An unsupervised SAR image denoising method based on double logarithmic speckle noise model

Abstract

The present application belongs to the technical field of remote sensing image processing, and particularly relates to an unsupervised SAR image denoising method based on a double-log spot noise model. The present application comprises obtaining a spot noise SAR image I' to be denoised, and using a double-log spot noise model to establish a double-log spot noise SAR image Z' to be denoised; inputting the double-log spot noise SAR image Z' to be denoised into a pre-trained convolutional neural network to obtain an output of the convolutional neural network, which is a denoised SAR image R' of the spot noise SAR image I' obtained through operation. Through the double-log spot noise model, the present application can train the denoising convolutional neural network in an unsupervised manner using a mean square error loss function without a spot noise-free SAR image, thereby completing the removal of the spot noise of the SAR image.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing image processing technology, specifically relating to an unsupervised SAR image denoising method based on a double logarithmic speckle noise model. Background Technology

[0002] Synthetic Aperture Radar (SAR) images are generated through an active coherent sensing process, acquiring radar echoes from ground targets and focusing them into a fully developed image. Based on their imaging mechanism, common remote sensing images are divided into optical remote sensing images and SAR images. Optical remote sensing images contain color information and are easier for humans to observe visually. However, in low light conditions at night or when severely obscured by clouds or fog, optical remote sensing images cannot provide complete and reliable ground observation information. Unlike optical remote sensing images, SAR images are not dependent on sunlight or weather conditions, thus enabling continuous all-weather coverage. However, because imaging relies on coherent sensing, SAR images are contaminated by speckle noise. Unlike Gaussian noise, which typically contaminates optical images, speckle noise is spatially and signal-dependent, manifesting as granular textures superimposed on the image, which significantly affects its interpretability and practical applications. Therefore, improving SAR image quality by reducing speckle noise has a significant positive impact on many practical applications using SAR images, such as ship detection and identification, ground change detection, and forest vegetation observation.

[0003] Based on algorithmic strategies, existing SAR image denoising methods can be divided into traditional mathematical methods and deep learning methods. Traditional mathematical methods include: local window-based filtering methods, nonlocal summation-based methods, partial differential equation-based methods, and variational methods. Deep learning methods mainly focus on convolutional neural network (CNN)-based methods. For example, the invention patent "A Synthetic Aperture Radar Image Denoising Method Based on Convolutional Neural Network" (application number: CN201911163279.4) discloses a SAR image denoising method based on a convolutional neural network. This method builds a convolutional neural network model based on a parameter-learnable activation function, uses mean squared error and total variation as loss functions, and completes the training of the SAR image denoising network in an end-to-end manner. Another example is the Chinese paper "Improved Convolutional Neural Network SAR Image Denoising Algorithm" (doi: 10.3778 / j.issn.1002-8331.1911-0060) published by Qian Man, Zhang Xiangyang, and Li Renchang in the journal "Computer Engineering and Applications". This paper proposes an improved convolutional neural network (CNN) method for SAR image denoising. This method first downsamples the image and then convolves the downsampled sub-images to extract features, effectively expanding the receptive field and improving the model's denoising performance. Another example is the foreign paper "Learning a dilated residual network for SAR image despeckling" (doi: 10.3390 / rs10020196) published in the journal "Remote Sensing" by Zhang Qiang, Yuan Qiangqiang, and Li Jie. This paper proposes a dilated residual network for SAR image denoising, which employs dilated convolution and residual learning to improve SAR image denoising performance without increasing network complexity. Compared to traditional mathematical methods, the aforementioned deep learning methods typically show significant performance improvements in SAR image denoising. However, these deep learning SAR image denoising methods usually use supervised training of the convolutional neural network. This supervision method requires clean (speckle-free) noise corresponding to the input speckle-noise image as a label, which is not practical because obtaining real SAR images without speckle noise is extremely difficult. This limits the deep learning SAR image denoising methods described above to training only on speckle images synthesized from optical remote sensing data, significantly restricting the application of deep learning in SAR image speckle noise removal. Therefore, how to train convolutional neural networks using real SAR speckle-noise images (i.e., training denoising networks in an unsupervised manner) remains a challenging problem.

[0004] A search of domestic and international patents and literature reveals numerous studies on SAR image denoising based on convolutional neural networks. However, existing research generally employs supervised learning, using speckle images synthesized from optical remote sensing data for training. No unsupervised SAR image denoising methods using real SAR images to train convolutional neural networks have been found. Summary of the Invention

[0005] The purpose of this invention is to provide an unsupervised SAR image denoising method based on a double logarithmic speckle noise model.

[0006] An unsupervised SAR image denoising method based on a double logarithmic speckle noise model includes the following steps:

[0007] Step 1: Obtain the speckle noise SAR image I′ to be denoised, and use the double log speckle noise model to construct the double log speckle noise SAR image Z′ to be denoised;

[0008]

[0009] Where log(I′) represents the logarithmic result of I′; M′ is the additional logarithmic speckle noise of the double logarithmic speckle noise SAR image Z′ to be denoised;

[0010] Step 2: Input the double logarithmic speckle noise SAR image Z′ to be denoised into the pre-trained convolutional neural network. In this process, a convolutional neural network is obtained. The output is

[0011] Step 3: Obtain the denoised SAR image R′ of the speckle noise SAR image I′;

[0012]

[0013] Furthermore, the convolutional neural network The specific training method is as follows:

[0014] The convolutional neural network is trained using mean squared error as the loss function. The training objective is to minimize the mean squared error loss function, as expressed in the following formula:

[0015]

[0016] Among them, Z k The input image for the convolutional neural network; Y k For the corresponding Z k The training target image of the convolutional neural network; f θ This represents a convolutional neural network used for SAR image denoising; θ represents f θLearnable parameters; f θ (Z k ) for Z k The output obtained after inputting into a convolutional neural network; Y represents k and f θ (Z k The mean squared error loss function between () is calculated as follows:

[0017]

[0018] Where W and H represent the width and height of the training image, respectively; (Y k ) w,h and (f) θ (Z k )) w,h They represent Y respectively k and f θ (Z k The pixel value at coordinates (w, h);

[0019] During training, the Adam optimizer is used to train the network until convergence; the final result is a trained convolutional neural network for SAR image denoising. This indicates the updated and optimized network parameters after training is complete.

[0020] Furthermore, it is used to train the convolutional neural network. The specific method for constructing the training dataset is as follows:

[0021] A training dataset was built using real SAR images with a double log-log speckle noise model.

[0022] A SAR image containing K speckle noise has its original speckle noise model represented as:

[0023]

[0024] Where k∈{1,2,…K}; I k R represents the k-th SAR image containing speckle noise; k This represents the k-th SAR image without speckle noise to be recovered. Indicates element-wise multiplication; S k This represents the k-th corresponding speckle noise;

[0025] By performing logarithmic operations, the original speckle noise model is transformed into:

[0026]

[0027] in, Indicates the sum of corresponding elements; Y k X k and N k They represent I respectively k R k and S k The result of the logarithmic operation;

[0028] Constructing a double log-speckle noise SAR image:

[0029]

[0030] Among them, Z k Represents a double logarithmic speckle noise SAR image; M k Indicates the use of Z to construct k Additional log-spot noise; the established training dataset is represented as:

[0031] {Z k ,Y k}, k∈{1,2,…K}.

[0032] Furthermore, the S k It follows a Gamma distribution; M k and N k Both conform to the Fisher-Tippett distribution, and they are independent and identically distributed.

[0033] The beneficial effects of this invention are as follows:

[0034] The double logarithmic speckle noise model proposed in this invention enables the unsupervised training of a denoising convolutional neural network using a mean squared error loss function, thereby removing speckle noise from SAR images, even without speckle-free SAR images. Existing technologies typically employ supervised training, limiting training to speckle images synthesized from optical remote sensing data. This invention, however, uses an unsupervised approach, allowing training of the denoising network on real SAR images. This is more practical and avoids the situation where denoising is effective on synthesized speckle images but poor on real speckle-noise SAR images. Attached Figure Description

[0035] Figure 1 This is a flowchart of an unsupervised SAR image denoising method based on a double logarithmic speckle noise model, as described in this invention. Detailed Implementation

[0036] The present invention will now be further described with reference to the accompanying drawings.

[0037] The purpose of this invention is to train a denoising convolutional neural network on real SAR images, and to provide an unsupervised SAR image denoising method based on a double logarithmic speckle noise model, which can be used to suppress speckle noise in SAR images, thereby improving SAR image quality and enhancing visual clarity.

[0038] The training dataset is built using real SAR images. It contains K real-world speckle noise SAR images in varying intensity formats. The original speckle noise model can be formally represented as follows:

[0039]

[0040] Where k∈{1,2,…K}, I k R represents the k-th speckle noise SAR image. k This represents the k-th clean (no speckle noise-free) SAR image to be recovered. S represents element-wise multiplication. k S represents the k-th corresponding speckle noise. k It follows a Gamma distribution, and its probability density function can be formally expressed as follows:

[0041]

[0042] Wherein, P(S) k ) represents S k The probability density function is given by Γ, where Γ represents the Gamma function and L represents the number of views of the SAR image. Through logarithmic operations, equation (1) can be formally transformed into the following equation:

[0043]

[0044] in, This indicates the addition of corresponding elements. For the sake of brevity, formula (3) can be rewritten as follows:

[0045]

[0046] Among them, Y k X k and N k They represent I respectively k R k and S k The result of the logarithmic operation. Where N k It conforms to the Fisher–Tippett distribution, and its probability density function can be formally expressed as follows:

[0047]

[0048] Wherein, P(N) k) represents N k The probability density function. Furthermore, a double-log speckle noise SAR image is constructed according to the following formula:

[0049]

[0050] Among them, Z k M represents a double log-speckle noise SAR image. k Indicates the use of Z to construct k The additional logarithmic speckle noise. M k and N k Both conform to the Fisher-Tippett distribution and are independent and identically distributed. The training dataset is now complete, formally represented as follows:

[0051] {Z k ,Y k},k∈{1,2,…K} (7)

[0052] Among them, Z k and Y k These serve as the input and target images for the subsequent convolutional neural network, respectively.

[0053] Convolutional neural networks (CNNs) are built and trained. The mean squared error (MSE) is used as the loss function for training the CNN. The training objective is to minimize the MSE loss function, which is formally expressed as follows:

[0054]

[0055] Among them, f θ This represents a convolutional neural network used for SAR image denoising, where θ represents f. θ The learnable parameters, f θ (Z k ) for Z k The output obtained after inputting into a convolutional neural network. Y represents k and f θ (Z k The mean squared error loss function between () can be formally expressed as the following formula:

[0056]

[0057] Where W and H represent the width and height of the training image, respectively, (Y) k ) w,h and (f) θ (Z k )) w,h They represent Y respectively k and f θ (Zk The pixel value at coordinates (w, h). During training, the Adam optimizer is used to train the network until convergence. The final result is a trained convolutional neural network for SAR image denoising, i.e., in This indicates the updated and optimized network parameters after training is complete.

[0058] Based on the double logarithmic speckle noise model, the trained network is used to denoise the test SAR image. Let the speckle noise SAR image to be denoised be I′. First, the double logarithmic speckle noise SAR image to be denoised is constructed using the double logarithmic speckle noise model, denoted as Z′. Its specific calculation method can be formally expressed as the following formula:

[0059]

[0060] Where log(I′) represents the logarithmic result of I′. M′ is the additional logarithmic speckle noise of the double-logarithmic speckle noise SAR image Z′ to be denoised, which conforms to the Fisher–Tippett distribution, and its probability density function can be formally expressed as follows:

[0061]

[0062] Where P(M′) represents the probability density function of M′, and L′ is the number of views of the SAR image I′ to be denoised. Next, Z′ is input into the trained convolutional neural network. The final denoised SAR image of I′ is obtained through calculation, and the specific calculation method is as follows:

[0063]

[0064] in, This means inputting Z′ to... The output obtained later, R′, represents the denoised SAR image corresponding to I′ obtained by applying the present invention.

[0065] In summary, the present invention provides an unsupervised SAR image denoising method based on a double logarithmic speckle noise model, comprising the following steps:

[0066] Step 1: Obtain the speckle noise SAR image I′ to be denoised, and use the double log speckle noise model to construct the double log speckle noise SAR image Z′ to be denoised;

[0067]

[0068] Where log(I′) represents the logarithmic result of I′; M′ is the additional logarithmic speckle noise of the double logarithmic speckle noise SAR image Z′ to be denoised;

[0069] Step 2: Input the double logarithmic speckle noise SAR image Z′ to be denoised into the pre-trained convolutional neural network. In this process, a convolutional neural network is obtained. The output is

[0070] Step 3: Obtain the denoised SAR image R′ of the speckle noise SAR image I′;

[0071]

[0072] The double logarithmic speckle noise model proposed in this invention enables the unsupervised training of a denoising convolutional neural network using the mean square error loss function, thereby achieving speckle noise removal from SAR images without requiring speckle-free SAR images.

[0073] Existing technologies typically employ a supervised approach, which limits training to speckle images synthesized from optical remote sensing data. This invention, however, uses an unsupervised approach, enabling training of the denoising network on real SAR images. This is more realistic and avoids the situation where denoising is effective on synthesized speckle images but poor on real speckle-noise SAR images.

[0074] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. An unsupervised SAR image denoising method based on a double logarithmic speckle noise model, characterized in that, Includes the following steps: Step 1: Acquire the speckle noise SAR image to be denoised A double log-speckle noise model was used to construct a double log-speckle noise SAR image to be denoised. ; in, express The result of the logarithmic operation; Double log-speckle noise SAR image to be denoised Additional log-spot noise; Step 2: Denoise the double logarithmic speckle noise SAR image to be denoised. Input to the pre-trained convolutional neural network In this process, a convolutional neural network is obtained. The output is ; Step 3: Acquire speckle noise SAR image SAR image after denoising ; The convolutional neural network The specific training method is as follows: A training dataset was built using real SAR images with a double log-log speckle noise model. Include The original speckle noise model of a SAR image with speckle noise is expressed as: in, ; Indicates the first A SAR image containing speckle noise; Indicates the number to be restored A SAR image without speckle noise. This indicates element-wise multiplication; Indicates the first One corresponding speckle noise; By performing logarithmic operations, the original speckle noise model is transformed into: in, This indicates that corresponding elements are added together; , and They represent , and The result of the logarithmic operation; Constructing a double log-speckle noise SAR image: in, This represents a double logarithmic speckle noise SAR image; Indicates used for building Additional log-spot noise; The established training dataset is represented as follows: The convolutional neural network is trained using mean squared error as the loss function. The training objective is to minimize the mean squared error loss function, as expressed in the following formula: in, The input image is the image used by the convolutional neural network. For the corresponding The target image for training a convolutional neural network; This represents a convolutional neural network used to denoise SAR images; express Learnable parameters; To be The output obtained after inputting into a convolutional neural network; express and The mean squared error loss function between them is calculated as follows: in, and These represent the width and height of the training image, respectively. and They represent and In coordinates Pixel value at; During training, the Adam optimizer is used to train the network until convergence; the final result is a trained convolutional neural network for SAR image denoising. ; This indicates the updated and optimized network parameters after training is complete.

2. The unsupervised SAR image denoising method based on a double logarithmic speckle noise model according to claim 1, characterized in that: The It conforms to the Gamma distribution; and Both conform to the Fisher-Tippett distribution, and they are independent and identically distributed.

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