is proposed. To avoid pixel grayscale overflow in sonar images, a sonar image filtering threshold based on weak texture block noise variance estimation is proposed for different frequency domain coefficients. The algorithm of this invention first starts from the noise characteristics of sonar images, transforming Rayleigh multiplicative noise in the sonar image into approximately Gaussian randomly distributed additive noise. Secondly, a Meyer window function is constructed and transformed to form shear wave filters at different scales and directions, and the noise-transformed image is subjected to shear wave transform to obtain coefficients in different frequency domains. Next, the estimated variance based on weak texture blocks proposed in this invention is combined with the mean square coefficients at different scales and in different directions obtained from the simulated Gaussian noise image to obtain the filtering thresholds in each scale and direction. Finally, the coefficients at each scale and in each direction are filtered, and the final denoising result is obtained through inverse shear wave transform and inverse noise model transform. Summary of the Invention

[0005] In view of this, the purpose of this invention is to propose a sonar image denoising method and system based on Meyer window function shear wave transform, so as to improve the accuracy of motion trajectory recognition of weak moving targets.

[0006] To achieve the above objectives, this invention proposes a sonar image denoising method based on Meyer window function shear wave transform, comprising:

[0007] The original sonar image is subjected to grayscale transformation to obtain a grayscale image, and the grayscale image is subjected to logarithmic transformation to obtain a grayscale transformed image. The grayscale image that conforms to the Rayleigh multiplicative noise model is transformed into the grayscale transformed image that is close to the additive noise model that conforms to the Gaussian random distribution through the logarithmic transformation.

[0008] The reverberant noise model image is scaled by non-subsampled Laplacian pyramid transform to obtain a set of scaled images at l scales; the set of scaled images includes a low-frequency scale image and l-1 high-frequency scale images.

[0009] Based on the number of decomposition directions at different scales of the scale-decomposed image set, a corresponding Meyer window function is constructed, and the Meyer window function is converted from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain filters.

[0010] The time-domain filter is transformed in the frequency domain and normalized to obtain a shear wave filter in the frequency domain. The scale-decomposed image set is convolved with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions.

[0011] A random noise image conforming to a Gaussian random distribution is simulated and generated. The random noise image is decomposed by noise image shear wave decomposition to obtain the root mean square coefficients at different scales and in different directions. The noise standard deviation is estimated by extracting weak texture blocks from the grayscale transformed image. A corresponding weighting coefficient constant term is assigned to the threshold of each scale.

[0012] The root mean square coefficients of different scales and directions obtained from the decomposition, the noise standard deviation, and the weighting coefficient constant are multiplied together to obtain the adaptive threshold of the decomposition coefficients of the grayscale transformed image at different scales and directions, and then filtered by a hard threshold function.

[0013] Shear wave reconstruction is performed on the coefficients of sonar images at different scales and in different directions after filtering, and then inverse logarithmic transform is performed to obtain the denoised sonar image.

[0014] In some embodiments, noisy image shearing decomposition includes:

[0015] The random noise image is scaled by non-subsampled Laplacian pyramid transform to obtain a set of scaled random noise images at l scales; the set of scaled random noise images includes a low-frequency random noise scale image and l-1 high-frequency random noise scale images.

[0016] Based on the number of decomposition directions at different scales of the scale-decomposed random noise image set, a corresponding Meyer window function is constructed, and the Meyer window function is converted from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain random noise filters.

[0017] The time-domain random noise filter is transformed and normalized in the frequency domain to obtain a shear wave random noise filter in the frequency domain. The scale-decomposed random noise image set of the sonar image is convolved with the shear wave random noise filter to obtain the root mean square coefficients of different scales and directions.

[0018] In some embodiments, l is 5.

[0019] In some embodiments, based on the number of decomposition directions at different scales of the scale-decomposed image set, a corresponding Meyer window function is constructed, and by converting the scale-decomposed image set from a pseudo-polar coordinate system to a Cartesian coordinate system using the Meyer window function, a time-domain filter with l-1 high-frequency scales is constructed, including:

[0020] Based on the number of decomposition directions at different scales 2 j Construct the corresponding Meyer window function, with a dimension of 2L×2. j , where j is the decomposition level and L is the dimension of the time-domain filter;

[0021] The Meyer window function is transformed from pseudo-polar coordinates to Cartesian coordinates to construct time-domain filters for l-1 high-frequency scales. The filter dimensions for each scale are L1×L1, L1×L1, L2×L2, and L2×L2, respectively. The number of time-domain filters is determined by the number of decomposition directions, 2. j The decision is made, where L1 is the filter dimension of the second and third scale components, L2 is the filter dimension of the fourth and fifth scale components, and j is the decomposition level. In some embodiments, the time-domain filter is frequency-domain transformed and normalized to obtain a frequency-domain shear wave filter. The scale-decomposed image set is convolved with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions, including:

[0022] The dimensions of the shear wave decomposition coefficients are W×H×2. j (j∈l), where W is the width of the original sonar image, H is the height of the original sonar image, j is the decomposition direction coefficient, and l is the decomposition horizontal coefficient.

[0023] To achieve the above objectives, this invention also proposes a sonar image denoising system based on Meyer window function shear wave transform, comprising:

[0024] The preparation module is used to perform grayscale transformation on the original sonar image to obtain a grayscale image, and to perform logarithmic transformation on the grayscale image to obtain a grayscale transformed image. The logarithmic transformation transforms the grayscale image that conforms to the Rayleigh multiplicative noise model into the grayscale transformed image that is close to the additive noise model that conforms to the Gaussian random distribution.

[0025] The decomposition module is used to perform scale decomposition on the reverberation noise model image through non-subsampled Laplacian pyramid transform to obtain a set of scaled images at l scales; the set of scaled images includes a low-frequency scale image and l-1 high-frequency scale images;

[0026] The conversion module is used to construct the corresponding Meyer window function according to the number of decomposition directions at different scales of the scale-decomposed image set, and convert the Meyer window function from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain filters.

[0027] The convolution module is used to perform frequency domain transformation and normalization on the time domain filter to obtain a shear wave filter in the frequency domain. The scale decomposition image set is convolved with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions.

[0028] The weighting module is used to simulate and generate a random noise image that conforms to a Gaussian random distribution, perform noise image shear wave decomposition on the random noise image to obtain root mean square coefficients at different scales and in different directions, and estimate the noise standard deviation by extracting weak texture blocks from the grayscale transformed image, and assign corresponding weighting coefficient constants to the threshold of each scale.

[0029] The filtering module is used to multiply the root mean square coefficients of different scales and directions obtained by the decomposition, the noise standard deviation, and the weighting coefficient constant term to obtain the adaptive threshold of the decomposition coefficients of the grayscale transformed image at different scales and directions, and then filter them through a hard threshold function.

[0030] The results module is used to reconstruct the sheared wave from the coefficients of the filtered sonar images at different scales and in different directions, and to perform an inverse logarithmic transform to obtain the denoised sonar images.

[0031] In some embodiments, the weighting module includes:

[0032] The scale decomposition unit is used to perform scale decomposition on the random noise image through non-subsampled Laplacian pyramid transform to obtain a set of scale-decomposed random noise images at l scales; the set of scale-decomposed random noise images includes a low-frequency random noise scale image and l-1 high-frequency random noise scale images.

[0033] The coordinate transformation unit is used to construct the corresponding Meyer window function according to the number of decomposition directions at different scales of the scale-decomposed random noise image set, and to convert the Meyer window function from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain random noise filters.

[0034] The noise convolution unit is used to perform frequency domain transformation and normalization on the time-domain random noise filter to obtain a shear wave random noise filter in the frequency domain. The scale decomposition random noise image set of the sonar image is convolved with the shear wave random noise filter to obtain root mean square coefficients of different scales and directions.

[0035] In some embodiments, the conversion module includes:

[0036] Window function building blocks are used to determine the number of decomposition directions at different scales. j Construct the corresponding Meyer window function, with a dimension of 2L×2. j , where j is the decomposition level and L is the dimension of the time-domain filter;

[0037] The filter construction unit is used to convert the Meyer window function from pseudo-polar coordinates to Cartesian coordinates, thereby constructing time-domain filters for l-1 high-frequency scales. The filter dimensions for each scale are L1×L1, L1×L1, L2×L2, and L2×L2, respectively. The number of time-domain filters is determined by the number of decomposition directions, 2. j The decision is made, where L1 is the filter dimension of the second and third scale components, L2 is the filter dimension of the fourth and fifth scale components, and j is the decomposition level.

[0038] In summary, this invention proposes a sonar image denoising method based on Meyer window function shear wave transform. Specifically, the algorithm has three improvements. First, to effectively apply the shear wave transform-based denoising method to sonar images, it proposes combining the transformation from a reverberation noise model to a Gaussian additive noise model with the shear wave transform. Second, considering the continuity, smoothness, and tight support performance of wavelet functions and scaling functions in both the time and frequency domains during the shear wave transform process, this invention proposes constructing a shear wave filter based on the Meyer window function, which exhibits excellent performance in both the time and frequency domains. Finally, to avoid the influence of grayscale overflow in sonar images and achieve better reverberation suppression, this invention proposes noise variance estimation based on weak texture blocks and combines it with the root mean square coefficient obtained by shear wave transforming simulated noise to obtain adaptive filtering thresholds for each scale and direction. Simulation and experimental results show that the proposed method can more effectively suppress reverberation noise and has a better edge preservation effect. Compared with other comparison algorithms, the proposed algorithm achieves the best results in terms of PSNR (Peak Signal-to-Noise Ratio) and SSMI (Structural Similarity) for the denoised images. Attached Figure Description

[0039] In the accompanying drawings, unless otherwise specified, the same reference numerals throughout the various drawings denote the same or similar parts or elements. These drawings are not necessarily drawn to scale. It should be understood that these drawings depict only some embodiments disclosed in the invention and should not be construed as limiting the scope of the invention.

[0040] Figure 1 A flowchart illustrating a sonar image denoising method based on Meyer window function shear wave transform according to an embodiment of the present invention is shown.

[0041] Figure 2 A schematic diagram of a sonar image denoising system based on Meyer window function shear wave transform according to an embodiment of the present invention is shown.

[0042] Figure 3 A structural diagram of a weighting module according to an embodiment of the present invention is shown.

[0043] Figure 4 A schematic diagram of the conversion module according to an embodiment of the present invention is shown.

[0044] Figure 5 A flowchart illustrating a sonar image denoising method based on Meyer window function shear wave transform according to an embodiment of the present invention is shown.

[0045] Figure 6a The simulated image is shown as a noise-free reference image.

[0046] Figure 6b The simulated image of Gaussian complex noise δ=2 is shown.

[0047] Figure 7a The denoising results of the D4_3 wavelet transform-hard thresholding algorithm are visualized.

[0048] Figure 7b The denoising results of the D4_3 wavelet transform-soft thresholding algorithm are visualized.

[0049] Figure 7c The denoising results of the DCT algorithm are visualized.

[0050] Figure 7d The denoising results of the KSVD algorithm are visualized.

[0051] Figure 7e The denoising results of the NLM algorithm are visualized.

[0052] Figure 7f The denoising results of the FNLM algorithm are visualized.

[0053] Figure 7g The results of the TV algorithm noise reduction are visualized.

[0054] Figure 7h The denoising results of the shearlet algorithm are visualized.

[0055] Figure 7i The denoising results of the sonar image denoising method based on the Meyer window function shear wave transform according to an embodiment of the present invention are visualized.

[0056] Figure 8a The performance curves of the PSNR algorithm under different signal-to-noise ratios are shown.

[0057] Figure 8b The performance curves of the SSIM algorithm under different signal-to-noise ratios are shown.

[0058] Figure 9a The results of noise reduction using the D4_3 wavelet transform-hard thresholding algorithm are shown for the side-scan sonar images of aircraft wreckage.

[0059] Figure 9b The results of noise reduction using the D4_3 wavelet transform-soft thresholding algorithm are shown for side-scan sonar images of aircraft wreckage.

[0060] Figure 9c The results of DCT algorithm noise reduction are shown for side-scan sonar images of aircraft wreckage.

[0061] Figure 9d The KSVD algorithm denoising results are shown for side-scan sonar images of aircraft wreckage.

[0062] Figure 9e The results of TV algorithm noise reduction are shown for side-scan sonar images of aircraft wreckage.

[0063] Figure 9f The results of NLM algorithm noise reduction are shown for side-scan sonar images of aircraft wreckage.

[0064] Figure 9g The results of FNLM algorithm noise reduction are shown for side-scan sonar images of aircraft wreckage.

[0065] Figure 9h The results of ANLM algorithm noise reduction are shown for side-scan sonar images of aircraft wreckage.

[0066] Figure 9i The results of noise reduction using the shearlet algorithm are shown for side-scan sonar images of aircraft wreckage.

[0067] Figure 9j The following describes the denoising results of side-scan sonar images of aircraft wreckage using a sonar image denoising method based on the Meyer window function shear wave transform according to an embodiment of the present invention.

[0068] Figure 10a The image shows a side-scan sonar image of human remains.

[0069] Figure 10b The results of noise reduction using the D4_3 wavelet transform-hard thresholding algorithm are shown for the side-scan sonar image of human remains.

[0070] Figure 10c The results of noise reduction using the D4_3 wavelet transform-soft thresholding algorithm are shown for the side-scan sonar image of human remains.

[0071] Figure 10d The results of DCT algorithm noise reduction are shown for side-scan sonar images of human remains.

[0072] Figure 10eThe KSVD algorithm denoising results are shown for side-scan sonar images of human remains.

[0073] Figure 10f The results of TV algorithm noise reduction are shown for side-scan sonar images of human remains.

[0074] Figure 10g The results of NLM algorithm noise reduction are shown for side-scan sonar images of human remains.

[0075] Figure 10h The results of FNLM algorithm noise reduction are shown for side-scan sonar images of human remains.

[0076] Figure 10i The results of noise reduction using the shearlet algorithm are shown for side-scan sonar images of human remains.

[0077] Figure 10j The illustration shows the denoising results of a side-scan sonar image of human remains using a sonar image denoising method based on the Meyer window function shear wave transform according to an embodiment of the present invention. Detailed Implementation

[0078] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0079] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0080] Noise characteristics of sonar image

[0081] Sonar detects underwater targets by emitting sound waves. However, underwater sound waves are often scattered by the target, the sea surface, the seabed, and various scattering objects, resulting in the received sound waves containing a large amount of scattered waves. Among these, seabed reverberation is the dominant effect. According to Middlenton's seabed reverberation model, assuming the emitted sound signal is S(t), its reverberation at time t is:

[0082]

[0083] Where N is the total number of scattering elements that contribute at time t; g(r n ) is located at r n Each infinitesimal element ΔV at the location n The number of scatterers in the f(r) n ) is the two-way propagation attenuation factor for each scatterer; |α n | represents the amplitude of the scattering coefficient of the scatterer; tn ω0 is the arrival time of the echo; ω0 is the center angular frequency of the sound wave. For α n The phase of g(r). n ),|α n | and They are independent of each other.

[0084] If we take V n (t) represents the instantaneous amplitude of the scattered wave from the nth scatterer at time t, φ n If (t) is its corresponding instantaneous phase value, then:

[0085] V n (t)=g(r n )f(r n )|α n ||s0(tt n (2)

[0086]

[0087] The reverberation at time t can be expressed in the complex form of equation (4).

[0088]

[0089] According to the central limit theorem, when N is sufficiently large, R(t) and I(t) both follow Gaussian distributions and are independent of each other. Therefore, the reverberation amplitude at each time step can be obtained. According to the probability distribution, the reverberation amplitude follows a Rayleigh distribution. Its probability density function is:

[0090]

[0091] Where σ is the attenuation coefficient of the Rayleigh distribution. Since the receiver has a certain gain, the mean of the reverberation changes but the distribution characteristics remain the same. When a gain offset k is introduced, the probability density function of the reverberation amplitude becomes:

[0092]

[0093] Based on the above analysis, a multiplicative noise model for reverberation noise can be obtained.

[0094] g(x,y)=f(x,y)n(x,y) (7)

[0095] Where f(x,y) is the ideal sonar image, n(x,y) is the reverberation noise, g(x,y) is the received real sonar image, and x and y represent the coordinates of the distance and azimuth detected by the sonar, respectively.

[0096] Shearlet transform

[0097] The shear wave transform possesses good time-frequency locality and extremely high direction sensitivity, making it a near-optimal multidimensional sparse representation method. This transform shares the same underlying principle as the wavelet transform, generating its basis functions through scaling, translation, and rotation of a given function.

[0098] For any a>0 and A represents the scaling matrix, B represents the shearing matrix, and both A and B are 2×2 invertible matrices, with |detB| = 1. This is typically set... and Where A0 and B0 are the scaling and shearing matrices for the horizontal cone region D0; and A1 and B1 are the scaling and shearing matrices for the vertical cone region D1. If the wavelet mother function The following equality conditions apply to D0 and D1:

[0099]

[0100]

[0101] in Let ψ be the Fourier transform of ψ. ψ1 and ψ2 are continuous wavelets, and their frequencies support... On (-1,1) And |ψ2| = 1. Therefore, based on the corresponding wavelet mother function, the time-domain shear wave function for different regions can be defined as:

[0102]

[0103] Where ψ a,s,t (x) is the shear wave function, d = 0, 1. and These represent shear wave systems in the horizontal and vertical cone regions, respectively. Therefore, the input function... For example, its continuous shear wave transform expression is:

[0104] SH ψ f(a,s,t)= <f,ψ a,s,t > (11)

[0105] Figure 1 A flowchart illustrating a sonar image denoising method based on Meyer window function shear wave transform according to an embodiment of the present invention is shown. Figure 1 As shown, this sonar image denoising method based on Meyer window function shear wave transform includes:

[0106] Step S11: Perform grayscale transformation on the original sonar image to obtain a grayscale image, and perform logarithmic transformation on the grayscale image to obtain a grayscale transformed image. Through the logarithmic transformation, the grayscale image that conforms to the Rayleigh distribution multiplicative noise model is transformed into the grayscale transformed image that is close to the additive noise model that conforms to the Gaussian random distribution.

[0107] Step S12: Scale decompose the reverberation noise model image by non-subsampled Laplacian pyramid transform to obtain a set of scale decomposed images at l scales; the set of scale decomposed images includes a low-frequency scale image and l-1 high-frequency scale images.

[0108] In one implementation, l is set to 5.

[0109] Step S13: Based on the number of decomposition directions at different scales of the scale-decomposed image set, construct the corresponding Meyer window function, and convert the Meyer window function from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain filters.

[0110] In one implementation, a corresponding Meyer window function is constructed based on the number of decomposition directions at different scales of the scale-decomposed image set. Then, by converting the scale-decomposed image set from a pseudo-polar coordinate system to a Cartesian coordinate system using the Meyer window function, a time-domain filter with l-1 high-frequency scales is constructed, including:

[0111] Based on the number of decomposition directions at different scales 2 j Construct the corresponding Meyer window function, with a dimension of 2L×2. j , where j is the decomposition level and L is the dimension of the time-domain filter;

[0112] The Meyer window function is transformed from pseudo-polar coordinates to Cartesian coordinates to construct time-domain filters for l-1 high-frequency scales. The filter dimensions for each scale are L1×L1, L1×L1, L2×L2, and L2×L2, respectively. The number of time-domain filters is determined by the number of decomposition directions, 2. j The decision is made, where L1 is the filter dimension of the second and third scale components, L2 is the filter dimension of the fourth and fifth scale components, and j is the decomposition level.

[0113] Step S14: Perform frequency domain transformation and normalization on the time domain filter to obtain a shear wave filter in the frequency domain. Convolve the scale decomposition image set with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions.

[0114] In one implementation, the dimension of the shear wave decomposition coefficients is W×H×2. j(j∈l), where W is the width of the original sonar image, H is the height of the original sonar image, j is the decomposition direction coefficient, and l is the decomposition horizontal coefficient.

[0115] Step S15: Simulate and generate a random noise image that conforms to a Gaussian random distribution, perform noise image shear wave decomposition on the random noise image to obtain the root mean square coefficients of different scales and directions, and obtain the noise standard deviation by extracting and estimating the weak texture blocks of the grayscale transformed image, and assign a corresponding weighting coefficient constant term to the threshold of each scale.

[0116] In one implementation, noisy image shearing decomposition includes:

[0117] The random noise image is scaled by non-subsampled Laplacian pyramid transform to obtain a set of scaled random noise images at l scales; the set of scaled random noise images includes a low-frequency random noise scale image and l-1 high-frequency random noise scale images.

[0118] Based on the number of decomposition directions at different scales of the scale-decomposed random noise image set, a corresponding Meyer window function is constructed, and the Meyer window function is converted from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain random noise filters.

[0119] The time-domain random noise filter is transformed and normalized in the frequency domain to obtain a shear wave random noise filter in the frequency domain. The scale-decomposed random noise image set of the sonar image is convolved with the shear wave random noise filter to obtain the root mean square coefficients of different scales and directions.

[0120] Step S16: Multiply the root mean square coefficients of different scales and directions obtained by the decomposition, the noise standard deviation, and the weighting coefficient constant term to obtain the adaptive threshold of the decomposition coefficients of the grayscale transformed image at different scales and directions, and filter them by the hard threshold function.

[0121] Step S17: Perform shear wave reconstruction on the sonar image coefficients of different scales and directions after filtering, and perform inverse logarithmic transformation to obtain the denoised sonar image.

[0122] pass Figure 5 The following descriptions can provide a more detailed understanding of steps S11-S17 above.

[0123] Noise transform

[0124] Current research on sonar image denoising mainly focuses on two directions: one is to add Gaussian white noise to sonar images without a reference image, and then perform denoising processing and evaluate the performance; the other is to denoise the sonar images themselves without a reference image, aiming to reduce the interference of complex background noise (such as seabed reverberation). Therefore, this invention aims to study the second case. However, based on the analysis of the seabed reverberation noise model in the noise characteristics of sonar images, it can be seen that the reverberation noise in sonar images is multiplicative noise following a Rayleigh distribution, while shear wave transform is suitable for removing additive Gaussian noise. Therefore, this invention needs to combine the transformation of the reverberation noise model with shear wave transform to ensure that shear wave transform is suitable for sonar image denoising processing.

[0125] Research has shown that the Fisher-Tippet distribution of multiplicative noise following a Rayleigh distribution, after a logarithmic transformation, is approximately similar to additive Gaussian random noise. Therefore, the reverberation noise model (7) of sonar images can be logarithmically transformed. The transformed additive noise model is then obtained, as shown in equation (8):

[0126]

[0127] in It is the result of the logarithmic transformation of the original desired signal. This is the logarithmic transformation result of the reverberation noise model n(x,y) that follows a Rayleigh distribution, and which approximately follows a Gaussian distribution. Therefore, the transformed sonar image... It can be used as a processing object in noise reduction systems based on shear wave transform.

[0128] Shearlet filter construction

[0129] As described in the section on shear wave transform, shear wave transform processes data by using continuous wavelets as basis functions for scaling, shearing, and translation transformations. Therefore, this invention considers the performance of wavelet functions and scaling functions in terms of continuity, smoothness, and tight support in the time and frequency domains. Haar wavelets exhibit poor frequency domain locality, Shannon wavelets have poor time domain locality, while Meyer wavelets offer locality performance in both the time and frequency domains that falls between the two. Therefore, this invention chooses to apply Meyer wavelets as the basis function for shear wave transformation and constructs a shear wave filter.

[0130] Both the Meyer wavelet function ψ and the scaling function φ are defined in the frequency domain and are compactly supported orthogonal wavelets. The frequency domain expression of the Meyer wavelet function is:

[0131]

[0132] Where v(ω) is any smooth function that satisfies the following conditions:

[0133]

[0134] v(ω)+v(1-ω)=1,0≤ω≤1 (14)

[0135] Daubechies proposed a smooth function:

[0136] v(ω)=ω 4 (35-84ω+70ω 2 -20ω 3 (15)

[0137] Thus, the wavelet function ψ of the shear wave filter is constructed. Image denoising via shear wave transform requires discretizing the shear wave function in equation (10). First, the continuous wave shear wave transform is sampled to obtain... The tight framework above specifically involves binary sampling of the scaling matrix and integer sampling of the shearing matrix, i.e., letting a = 2. -j s = -l (j, l ∈ Z), in discrete coordinates Z 2 Points k∈Z on the y-axis replace the continuously translated points. The final discrete shear wave function is as follows:

[0138]

[0139] Secondly, by defining the scaling and shearing matrices for regions D0 and D1, we can obtain a compact frame of regions D0 and D1 as a function set:

[0140]

[0141]

[0142] Where j≥0, -2 j ≤l≤2 j -1, k∈Z 2 d = 0, 1. Then, according to equation (11), the shear wave transform of a two-dimensional image can be equivalent to... arrive The mapping on the sampled time-domain shear wave transform is finally obtained.

[0143] However, Meyer's scaling function and wavelet function are defined in the frequency domain. According to the definition of the shear wave filter, equations (19) and (20) are used to construct the shear wave filter:

[0144]

[0145]

[0146] in Therefore, we can construct 2 at each decomposition level l. j Meyer window functions in each direction are used, and shear wave filters for each scale and direction are obtained through specific discrete resampling from pseudopolar coordinates to Cartesian coordinates. The shear wave function in the frequency domain can be obtained through the shear wave filter as follows:

[0147]

[0148] in, Final two-dimensional function The shear wave transform can be expressed as:

[0149]

[0150] Shearlet denoising and noise estimation

[0151] Shear wave transform achieves multi-scale decomposition and directional localization of noisy images through multi-scale and multi-directional shear wave filters, providing a near-optimal representation of image edge details. The noisy image is decomposed to obtain coefficients at different scales and directions in the frequency domain. Thresholding is then applied to these decomposed coefficients to achieve image denoising.

[0152] Regarding the selection of the threshold, considering that the different frequency domain coefficient components obtained after the shear wave transform of the noisy image are relatively small, in order to perform adaptive noise reduction processing on each frequency domain coefficient, the threshold selected in this invention is as follows:

[0153]

[0154] Where T(l,j) represents the threshold of the j-direction coefficient at scale l; k is a constant; ε is the noise standard deviation of the input image; l,j The root mean square coefficients are obtained by constructing a Gaussian random noise image with zero mean and variance of 1 in the same dimension as the input image, transforming it using the constructed shear wave filter, and then performing a nonlinear transformation according to equation (24).

[0155]

[0156] in The frequency domain coefficients at each scale and direction after shear wave transformation of Gaussian random noise are denoted by Med, which represents the median. According to equations (23) and (24), this threshold can adaptively denoise the coefficients of different frequency domain components obtained from the decomposition of the noisy image. In addition, since this threshold is processed by Gaussian random variables, it is necessary to Gaussianize the noise model of the noisy image in the noise transformation part.

[0157] However, in real-world scenarios, the noise standard deviation of an image is unknown, so we need to estimate the image noise standard deviation in equation (23). Because of the presence of targets in sonar images, the target echo regions in the images may experience grayscale overflow due to multiplicative noise. Specifically, due to the influence of the upper limit of image grayscale, the effect of reverberation in the target echo region may exceed the grayscale upper limit of 255. However, the upper limit of grayscale image presentation in the image is 255, so selecting the grayscale of the target echo region for noise estimation will result in a large error. Moreover, since the reverberation noise model is multiplicative, the presence of 0 pixel values ​​will eliminate the effect of reverberation when selecting the shadow area as the estimation object. Therefore, in order to solve the above problems and considering the factors of computational load and rapid application in real-world scenarios, this invention proposes a statistical estimation of the noise standard deviation of weak texture blocks in sonar images. As shown in formula (25), the weak texture block is the region of reverberant background in the sonar image, which is not affected by shadow areas and highlight areas.

[0158]

[0159] in The weak texture blocks are selected after logarithmic processing of the sonar image. By combining equations (23), (24) and (25), the corresponding thresholds can be obtained for the coefficients of each frequency domain component.

[0160] Sonar image denoising algorithm based on Meyer window function shearlet transform

[0161] Based on the preceding theoretical analysis, this invention ultimately proposes a sonar image denoising algorithm based on Meyer window function shear wave transform. For example... Figure 1 and Figure 5As shown, firstly, the received sonar image is subjected to grayscale transformation; secondly, in order to adapt to the denoising properties based on shear wave transform, the grayscale sonar image is subjected to logarithmic transformation, so that the multiplicative noise model following the Rayleigh distribution is further transformed into an additive noise model that approximately follows a Gaussian random distribution. Then, we propose to combine reverberation noise transformation with shear wave transform. We decompose the transformed reverberation noise model in the scale decomposition module through non-subsampled Laplace pyramid transform to obtain l scales, where the decomposition scale l is set to 5, including one low-frequency scale and l-1 high-frequency scales, and l-1 high-frequency scales are used for shear wave transform.

[0162] Third, in the shear wave filter construction module shown in the figure, this invention proposes a shear wave filter construction based on the Meyer window function. This is based on the number of decomposition directions at different scales l. j Construct the corresponding Meyer window function, with a dimension of 2L×2. j Next, the Meyer window function is converted from pseudo-polar coordinates to Cartesian coordinates to construct time-domain filters for l-1 high-frequency scales. The filter dimensions for each scale are L1×L1, L1×L1, L2×L2, and L2×L2, respectively, and the number of filters is increased by the number of decomposition directions. j The decision is made. Finally, the filter is transformed in the frequency domain and normalized to obtain the shear wave filter in the frequency domain. The l-1 scales are convolved with the shear wave filter to obtain the final shear wave decomposition coefficients at different scales and in different directions, with dimensions W×H×2. j (j∈l).

[0163] Fourth, by combining the simulated noise shear wave transform with the sonar image noise standard deviation estimation based on weak texture blocks proposed in this invention, adaptive noise removal is achieved for the decomposition coefficients at different scales and in different directions. Specifically, a Gaussian random noise image is first simulated and generated. Then, this noise undergoes a process consistent with the shear wave decomposition of the transformed sonar image to obtain the root mean square coefficients ε at different scales and in different directions. l，j Then, by extracting weak texture blocks from the transformed sonar image, the noise standard deviation σ is estimated. Subsequently, a corresponding constant term k is assigned to the threshold of each scale. Then, the threshold of each decomposition coefficient is obtained according to equation (23), and filtering is performed through a hard thresholding function. Finally, the shear wave reconstruction of the coefficients of each scale and direction of the filter is performed and the inverse logarithmic transform is performed to obtain the denoised sonar image.

[0164] Figure 2 A schematic diagram of a sonar image denoising system based on Meyer window function shear wave transform according to an embodiment of the present invention is shown. Figure 2 As shown, the sonar image denoising system based on Meyer window function shear wave transform can be divided into the following components:

[0165] Preparation module 21 is used to perform grayscale transformation on the original sonar image to obtain a grayscale image, and to perform logarithmic transformation on the grayscale image to obtain a grayscale transformed image. The logarithmic transformation transforms the grayscale image that conforms to the Rayleigh distribution multiplicative noise model into the grayscale transformed image that is close to the Gaussian random distribution additive noise model.

[0166] The decomposition module 22 is used to perform scale decomposition on the reverberation noise model image through non-subsampled Laplacian pyramid transform to obtain a set of scaled images at l scales; the set of scaled images includes a low-frequency scale image and l-1 high-frequency scale images;

[0167] The conversion module 23 is used to construct a corresponding Meyer window function based on the number of decomposition directions at different scales of the scale-decomposed image set, and to convert the Meyer window function from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain filters.

[0168] The convolution module 24 is used to perform frequency domain transformation and normalization on the time domain filter to obtain a shear wave filter in the frequency domain, and to convolve the scale decomposition image set with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions.

[0169] The weighting module 25 is used to simulate and generate a random noise image that conforms to a Gaussian random distribution, perform noise image shear wave decomposition on the random noise image to obtain root mean square coefficients at different scales and in different directions, and estimate the noise standard deviation by extracting weak texture blocks from the grayscale transformed image, and assign a corresponding weighting coefficient constant term to the threshold of each scale.

[0170] The filtering module 26 is used to multiply the root mean square coefficients of different scales and directions obtained by the decomposition, the noise standard deviation and the weighting coefficient constant term to obtain the adaptive threshold of the decomposition coefficients of the grayscale transformed image at different scales and directions, and to perform filtering through a hard threshold function;

[0171] Result module 27 is used to reconstruct the sheared wave from the sonar image coefficients of different scales and directions after filtering, and to perform inverse logarithmic transformation to obtain the denoised result sonar image.

[0172] Figure 3 A structural diagram of a weighting module according to an embodiment of the present invention is shown. Figure 3 As shown, the weighting module 25 may include:

[0173] The scale decomposition unit 251 is used to perform scale decomposition on the random noise image through non-subsampled Laplacian pyramid transform to obtain a set of scale-decomposed random noise images at l scales; the set of scale-decomposed random noise images includes a low-frequency random noise scale image and l-1 high-frequency random noise scale images.

[0174] The coordinate transformation unit 252 is used to construct the corresponding Meyer window function according to the number of decomposition directions at different scales of the scale-decomposed random noise image set, and to convert the Meyer window function from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain random noise filters.

[0175] The noise convolution unit 253 is used to perform frequency domain transformation and normalization on the time-domain random noise filter to obtain a shear wave random noise filter in the frequency domain. The scale decomposition random noise image set of the sonar image is convolved with the shear wave random noise filter to obtain root mean square coefficients of different scales and directions.

[0176] Figure 4 A structural diagram of a conversion module according to an embodiment of the present invention is shown. Figure 4 As shown, the conversion module 23 may include:

[0177] Window function building unit 231 is used to determine the number of decomposition directions at different scales. j Construct the corresponding Meyer window function, with a dimension of 2L×2. j , where j is the decomposition level and L is the dimension of the time-domain filter;

[0178] The filter construction unit 232 is used to convert the Meyer window function from a pseudo-polar coordinate system to a Cartesian coordinate system, thereby constructing time-domain filters for l-1 high-frequency scales. The filter dimensions for each scale are L1×L1, L1×L1, L2×L2, and L2×L2, respectively. The number of time-domain filters is determined by the number of decomposition directions, 2. j The decision is made, where L1 is the filter dimension of the second and third scale components, L2 is the filter dimension of the fourth and fifth scale components, and j is the decomposition level.

[0179] The feasibility and effectiveness of the present invention are verified through simulation experiments.

[0180] Experimental verification

[0181] 1. Simulation experimental verification

[0182] The method proposed in this invention was tested in an experimental environment using an Intel(R) Core(TM) i7-10710U CPU. In the simulation experiment, the decomposition level l was set to 5, including the low-frequency component, and the number of directions for each high-frequency component of the decomposition was 2. j The shear wave filters for each sub-decomposition are 16, 16, 8, and 8, with dimensions L1 and L2 of 16 and 32 respectively. The coefficient k in the threshold expression is [2, 3, 4], where k represents the coefficients of the low-frequency component, the intermediate component, and the high-frequency component, respectively. The performance of the algorithm of this invention is compared with other mainstream sonar image denoising algorithms by simulating a reverberation noise model.

[0183] Evaluation index

[0184] In the simulation experiments, Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity-to-Simple (SSIM) were selected as the two criteria for evaluating the denoising performance of the simulated images. PSNR is defined as follows:

[0185]

[0186] Where MSE is the mean squared error, which is defined as follows: The denoising result is shown in the image, where M and N are the image height and width, respectively. By definition, a higher PSNR indicates better denoising results. Furthermore, the SSIM metric is used to evaluate the structural similarity between the denoised image and the reference image.

[0187]

[0188] Where, μ f , σ f These represent the mean and standard deviation of the reference image, respectively. C1 and C2 represent the mean and standard deviation of the noise reduction results, respectively. C1 and C2 are used to prevent zero terms in the denominator. i =(K i L) 2 i = 0, 1, and K1 = 0.01, K2 = 0.03, L = 255.

[0189] Simulation noise model

[0190] Based on the analysis of the reverberation noise model of sonar images according to the noise characteristics of sonar images, the reverberation noise in sonar images is multiplicative Rayleigh noise. Therefore, a noise model for the simulation image is constructed.

[0191]

[0192]

[0193] g(x,y)=f(x,y)n(x,y) (30)

[0194] Where n1(x,y) and n2(x,y) are random noises following a Gaussian distribution, f(x,y) is the simulation reference image, and g(x,y) is the simulation noise image.

[0195] Simulation experimental performance evaluation

[0196] Based on the simulation noise model construction in the simulation noise model section, we can obtain, as follows: Figure 6a and 6b As shown, reverberation noise is simulated on a noise-free reference image. Two Gaussian white noises with a mean of 0 and a variance of 1 are generated as the real and imaginary parts of the complex Gaussian noise. According to the probability distribution principle, the variance of the complex noise is 2. The amplitude of the complex noise is then calculated and used as the multiplicative noise of the noise-free reference image.

[0197] First, this invention performs noise reduction processing on the noisy image in Figure 6, as shown in Figure 7, and analyzes the reverberation suppression effect of each algorithm. Besides... Figure 7h Surprisingly, each algorithm performed corresponding noise transformations and noise standard deviation estimations on the noisy images. Figure 7a and 7b In this invention, the D4 wavelet transform, which is widely used in noise reduction processing, was used to conduct experiments on hard thresholding and soft thresholding denoising methods. However, the results showed that when dealing with reverberation noise models, the overall grayscale value of the image was reduced after denoising. Moreover, the D4 wavelet transform was not very effective in suppressing reverberation noise. Figure 7c The result is the noise reduction of the image using Discrete Cosine Transform (DCT), which shows good performance in simulated noisy images after noise transformation. Figure 7d This is the denoising result after KSVD transformation. This method involves constructing a DCT dictionary, updating the dictionary and sparse matrix, and finally reconstructing the denoising result using the dictionary and sparse matrix. It can be seen that its denoising result is comparable to that of DCT. However, KSVD requires updating the DCT dictionary and sparse matrix, indicating that denoising using DCT has reached the upper limit of removing reverberation noise using dictionary representation methods. Experimental tests show that the denoising performance of the KSVD method tends to stabilize after 10 training rounds. Therefore, this invention sets the dictionary update rounds to 10, demonstrating that the computational performance of the KSVD method is far inferior to that of the DCT method. Figure 7e and 7f These are all noise reduction results based on NLM and its improved algorithms.Figure 7e The result is a noise reduction using the Non-LinearMinimization (NLM) algorithm. The noise reduction result shows that speckle noise has been suppressed to some extent. However, this method requires traversing all pixels when filtering each pixel, so the computational efficiency is low. Figure 7f It is the denoising result of the improved NLM algorithm Fast Pixelwise Non-Local Means (FNLM). Its essence is that instead of filtering each pixel individually like NLM, it calculates the weights of the relative positions of all pixels and then performs filtering. Although FNLM achieves the same denoising effect as NLM, it has a huge improvement in computational efficiency. Figure 7g The denoising result is based on total variation (TV) regularization. This method has a good effect on preserving the edges of the denoised image, but it is not good at suppressing speckle noise. Figure 7h The result is the image obtained by directly processing the reverberation noise model using shear wave transform. However, based on the description of the noise conversion part and the denoising results, it can be seen that shear wave transform cannot be directly applied to the denoising of the reverberation noise model effectively, and its denoising results still contain some speckle noise. Finally... Figure 7i This invention proposes an algorithm that combines the multi-scale and multi-directional decomposition characteristics of the shear wave transform in the frequency domain, its excellent performance in handling Gaussian noise, and the excellent continuity, smoothness, and tight support characteristics of the Meyer window function in both the time and frequency domains. This invention transforms the reverberation noise model, constructs a shear wave filter using the Meyer window function, and denoises the noise image of the reverberation model. Figure 7i The noise reduction results show that the method proposed in this invention has good reverberation noise suppression capability and edge detail preservation capability.

[0198] Secondly, to more accurately assess the denoising performance of each algorithm, this invention applies different methods to denoise images with different signal-to-noise ratios and calculates their performance metrics. For example... Figure 8a and Figure 8b As shown, the denoising performance of each algorithm can be intuitively seen by calculating the evaluation index of the denoising results of each algorithm. The method proposed in this invention has higher performance in both PSNR and SSIM than other mainstream sonar image denoising methods.

[0199] Furthermore, Tables 1, 2, and 3 specifically illustrate the performance values ​​of different algorithms when the variance of the reverberant complex signal is 2, 3, and 4. The algorithm of this invention outperforms other algorithms in both PSNR and SSIM metrics, and also demonstrates superior computational efficiency. However, it falls far short of wavelet transform. This is because the shear wavelet transform decomposes at a higher resolution scale than the wavelet transform. The shear wavelet transform requires constructing filters at different scales and directions, and calculating the root mean square coefficients of the filtering thresholds at different scales and directions, thus increasing the computational load compared to the wavelet transform. Nevertheless, it still holds a significant advantage over other algorithms, and its noise reduction performance is far superior to that of the wavelet transform.

[0200] Table 1. Noise reduction performance metrics and computation speed of different algorithms, σ 2 =2

[0201] Method PSNR / dB SSIM Time / s Noise image 11.1786 0.1664 \ D4_3_hard 25.1011 0.7164 0.402 D4_3_soft 13.8397 0.6717 0.407 DCT 27.3883 0.8307 5.065 KSVD 26.4788 0.8259 188.370 NLM 25.3737 0.8342 242.363 FNLM 25.3737 0.8342 15.255 TV 23.3452 0.6940 2.122 Shearlet 19.7654 0.9015 4.540 Our method 29.0447 0.9575 4.556

[0202] Table 2. Noise reduction performance metrics and computation speed of different algorithms, σ 2 =3

[0203] Method PSNR / dB SSIM Time / s Noise image 8.4427 0.1247 \ D4_3_hard 17.7114 0.6376 0.450 D4_3_soft 15.9611 0.7360 0.456 DCT 18.5544 0.7651 5.565 KSVD 18.5169 0.7555 190.971 NLM 17.8119 0.7718 233.921 FNLM 17.8119 0.7717 16.811 TV 15.8684 0.5970 2.114 Shearlet 13.5350 0.8201 5.009 Our method 19.7386 0.9116 5.056

[0204] Table 3. Noise reduction performance metrics and computation speed of different algorithms, σ 2 =4

[0205]

[0206]

[0207] Real data verification

[0208] The performance of the algorithm of this invention and other algorithms was tested using real-world data. The real-world data used for the algorithm of this invention were side-scan sonar images, available at https: / / www.edgetech.com / underwater-technology-gallery / . Since there were no reference images for the actual sonar images, the quality of the denoised images could only be evaluated subjectively.

[0209] like Figure 9a-9j and Figure 10a-10j As shown, side-scan sonar images of aircraft wreckage and human remains were subjected to grayscale transformation and then filtered using various algorithms. A comprehensive comparison of the noise reduction performance of each algorithm shows that the method proposed in this invention has stronger seabed reverberation suppression capabilities and better preservation of target edge information compared to other algorithms.

[0210] In summary, this invention proposes a sonar image denoising method based on Meyer window function shear wave transform. Complex reverberation noise severely affects the quality of sonar images and the difficulty of target detection. The method proposed in this invention can effectively suppress the influence of reverberation noise. First, this invention transforms the reverberation noise model into a noise image that approximately follows a Gaussian distribution, ensuring the effective application of shear wave transform. Second, to ensure the continuity, smoothness, and tight support performance of the wavelet function in the time and frequency domains, this invention proposes a shear wave filter construction method based on Meyer window function. Finally, to avoid the influence of grayscale overflow in sonar images and improve the suppression effect of reverberation noise, this invention combines the proposed noise estimation variance based on weak texture blocks with the root mean square coefficient of simulated noise to obtain adaptive filtering thresholds at each scale and in each direction, achieving a more effective filtering method.

[0211] The proposed method was applied to simulated reverberant noise images and actual sonar images. Experimental results show that the proposed denoising method can effectively suppress reverberant noise while preserving the edge details of the target well. Compared with the comparison algorithm, the proposed denoising method has greater advantages in PSNR and SSMI, and also shows better reverberation suppression effect in actual sonar image denoising. This invention provides an effective and important reverberant noise suppression method for sonar images, which has practical significance and reference value for subsequent target segmentation and target detection in sonar images.

[0212] The functions of each module in each system of the embodiments of the present invention can be found in the corresponding descriptions in the above methods, and will not be repeated here.

[0213] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0214] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process, and the scope of the preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

[0215] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a ordered list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and portable read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0216] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0217] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0218] Furthermore, the functional units in the various embodiments of the present invention can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. The storage medium can be a read-only memory, a disk, or an optical disk, etc.

[0219] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in the present invention, and these should all be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A sonar image denoising method based on Meyer window function shear wave transform, characterized in that, include: The original sonar image is subjected to grayscale transformation to obtain a grayscale image, and the grayscale image is subjected to logarithmic transformation to obtain a grayscale transformed image. The grayscale image that conforms to the Rayleigh multiplicative noise model is transformed into the grayscale transformed image that is close to the additive noise model that conforms to the Gaussian random distribution through the logarithmic transformation. The grayscale transformed image is scaled by non-subsampled Laplacian pyramid transform to obtain a set of scaled images at l scales. The scale-decomposed image set includes one low-frequency scale image and l-1 high-frequency scale images; Based on the number of decomposition directions at different scales of the scale-decomposed image set, a corresponding Meyer window function is constructed, and the Meyer window function is converted from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain filters. The time-domain filter is transformed in the frequency domain and normalized to obtain a shear wave filter in the frequency domain. The scale-decomposed image set is convolved with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions. A random noise image conforming to a Gaussian random distribution is simulated and generated. The random noise image is decomposed by noise image shear wave decomposition to obtain the root mean square coefficients at different scales and in different directions. The noise standard deviation is estimated by extracting weak texture blocks from the grayscale transformed image. A corresponding weighting coefficient constant term is assigned to the threshold of each scale. The root mean square coefficients of different scales and directions obtained from the decomposition, the noise standard deviation, and the weighting coefficient constant are multiplied together to obtain the adaptive threshold of the decomposition coefficients of the grayscale transformed image at different scales and directions, and then filtered by a hard threshold function. Shear wave reconstruction is performed on the coefficients of sonar images at different scales and in different directions after filtering, and then inverse logarithmic transform is performed to obtain the denoised sonar image.

2. The method according to claim 1, characterized in that, The noise image shearing decomposition includes: The random noise image is scaled by non-subsampled Laplacian pyramid transform to obtain a set of scaled random noise images at l scales; the set of scaled random noise images includes a low-frequency random noise scale image and l-1 high-frequency random noise scale images. Based on the number of decomposition directions at different scales of the scale-decomposed random noise image set, a corresponding Meyer window function is constructed, and the Meyer window function is converted from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain random noise filters. The time-domain random noise filter is transformed and normalized in the frequency domain to obtain a shear wave random noise filter in the frequency domain. The scale-decomposed random noise image set of the sonar image is convolved with the shear wave random noise filter to obtain the root mean square coefficients of different scales and directions.

3. The method according to claim 1, characterized in that, The value of l is 5.

4. The method according to claim 1, wherein a corresponding Meyer window function is constructed based on the number of decomposition directions at different scales of the scale-decomposed image set, and a time-domain filter with l-1 high-frequency scales is constructed by converting the scale-decomposed image set from a pseudo-polar coordinate system to a Cartesian coordinate system using the Meyer window function, characterized in that, include: The corresponding Meyer window function is constructed based on the number of decomposition directions 2j at different scales, with a dimension of 2L×2j, where j is the decomposition level and L is the dimension of the time-domain filter. The Meyer window function is transformed from pseudo-polar coordinates to Cartesian coordinates to construct time-domain filters for l-1 high-frequency scales. The filter dimensions for each scale are L1×L1, L1×L1, L2×L2, and L2×L2, respectively. The number of time-domain filters is determined by the number of decomposition directions, 2. j The decision is made, where L1 is the filter dimension of the second and third scale components, L2 is the filter dimension of the fourth and fifth scale components, and j is the decomposition level.

5. The method according to claim 1, wherein the time-domain filter is subjected to frequency-domain transformation and normalization to obtain a shear wave filter in the frequency domain, and the scale-decomposed image set is convolved with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions, characterized in that, include: The dimensions of the shear wave decomposition coefficients are W×H×2j, j∈l, where W is the width of the original sonar image, H is the height of the original sonar image, j is the decomposition direction coefficient, and l is the decomposition horizontal coefficient.

6. A sonar image denoising system based on Meyer window function shear wave transform, characterized in that, include: The preparation module is used to perform grayscale transformation on the original sonar image to obtain a grayscale image, and to perform logarithmic transformation on the grayscale image to obtain a grayscale transformed image. The logarithmic transformation transforms the grayscale image that conforms to the Rayleigh multiplicative noise model into the grayscale transformed image that is close to the additive noise model that conforms to the Gaussian random distribution. The decomposition module is used to perform scale decomposition on the grayscale transformed image through non-subsampled Laplacian pyramid transform to obtain a set of scale decomposed images at l scales. The scale-decomposed image set includes one low-frequency scale image and l-1 high-frequency scale images; The conversion module is used to construct the corresponding Meyer window function according to the number of decomposition directions at different scales of the scale-decomposed image set, and convert the Meyer window function from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain filters. The convolution module is used to perform frequency domain transformation and normalization on the time domain filter to obtain a shear wave filter in the frequency domain. The scale decomposition image set is convolved with the shear wave filter to obtain shear wave decomposition coefficients at different scales and in different directions. The weighting module is used to simulate and generate a random noise image that conforms to a Gaussian random distribution, perform noise image shear wave decomposition on the random noise image to obtain root mean square coefficients at different scales and in different directions, and estimate the noise standard deviation by extracting weak texture blocks from the grayscale transformed image, and assign corresponding weighting coefficient constants to the threshold of each scale. The filtering module is used to multiply the root mean square coefficients of different scales and directions obtained by the decomposition, the noise standard deviation, and the weighting coefficient constant term to obtain the adaptive threshold of the decomposition coefficients of the grayscale transformed image at different scales and directions, and then filter them through a hard threshold function. The results module is used to reconstruct the sheared wave from the coefficients of the filtered sonar images at different scales and in different directions, and to perform an inverse logarithmic transform to obtain the denoised sonar images.

7. The system according to claim 6, characterized in that, The weighting module includes: The scale decomposition unit is used to perform scale decomposition on the random noise image through non-subsampled Laplacian pyramid transform to obtain a set of scale-decomposed random noise images at l scales; the set of scale-decomposed random noise images includes a low-frequency random noise scale image and l-1 high-frequency random noise scale images. The coordinate transformation unit is used to construct the corresponding Meyer window function according to the number of decomposition directions at different scales of the scale-decomposed random noise image set, and to convert the Meyer window function from the pseudo-polar coordinate system to the Cartesian coordinate system to construct l-1 high-frequency scale time-domain random noise filters. The noise convolution unit is used to perform frequency domain transformation and normalization on the time-domain random noise filter to obtain a shear wave random noise filter in the frequency domain. The scale decomposition random noise image set of the sonar image is convolved with the shear wave random noise filter to obtain root mean square coefficients of different scales and directions.

8. The system according to claim 6, characterized in that, The conversion module includes: The window function construction unit is used to construct the corresponding Meyer window function according to the number of decomposition directions 2j at different scales. Its dimension is 2L×2j, where j is the decomposition level and L is the dimension of the time-domain filter. The filter construction unit is used to convert the Meyer window function from pseudo-polar coordinates to Cartesian coordinates, thereby constructing time-domain filters for l-1 high-frequency scales. The filter dimensions for each scale are L1×L1, L1×L1, L2×L2, and L2×L2, respectively. The number of time-domain filters is determined by the number of decomposition directions, 2. j The decision is made, where L1 is the filter dimension of the second and third scale components, L2 is the filter dimension of the fourth and fifth scale components, and j is the decomposition level.

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