Interferogram frequency division noise reduction method based on adaptive center weighted filtering and wavelet transformation

Abstract

The invention discloses an interference pattern frequency division noise reduction method based on adaptive center weighted filtering and wavelet transform, which comprises the following steps of: performing multi-scale decomposition on an original interference pattern by adopting two-dimensional discrete wavelet transform to obtain a low-frequency component and a high-frequency component; a self-adaptive center weighted median filter is introduced, speckle noise in low-frequency components of an interferogram is reduced by adopting weighted median filtering, low-frequency components after noise reduction are obtained, a multi-level wavelet threshold denoising strategy is designed, speckle noise in high-frequency components of the interferogram is reduced by adopting wavelet transformation, and meanwhile edge and texture information is reserved to the maximum extent. Obtaining a high-frequency component after noise reduction; and performing image reconstruction on the low-frequency component and the high-frequency component after noise reduction through inverse wavelet transform to obtain a high-quality noise reduction interferogram. The method not only can improve the interference pattern frequency division noise reduction precision, but also has good interpretability, and can be directly applied to an interference pattern frequency division noise reduction system.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radar signal processing, and particularly relates to an interferogram frequency division noise reduction method combining adaptive center weighted filtering and wavelet transform. BACKGROUND

[0002] Synthetic Aperture Radar Interferometry (InSAR) has great significance for national security and economic development due to its wide monitoring range, all-weather and all-day observation advantages. SAR imaging is achieved by transmitting and receiving coherent electromagnetic waves, but the electromagnetic wave reflection signal is easily affected by factors such as surface roughness of ground objects and antenna platform movement, resulting in changes in echo signal distance, forming scattered, light and dark coherent speckle noise in the interferogram.

[0003] This noise reduces the quality of SAR images and hinders subsequent applications such as image feature extraction and segmentation, so noise suppression is the key to the application of InSAR technology. Existing filtering methods are mainly divided into two categories: spatial domain and transform domain. The mean filter in the spatial domain reduces the resolution, the median filter blurs the details, and the adaptive center weighted filter (ACWMF) improves the defects of the former two, but it may still lose high-frequency edge information. The Fourier transform in the transform domain has fixed resolution, and the wavelet threshold method has limited effect on low-frequency noise.

[0004] Due to the coherent superposition characteristics of SAR imaging, coherent speckle noise is distributed in the full frequency domain, and the low-frequency region is mixed with real image features to form uneven bright and dark areas, and the high-frequency region presents scattered granular bright or dark spots. Traditional single filtering method cannot meet the noise processing needs of different frequency scales, and cannot reduce noise while fully protecting useful image information, so there is an urgent need for a frequency division noise reduction scheme that combines the advantages of various filters. SUMMARY

[0005] The purpose of the present application is to provide an interferogram frequency division noise reduction method combining adaptive center weighted filtering and wavelet transform.

[0006] To achieve the above purpose, the present application is implemented according to the following technical scheme: The present application comprises the following steps: A two-dimensional discrete wavelet transform is used to perform multi-scale decomposition on the original interferogram to obtain low-frequency components and high-frequency components; An adaptive center weighted median filter is introduced to reduce speckle noise in the low-frequency components of the interferogram using the weighted median filter to obtain noise-reduced low-frequency components, and a multi-level wavelet threshold denoising strategy is designed to reduce speckle noise in the high-frequency components of the interferogram using wavelet transform while maximizing the preservation of edge and texture information to obtain noise-reduced high-frequency components; The low-frequency components and the high-frequency components after noise reduction are reconstructed by inverse wavelet transform to obtain a high-quality noise-reduced interferogram.

[0007] Further, the method for multi-scale decomposition of original interferogram by using two-dimensional discrete wavelet transform comprises: performing inner product of original interferogram and wavelet base, and then performing two-layer interval sampling in horizontal and vertical directions to decompose the image into four quarter-size images; the image comprises one low-frequency component and three high-frequency components representing horizontal, vertical and diagonal directions respectively; the main process can be represented as follows: 1) let input two-dimensional image signal be represented as wherein is horizontal coordinate of the image, is vertical coordinate of the image; 2) in the process of first-level decomposition, perform inner product of original image and wavelet base, and then perform sampling in horizontal and vertical directions, which can be represented by the following equations: ; ; ; ; ; ; wherein is orthogonal wavelet, is two-dimensional basic wavelet, and are displacement parameters in horizontal and vertical directions respectively, is low-frequency part of the image signal, is high-frequency part in horizontal direction of the image signal, is high-frequency part in vertical direction of the image signal, is high-frequency part in diagonal direction of the image signal.

[0008] Further, the method for reducing speckle noise in low-frequency component of interferogram by using weighted median filter comprises: set window size of the filter to 3x3; calculate weight of central pixel of each window in low-frequency component relative to other neighborhood pixels : (7); ; ; wherein is offset in horizontal direction, For the offset in the vertical direction, if s = 0 and t = 0, it represents the center pixel itself; is a non-negative integer, and round() is a nearest integer operator, represents the sample variance of the pixels in the filter window, is the noise variance, is the ratio of the pixel signal variance to the noise variance; The value of the center pixel is repeatedly weighted, together with the values of the neighboring pixels, to form an extended data set, the median of the data set is calculated, and the obtained median is assigned to the center pixel of the current window; Repeat the above steps until all pixels in the image are processed, and output the low-frequency component after noise reduction after all pixels are processed , the expression is: ; wherein is a median calculation operation, represents copying the pixel value at position .

[0009] Further, the method for reducing speckle noise in the high-frequency component of the interference pattern by using wavelet transform comprises: In combination with the operation performance and applicability, the Haar wavelet basis for processing the sudden signal of the image is selected, the Haar wavelet basis is denoted by H, and the decomposition layer is selected to be 2 layers; The heuristic threshold rule combines the fixed threshold rule and the adaptive threshold rule, and the heuristic threshold method is used to automatically select the optimal threshold according to different situations, when the signal-to-noise ratio of the interference pattern is low, the fixed threshold is used, otherwise the adaptive threshold is used, the expression is: ; ; ; wherein a and b are parameters for comparison, w is the square sum of the wavelet coefficients after decomposition, n is the number of wavelet coefficients after decomposition; log represents the binary logarithm of n, and represents the logarithm of the number of wavelet coefficients; is a fixed threshold, is an adaptive threshold, is the number of wavelet coefficients after decomposition, is the square sum of the wavelet coefficients after decomposition, is a threshold value; The threshold function is determined, and the hard threshold function is used for noise reduction processing, wherein the expression of the hard threshold function is as follows: ; After obtaining the threshold Then, the hard threshold rule sets the wavelet coefficients below the threshold to zero, while keeping the wavelet coefficients above the threshold unchanged.

[0010] Furthermore, the method for obtaining the high-quality denoised interferogram includes: The high-frequency components obtained after wavelet thresholding This will be combined with the low-frequency components that have undergone adaptive filtering. Recombination; The high-frequency and low-frequency components are superimposed and reconstructed using discrete wavelet inverse transform to obtain the final denoised interferogram. .

[0011] The beneficial effects of this invention are: This invention is an interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform. Compared with existing technologies, this invention has the following technical advantages: This invention employs multi-scale decomposition, low-frequency component denoising, high-frequency component denoising, and image reconstruction. Adaptive center-weighted median filtering automatically adjusts parameters based on local pixel features, effectively avoiding excessive smoothing of the interferogram and ensuring detail preservation. This enhances the method's adaptability, enabling flexible handling of different noise distributions. Both the global structure and local details in the high-frequency components are effectively processed, preventing information loss and improving overall image accuracy. Especially in speckle noise processing, it maximizes the preservation of important image features, improving the accuracy and quality after denoising. Attached Figure Description

[0012] Figure 1 This is a flowchart illustrating the steps of the interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform of the present invention. Detailed Implementation

[0013] The present invention will be further described below through specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0014] The interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform of this invention includes the following steps: like Figure 1 As shown, this embodiment includes the following steps: Two-dimensional discrete wavelet transform is used to decompose the original interferogram into multiple scales to obtain low-frequency and high-frequency components. In the actual evaluation, a SAR interferogram of a certain region was selected as the original experimental data. The image size was 512×512 pixels, and the data existed in complex form. The core observation was the wrapped phase, and the phase values ​​were visualized. The coherent speckle noise intensity is medium (noise variance is 16) in the gray scale range of 0-255 linearly mapped to 0-255, and typical image features such as terrain stripes and edge textures are included, which conforms to the actual InSAR application scene; Experimental environment: hardware: Intel Core i7-12700H processor, 32GB DDR5 memory, NVIDIA RTX3060 graphics card; software: Python 3.9, OpenCV 4.5.5, PyWavelets 1.4.1, NumPy 1.23.5; The adaptive center weighted median filter is introduced, the weighted median filter is used to reduce the speckle noise in the low-frequency component of the interferogram, the denoised low-frequency component is obtained, a multi-level wavelet threshold denoising strategy is designed, the wavelet transform is used to reduce the speckle noise in the high-frequency component of the interferogram, and the edge and texture information are retained to the maximum extent, and the denoised high-frequency component is obtained. The denoised low-frequency component and the high-frequency component are reconstructed by inverse wavelet transform, and a high-quality denoised interferogram is obtained.

[0015] In the embodiment, the method for multi-scale decomposition of the original interferogram by using two-dimensional discrete wavelet transform includes: The inner product of the original interferogram and the wavelet basis is used, and then two-layer interval sampling is performed in the horizontal and vertical directions, and the image is decomposed into four quarter-size images; the image includes a low-frequency component and three high-frequency components representing horizontal, vertical and diagonal directions respectively; the main process can be represented as follows: 1) Let the input two-dimensional image signal be represented as , wherein is the horizontal coordinate of the image, is the vertical coordinate of the image. 2) In the first decomposition process, the inner product of the original image and the wavelet basis is performed, and sampling is performed in the horizontal and vertical directions, which can be represented by the following equation: ; ; ; ; ; ; , wherein is an orthogonal wavelet, is a two-dimensional basic wavelet, and are displacement parameters in the horizontal and vertical directions respectively, is the low-frequency part of the image signal, is the high frequency part in horizontal direction of the image signal, is the high frequency part in vertical direction of the image signal, is the high frequency part in diagonal direction of the image signal; In the actual evaluation, the original interferogram two-dimensional signal is defined as wherein is the horizontal coordinate is the vertical coordinate The Haar wavelet base is selected The wavelet base function is defined according to formula (1)-(2), and the inner product operation of the original image and the wavelet base is performed Two-layer interval sampling is performed in the horizontal and vertical directions, and one low-frequency component and three high-frequency components (horizontal , vertical , diagonal ) are obtained, and the size of each component is 256*256 pixels.

[0016] In the embodiment, the method for reducing the speckle noise in the low-frequency component of the interferogram by using the weighted median filter includes: The window size of the filter is set to 3*3; The weight of the center pixel of each window in the low-frequency component relative to other neighborhood pixels is calculated : (7) ; ; ; wherein is the horizontal offset, is the vertical offset, if s=0 and t=0, it represents the center pixel itself; is a non-negative integer, round( ) is the nearest integer operator, represents the sample variance value of the pixel in the filter window, is the noise variance, is the ratio of the pixel signal variance and the noise variance; The value of the center pixel is repeatedly weighted, and the neighborhood pixel values are used to form an extended data set, the median of the data set is calculated, and the obtained median is assigned to the center pixel of the current window; The above steps are repeated until all the pixels in the image are processed, and the low-frequency component after noise reduction is output after all the pixels are processed, and the expression is: ; wherein For calculating the median operation, represents copying the pixel value at position ; In actual evaluation, the low-frequency component of the interferogram contains the main structure of the interferogram, which usually corresponds to large-scale changes in the interferogram image; the main structure includes the basic shape of the image, the smooth background, and the uniform features of larger areas; speckle noise presents regional gray value fluctuations in the low-frequency component, making the originally smooth area appear irregular light and dark changes, thereby affecting the image quality; when processing this part of the component, the speckle noise in different areas cannot use the same parameters, otherwise it will cause the transition smoothing of the overall structure, causing blurring; therefore, the ACWMF with local feature adaptability is selected for processing, which adjusts the window size and center weight of the median filter to adapt to the noise in different areas; For adjusting the processing weight of the pixel in filtering according to the relationship between the signal variance and the noise variance of the pixel; Select L=2 (empirical coefficient), the center pixel of a window is 100, is 100, is 36, the noise variance is 16, R=(36-16) / 36≈0.556, K=round(2×0.556)=1, the center pixel weight h=2×1+1=3, and the neighborhood pixel weight is 1; The center pixel value is repeated three times to form an extended data set with 8 neighborhood pixel values, the median is calculated and the center pixel is replaced, and all pixels are traversed to obtain the denoised low-frequency component .

[0017] In this embodiment, the method for reducing speckle noise in high-frequency components of the interferogram by wavelet transform comprises: Combining the operation performance and applicability, the Haar wavelet basis for processing image mutation signals is selected, the Haar wavelet basis is denoted by H, and the decomposition layer is selected to be 2 layers; The heuristic threshold rule combines the fixed threshold rule and the adaptive threshold rule, and the heuristic threshold method is used to automatically select the optimal threshold according to different situations; when the signal-to-noise ratio of the interferogram is low, the fixed threshold is used, otherwise the adaptive threshold is used, and the expression is: ; ; ; wherein and Both are parameters used for comparison. w is the sum of squares of the decomposed wavelet coefficients, n is the number of decomposed wavelet coefficients, and log represents the binary logarithm of n and the logarithm of the number of wavelet coefficients. For a fixed threshold, For adaptive threshold, The number of wavelet coefficients after decomposition. The sum of squares of the decomposed wavelet coefficients. For threshold; Determine the threshold function and use a hard threshold function for noise reduction. The hard threshold function is expressed as follows: ; After obtaining the threshold Then, the hard thresholding rule sets wavelet coefficients smaller than the threshold to zero, while keeping wavelet coefficients larger than the threshold unchanged; In actual assessments, high-frequency components of the interferogram The main components of the image include detailed information such as edges, textures, and other small-scale structural changes. High-frequency components correspond to rapidly changing parts of the image, revealing more detailed layers and subtle structural changes. Speckle noise typically manifests as random, sharp bright or dark spots, affecting subsequent edge detection and texture analysis of the interferogram. For speckle noise in non-periodic signals, wavelet thresholding is chosen for processing. Wavelet thresholding offers flexible threshold selection capabilities, allowing different thresholds to be set based on the characteristics of different wavelet coefficients. The challenge of wavelet thresholding lies in the selection of the threshold. While an excessively small threshold may retain more image details, it may also result in insufficient noise suppression. Conversely, an excessively large threshold may over-filter noise while losing important image details. Therefore, a heuristic thresholding rule suitable for processing high-frequency components is adopted to balance excessively large and small thresholds. During the hard thresholding denoising process, the target region will not deviate much from the target region of the original input image: because during the hard thresholding process, only wavelet coefficients smaller than a certain threshold will be set to zero, while larger coefficients will remain unchanged. Maintaining a decomposition level of 2, and using the Haar wavelet basis, process the three high-frequency components separately and calculate the heuristic threshold. ; High frequency components in the horizontal direction For example, after decomposition, the number of wavelet coefficients is 65,536, and the sum of squares of the coefficients is 128,000; , ,because , ; Calculated fixed threshold The adaptive threshold is 3.21, and the final... is 3.21; The wavelet coefficients less than 3.21 in absolute value are set to zero by using a hard threshold function, and the coefficients greater than or equal to the threshold are reserved to obtain the high-frequency component after noise reduction .

[0018] In the embodiment, the method for obtaining the high-quality noise-reduced interferogram includes: The high-frequency component obtained after the wavelet threshold method is processed The low-frequency component processed by the adaptive filtering is combined with the high-frequency component Recombine; The processed high-frequency and low-frequency components are superimposed and reconstructed by using a discrete wavelet inverse transform to obtain the final noise-reduced interferogram ; In actual evaluation, the low-frequency component after noise reduction is combined with three high-frequency components , , The final noise-reduced interferogram is obtained by reconstruction through a discrete inverse wavelet transform .

[0019] Figure 1 The two-dimensional discrete wavelet transform is 2D-DWT, the wavelet transform is WT, the adaptive center weighted median filter is ACWMF, and the inverse wavelet transform is IDWT.

[0020] The above description is only the preferred embodiment of the present application, and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. An interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform, characterized in that, Includes the following steps: Two-dimensional discrete wavelet transform is used to decompose the original interferogram into multiple scales to obtain low-frequency and high-frequency components. A weighted median filter based on adaptive center is introduced to reduce speckle noise in the low-frequency components of the interferogram, thereby obtaining the denoised low-frequency components. A multi-level wavelet threshold denoising strategy is designed to reduce speckle noise in the high-frequency components of the interferogram by wavelet transform, while preserving edge and texture information to the maximum extent, thereby obtaining the denoised high-frequency components. Image reconstruction is performed on the denoised low-frequency and high-frequency components using inverse wavelet transform to obtain a high-quality denoised interferogram.

2. The interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform according to claim 1, characterized in that, The method for multi-scale decomposition of the original interferogram using two-dimensional discrete wavelet transform includes: The image is decomposed into four quarter-sized images by performing an inner product of the original interferogram and a wavelet basis, followed by two-level interval sampling in the horizontal and vertical directions. Each image includes a low-frequency component and three high-frequency components representing the horizontal, vertical, and diagonal directions, respectively. The main process can be represented as follows: 1) Let the input two-dimensional image signal be represented as ,in The horizontal coordinates of the image, Represents the vertical coordinates of the image; 2) During the first-level decomposition process, the inner product of the original image and the wavelet basis is performed, and sampling is carried out in the horizontal and vertical directions, as expressed by the following equation: ； ； ； ； ； ； in Orthogonal wavelets, For two-dimensional basic wavelets, and These are the displacement parameters in the horizontal and vertical directions, respectively. This refers to the low-frequency component of the image signal. This refers to the high-frequency component in the horizontal direction of the image signal. This refers to the high-frequency component in the vertical direction of the image signal. This refers to the high-frequency component along the diagonal direction of the image signal.

3. The interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform according to claim 1, characterized in that, The method for reducing speckle noise in low-frequency components of an interferogram using the weighted median filter includes: Set the filter window size to 3×3; Calculate low-frequency components The weight of the center pixel of each window relative to its neighboring pixels. : (7)； ； ; in This represents the horizontal offset. This represents the offset in the vertical direction; if s=0 and t=0, it represents the center pixel itself. For non-negative integers, round() is the nearest neighbor operator. This represents the sample variance of the pixels within the filter window. It is the noise variance. It is the ratio of pixel signal variance to noise variance; The value of the center pixel is repeatedly weighted and combined with the values ​​of neighboring pixels to form an expanded dataset. The median of the dataset is calculated and assigned to the center pixel of the current window. Repeat the above steps until all pixels in the image have been processed. After all pixels have been processed, output the noise-reduced low-frequency component. The expression is: ； in To calculate the median, Indicates position The pixel value at that location is copied.

4. The interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform according to claim 1, characterized in that, The method for reducing speckle noise in high-frequency components of an interferogram using wavelet transform includes: Considering computational performance and applicability, the Haar wavelet basis for processing abrupt changes in image signals is selected. The Haar wavelet basis is denoted by H, and the number of decomposition layers is selected as 2. The heuristic thresholding rule combines fixed and adaptive thresholding rules. It automatically selects the optimal threshold based on different situations. When the signal-to-noise ratio of the interferogram is low, a fixed threshold is used; otherwise, an adaptive threshold is used. The expression is: ； ； ； Where a and b are both parameters used for comparison, w is the sum of squares of the decomposed wavelet coefficients, n is the number of decomposed wavelet coefficients, and log represents the binary logarithm of n, which represents the logarithm of the number of wavelet coefficients. For a fixed threshold, For adaptive threshold, The number of wavelet coefficients after decomposition. The sum of squares of the decomposed wavelet coefficients. For the threshold; Determine the threshold function and use a hard threshold function for noise reduction. The hard threshold function is expressed as follows: ； After obtaining the threshold Then, the hard threshold rule sets the wavelet coefficients below the threshold to zero, while keeping the wavelet coefficients above the threshold unchanged.

5. The interferogram frequency division and noise reduction method based on adaptive center-weighted filtering and wavelet transform according to claim 1, characterized in that, The method for obtaining the high-quality denoised interferogram includes: The high-frequency components obtained after wavelet thresholding This will be combined with the low-frequency components that have undergone adaptive filtering. Recombination; The high-frequency and low-frequency components are superimposed and reconstructed using discrete wavelet inverse transform to obtain the final denoised interferogram. .

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