Interferometric phase denoising method and apparatus

Abstract

The embodiment of the application provides an interferometric phase denoising method and device, relates to data processing technology, and the interferometric phase denoising method comprises the following steps: performing multi-scale frequency decomposition on an original interferometric phase map based on a preset frequency domain filtering window to obtain hierarchical phase signals containing different frequency components; calculating residual components of adjacent levels according to the difference between principal component signals of adjacent levels to obtain residual domain signals corresponding to each level respectively; performing denoising processing on the residual domain signals by using a pre-trained denoising model to obtain denoised residual domain signals corresponding to each level respectively; and performing phase reconstruction on the denoised residual domain signals corresponding to each level respectively to obtain a target interferometric phase map.The application can effectively maintain the authenticity and integrity of the phase structure while suppressing noise, effectively reduce the generation of artifacts and improve the convergence stability, and ensure the reliability of phase unwrapping and subsequent deformation inversion.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to an interferometric phase denoising method and apparatus. Background Technology

[0002] InSAR (Interferometric Synthetic Aperture Radar) is an important technology that uses radar imaging systems to acquire surface phase information and then performs interferometric processing to generate high-precision digital elevation models and monitor surface deformation. Its basic principle is to perform interferometric operations on two complex radar images of the same area acquired at different times or under different orbital conditions to obtain an interferometric fringe pattern (i.e., an interferogram). After phase unwrapping and subsequent processing, the surface height or deformation information can be retrieved. Because it can acquire data in all weather conditions, at all times, and over a wide area, InSAR has become an important tool in earth science and disaster monitoring.

[0003] However, InSAR interferometric phase maps are inevitably affected by various noises in practical applications. The main sources of noise include: (1) temporal decoherence: due to vegetation growth, snow cover changes, water body fluctuations, etc., the surface scattering characteristics change over time, resulting in a decrease in signal coherence; (2) spatial baseline effect: due to the difference in geometric conditions between two radar images, spatial registration deviation of the echo signal is caused, thus introducing noise; (3) system thermal noise: generated by the instability of the radar sensor itself; (4) atmospheric delay: tropospheric water vapor and ionospheric disturbances will cause phase delay, increasing phase error; (5) volume scattering effect: for example, volume scattering targets such as forests will cause phase randomization of the signal during propagation. These noises not only reduce the signal-to-noise ratio of the interferogram, but also directly affect the stability of phase unwrapping and the accuracy of the final deformation result.

[0004] To address these issues, various interferometric phase denoising methods have been proposed. One approach utilizes spatial domain filters to eliminate noise. However, while spatial domain filters offer high computational efficiency, they rely on the assumption of local homogeneity, leading to phase distortion and detail loss in regions with low coherence or large phase gradients. Nonlocal filtering methods improve denoising performance by leveraging globally similar structures, but they are still prone to introducing artifacts under strong noise conditions and are computationally intensive, making them unsuitable for large-scale and real-time applications. Frequency domain methods (such as the Goldstein filter) are relatively stable in decoherent regions, but their inherent high-frequency attenuation effects cause detail blurring, hindering the preservation of subtle deformation signals. Another approach is deep learning-based InSAR phase denoising methods. For example, the PhiNet network uses a residual learning framework to map noisy input phases to clean phases; the MONet network employs a multi-objective optimization strategy to achieve a balance between noise suppression and structure preservation; and MSFF-DCNN utilizes dynamic fusion of multi-scale features to enhance denoising performance. These methods share the common feature of using interferometric phase maps as input, extracting features and performing nonlinear mapping through deep convolutional networks or attention mechanisms, and outputting estimated denoised phase results. Although they outperform traditional filters on simulated datasets, their training process generally relies on idealized synthetic noise data, making it difficult to reflect the complex and diverse noise features in real interferograms. Therefore, they are prone to artifacts or incorrect recovery under low signal-to-noise ratio conditions, affecting the reliability of phase unwrapping and deformation inversion. Summary of the Invention

[0005] This application provides an interference phase denoising method and apparatus to alleviate or solve one or more technical problems existing in the prior art.

[0006] In a first aspect, embodiments of this application provide an interferometric phase denoising method, including:

[0007] The original interferometric phase map is decomposed into multiple scales based on a preset frequency domain filtering window to obtain hierarchical phase signals containing different frequency components; the size of the frequency domain filtering window increases layer by layer in order from low to high level.

[0008] Based on the differences between the principal component signals of adjacent levels, the residual components of the adjacent levels are calculated to obtain the residual domain signals corresponding to each level.

[0009] The residual domain signal is denoised using a pre-trained denoising model to obtain the denoised residual domain signal corresponding to each level.

[0010] Phase reconstruction is performed on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map.

[0011] Secondly, embodiments of this application provide an interferometric phase denoising device, comprising:

[0012] The decomposition module is used to perform multi-scale frequency decomposition on the original interferometric phase map based on a preset frequency domain filtering window to obtain hierarchical phase signals containing different frequency components; the size of the frequency domain filtering window increases layer by layer in order from low to high level.

[0013] The calculation module is used to calculate the residual components of adjacent levels based on the differences between the principal component signals of adjacent levels, so as to obtain the residual domain signals corresponding to each level.

[0014] The processing module is used to denoise the residual domain signal using a pre-trained denoising model to obtain the denoised residual domain signal corresponding to each level.

[0015] The reconstruction module is used to perform phase reconstruction on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map.

[0016] Thirdly, embodiments of this application provide an electronic device, including a memory, a processor, and a computer program stored in the memory, wherein the processor implements any of the methods of embodiments of this application when executing the computer program.

[0017] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the method of any one of the embodiments of this application.

[0018] Fifthly, embodiments of this application provide a computer program product, including a computer program, which, when executed by a processor, implements any of the methods described in the embodiments of this application.

[0019] According to the technical solution of this application embodiment, the original interferometric phase map is decomposed into multiple scales based on a preset frequency domain filtering window to obtain hierarchical phase signals containing different frequency components. The size of the frequency domain filtering window increases layer by layer from low to high. Based on the difference between the principal component signals of adjacent layers, the residual components of adjacent layers are calculated to obtain the residual domain signals corresponding to each layer. The residual domain signals are denoised using a pre-trained denoising model to obtain the denoised residual domain signals corresponding to each layer. Phase reconstruction is performed on the denoised residual domain signals corresponding to each layer to obtain the target interferometric phase map. Therefore, by extracting low-frequency principal components through hierarchical frequency domain decomposition and then reconstructing high-frequency details layer by layer in the residual domain, a step-by-step optimization process from coarse to fine is constructed, thereby effectively maintaining the authenticity and integrity of the phase structure while suppressing noise. Furthermore, by optimizing within the residual domain rather than the global phase domain, artifact generation can be effectively reduced and convergence stability improved. Thus, it achieves comprehensive advantages that are difficult to achieve simultaneously in terms of noise suppression, detail preservation, computational efficiency, and adaptability to complex noise environments, thereby effectively ensuring the reliability of phase unwrapping and subsequent deformation inversion.

[0020] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application, it can be implemented according to the contents of the specification. In order to make the above and other objects, features and advantages of this application more obvious and understandable, specific embodiments of this application are given below. Attached Figure Description

[0021] 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 according to this application and should not be construed as limiting the scope of this application.

[0022] Figure 1 A structural diagram of the denoising model provided in an embodiment of this application is shown;

[0023] Figure 2 A flowchart of the interferometric phase denoising method provided in an embodiment of this application is shown;

[0024] Figure 3 The diagram illustrates the training principle of the denoising model provided in the embodiments of this application;

[0025] Figure 4 This diagram illustrates the scalable reconstruction principle of the denoising model provided in an embodiment of this application.

[0026] Figure 5 The figure shows a comparison of the scalable reconstruction performance of the denoising model provided in the embodiments of this application at different scale levels;

[0027] Figure 6 This diagram illustrates the iterative reconstruction process of the denoising model provided in an embodiment of this application.

[0028] Figure 7 A structural diagram of the interferometric phase denoising device provided in an embodiment of this application is shown;

[0029] Figure 8 A block diagram of an electronic device provided in an embodiment of this application is shown. Detailed Implementation

[0030] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the concept or scope of this application. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0031] To facilitate understanding of the technical solutions of the embodiments of this application, the relevant technologies of the embodiments of this application are described below. The following relevant technologies are optional solutions and can be combined with the technical solutions of the embodiments of this application in any way, and all of them fall within the protection scope of the embodiments of this application.

[0032] This application proposes an MSRD-Net (Multi-Scale Residual Denoising Network) to address the denoising challenges of InSAR interferometric phase signals under varying noise intensities. The core idea is to employ a frequency-space hybrid strategy: first, multi-scale phase signals are constructed using hierarchical frequency domain decomposition; then, phase reconstruction is performed progressively in the residual domain, achieving a coarse-to-fine stepwise optimization that effectively suppresses noise while maintaining structural integrity. Figure 1 As shown, the overall network consists of three key modules: a multi-scale principal component construction module, a residual-based phase reconstruction module (PR-Block), and a denoising network designed for complex inputs. The multi-scale phase principal components are processed by difference to obtain multi-scale phase residual components, which are then denoised to obtain multi-scale denoised residual components. Finally, they are fused to obtain the multi-scale reconstructed phase.

[0033] Using the described method, low-frequency principal components are extracted through hierarchical frequency domain decomposition, and then high-frequency details are reconstructed layer by layer in the residual domain, constructing a coarse-to-fine stepwise optimization process. This effectively maintains the integrity of the phase structure while suppressing noise. Furthermore, by optimizing in the residual domain rather than the global phase domain, artifact generation can be effectively reduced and convergence stability improved. Simultaneously, combined with a self-reinforcing training strategy based on real noise, the denoising model can continuously evolve and enhance its adaptability and robustness to complex noise environments.

[0034] The technical solution provided in this application achieves balanced performance improvements across various typical scenarios, including earthquakes, landslides, rainforests, and urban environments. It not only outperforms traditional methods in noise suppression but also offers significant advantages in structure preservation and computational efficiency. Its multi-scale layer count can be flexibly adjusted to adapt to varying noise intensities; its iterative reconstruction characteristics ensure reliable phase results can be gradually recovered even in extreme noise environments. Therefore, it effectively resolves the technical contradiction in existing technologies that struggle to balance denoising effectiveness, structure preservation, and computational efficiency, providing a practical and reliable technical means for large-scale operational monitoring and high-precision Earth science research.

[0035] The technical solution of this application and how it solves the aforementioned technical problems are described in detail below with specific embodiments. The listed specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0036] Figure 2 A flowchart of the interferometric phase denoising method provided in an embodiment of this application is shown, as follows: Figure 2 As shown, the method may include steps S201, S202, S203 and S204.

[0037] Step S201: Perform multi-scale frequency decomposition on the original interferometric phase map based on a preset frequency domain filtering window to obtain hierarchical phase signals containing different frequency components; the size of the frequency domain filtering window increases layer by layer in order from low to high level.

[0038] In this step, for the input raw interferometric phase map, multi-scale frequency decomposition is performed based on a preset frequency domain filtering window to extract low-frequency principal components and high-frequency detail components, thereby achieving multi-scale hierarchical division in the frequency domain without changing the spatial resolution. The multi-scale hierarchical signal obtained after decomposition includes several principal component signals with different frequency ranges, and each layer can reflect the structural and noise characteristics at different scales.

[0039] Step S202: Based on the differences between the principal component signals of adjacent levels, calculate the residual components of adjacent levels to obtain the residual domain signals corresponding to each level.

[0040] Step S203: Using a pre-trained denoising model, the residual domain signal is denoised to obtain the denoised residual domain signal corresponding to each level.

[0041] The residual domain signal mainly contains high-frequency information and noise components corresponding to that level. For the residual domain signal of each level, a pre-trained denoising model or filtering module is used to suppress noise and restore details to obtain the reconstructed residual domain signal. By performing denoising in the residual domain, it is possible to avoid directly performing strong filtering operations on the complete phase image, reducing the risk of artifacts and improving the stability and fidelity of denoising.

[0042] Step S204: Perform phase reconstruction on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map.

[0043] According to the technical solution of this application embodiment, the original interferometric phase map is decomposed into multiple scales based on a preset frequency domain filtering window to obtain hierarchical phase signals containing different frequency components. The size of the frequency domain filtering window increases layer by layer from low to high. Based on the difference between the principal component signals of adjacent layers, the residual components of adjacent layers are calculated to obtain the residual domain signals corresponding to each layer. The residual domain signals are denoised using a pre-trained denoising model to obtain the denoised residual domain signals corresponding to each layer. Phase reconstruction is performed on the denoised residual domain signals corresponding to each layer to obtain the target interferometric phase map. Therefore, by extracting low-frequency principal components through hierarchical frequency domain decomposition and then reconstructing high-frequency details layer by layer in the residual domain, a step-by-step optimization process from coarse to fine is constructed, thereby effectively maintaining the authenticity and integrity of the phase structure while suppressing noise. Furthermore, by optimizing within the residual domain rather than the global phase domain, artifact generation can be effectively reduced and convergence stability improved. Thus, it achieves comprehensive advantages that are difficult to achieve simultaneously in terms of noise suppression, detail preservation, computational efficiency, and adaptability to complex noise environments, thereby effectively ensuring the reliability of phase unwrapping and subsequent deformation inversion.

[0044] In some embodiments, when performing multi-scale frequency decomposition on the original interferometric phase map based on a preset frequency domain filtering window to obtain a hierarchical phase signal containing different frequency components, the following steps A1 and A2 can be performed:

[0045] Step A1: Determine multiple filtering windows corresponding to multiple levels; wherein, the filtering window corresponding to each level is an integer multiple of the filtering window corresponding to its adjacent next level.

[0046] Step A2: Based on the original interference phase signal, frequency decomposition is performed sequentially using the filtering window corresponding to each level in order of multi-scale hierarchy from low to high (i.e. from high frequency to low frequency) to obtain phase signals of multiple levels.

[0047] Optionally, the denoising model first constructs multi-scale phase principal components using hierarchical Goldstein filters. Let the original interference phase be... The initial size of the filtering window is 32 pixels. The filtering window size doubles sequentially from low to high level, meaning the filtering window of the previous level is twice the size of the filtering window of the adjacent next level. The constructed multi-scale principal component signal can be expressed by the following formula:

[0048]

[0049] in, This indicates that the filter window size is Goldstein filter, This represents the original interference phase. The multi-scale phase principal component signal generated by this layered processing can cover signals of different scales from high to low frequencies. The top layer component is a smooth low-frequency structure obtained under a larger filtering window with less noise; the bottom layer contains more high-frequency details, but also has more severe noise contamination, see [reference needed]. Figure 1 The (a, b) part.

[0050] In some embodiments, the residual domain signal includes high-frequency signals and noise components corresponding to the corresponding levels. When denoising the residual domain signal using a pre-trained denoising model to obtain denoised residual domain signals for each level, the high-frequency signals in the residual domain signal can be extracted using the pre-trained denoising model to obtain the denoised residual domain signal. The training method of the denoising model will be described in detail in the following embodiments.

[0051] In this embodiment, step S202 can be executed as step B1, and step S203 can be executed as step B2:

[0052] Step B1: For the first layer in the multi-scale hierarchical phase signal, determine the residual high-frequency component signal of the first layer based on the low-frequency component signal corresponding to the previous layer (second layer); wherein, the first layer is any one of the multiple layers; the second layer is the layer above the first layer.

[0053] Step B2 involves denoising the high-frequency component signal of the residual to obtain the denoised interference phase signal corresponding to the first layer, which is the denoised residual domain signal.

[0054] In some embodiments, step S204 can be specifically performed as follows: using the lowest-level principal component signal as a reference, the denoised residual domain signals are superimposed layer by layer in ascending order of level to obtain the target interferometric phase map. Specifically, using the lowest-level principal component signal as a reference, the reconstructed residual domain signals are superimposed layer by layer in ascending order of frequency to complete the hierarchical phase reconstruction. In the phase reconstruction of each level, the denoised residual of the current level is superimposed on the principal component signal of the next level, thereby gradually restoring high-frequency details and finally outputting the denoised target interferometric phase map, achieving high-precision phase reconstruction that balances structure preservation and noise suppression.

[0055] In this embodiment, to restore a clean phase, the denoising model introduces a phase reconstruction block (PR-module) at each layer of the multi-scale hierarchical data. For example... Figure 1 As shown in part (b) of the document, the first The PR-module of the layer first preserves the low-frequency baseline. Then, the high-frequency component signal of the residual is extracted, expressed as the following formula:

[0056]

[0057] in, It primarily contains noise and fine structural information. Unlike traditional filtering that directly affects the entire phase... Denoising, the denoising model exists only in the residual domain Denoising is performed to limit the optimization space to a smaller range. This not only helps to accelerate convergence and improve stability, but also reduces the risk of generating spurious fringes. Then, a dedicated denoising network is used. For residual high-frequency component signals After restoring the details, the phase reconstructed from the high-frequency information can be represented as:

[0058]

[0059] This residual-based phase optimization strategy can suppress high-frequency noise while maintaining the integrity of the low-frequency phase structure.

[0060] Reference Figure 1 In parts (b) and (c), the denoising model optimizes phase estimation progressively at multiple levels by cascading multiple PR modules. For Layer configuration, denoising model starts from the coarsest low-frequency baseline Initially, through structure estimation, feature recovery, and detail enhancement, fine-grained phase information is recovered layer by layer. This coarse-to-fine strategy utilizes multi-scale frequency decomposition to suppress noise while maintaining structural integrity. The low-frequency baseline serves as an anchor point, providing a robust phase foundation and reducing artifacts generated when directly applying full-phase filtering.

[0061] Furthermore, the number of layers in multi-scale structural data can be adaptively configured according to noise intensity. Deeper layers of data can be reconstructed starting from cleaner interferometric phases, improving denoising performance under high-noise conditions. It's important to note that, unlike traditional frequency domain filtering which irreversibly loses high-frequency information, each PR-module can recover phase details from the residual domain, giving the network non-destructive, iterative frequency filtering characteristics. Because of this, the denoising model can be applied sequentially multiple times under extreme noise conditions to gradually recover phase information.

[0062] like Figure 1 As shown in section (d), the denoising model is an encoder-decoder architecture designed for complex residual inputs. Both input and output are 2-channel tensors, encoding the real and imaginary parts of the complex residual components, respectively. The encoder contains four downsampling blocks (Down1–4), which reduce spatial resolution through stride convolutions while increasing the channel depth from 256 to 1024. Residual blocks and a self-attention mechanism are embedded in the encoder to capture long-range dependencies and non-local features. The bottleneck consists of three residual-attention blocks (Mid1–3) with a fixed number of 1024 channels, used to aggregate the global context at the lowest resolution. The decoder path is symmetric to the encoder, employing transposed convolution upsampling (Up1–4) and fusing encoder features through skip connections to recover high-frequency details using multi-scale information, ultimately obtaining the denoised residual. The complete network architecture of the denoising model is shown in Table 1.

[0063] Table 1

[0064]

[0065] In some embodiments, before performing step S201, based on Figure 1 The structure shown pre-trains a denoising model. In this embodiment, a semi-supervised self-reinforcement training strategy is employed, and the denoising model is trained using real noise. The training method for the denoising model may include the following steps C1, C2, and C3:

[0066] Step C1: Obtain the sample noise pool and the sample label pool; the sample noise pool includes multi-scale noise samples extracted from the noise residual components of the actual interferogram, and the sample label pool includes multi-scale label samples composed of the residual components of the label phase map.

[0067] Optionally, step C1 is specifically performed as follows:

[0068] First, obtain the actual interferogram (i.e., the real phase interferogram), and extract the noise residual components from the actual interferogram to construct the sample noise pool.

[0069] Secondly, multiple phase components of the actual interferogram are simulated and combined to obtain the label phase map corresponding to the actual interferogram, and a sample label pool is constructed based on the label phase map.

[0070] Next, multi-scale frequency domain decomposition is performed on the noise interferogram in the sample noise pool to obtain multi-scale residual data; multi-scale frequency domain decomposition is performed on the label phase map in the sample label pool to obtain multi-scale label samples.

[0071] Figure 3 The diagram illustrates the training principle of the denoising model. To capture the complete characteristics of real noise and comprehensively cover its feature distribution, sample noise interferograms can be selected from the following four representative scene types: vegetated areas, affected by seasonal changes and dynamic land cover images, exhibiting moderate temporal incoherence; mountainous terrain, commonly characterized by steep slopes and geometric distortion; tropical rainforest areas, with dense canopies leading to continuous and strong volume scattering incoherence; and plains, possessing moderate coherence but exhibiting significant temporal variations due to agricultural activities or hydrological changes (see [link to relevant documentation]). Figure 3 Part (a) in the diagram: Interferogram used for noise extraction.

[0072] Clean sample label maps (i.e., clean phase labels) are generated through simulation by randomly combining four phase components, including trend components, topographic components, atmospheric turbulence components, and deformation components, such as... Figure 3 As shown in section (f), these simulated clean-phase and real-noise interferograms are used to construct their multi-scale residual components. A denoising network is applied to the residual components of the noisy interferogram to extract noise, forming a noise pool; while the residual components of the clean phase constitute the corresponding label pool (e.g., ...). Figure 3 (As shown in sections (d) and (e)). Subsequently, residual sample pairs are randomly drawn from these two pools and combined into synthetic "noisy-clean" sample pairs, which are used to train the denoising branch of MSRD-Net.

[0073] Step C2 involves inputting the training data into the neural network model to be trained, and using the neural network model to predict the clean phase map corresponding to the actual interferogram. The training data is determined based on a sample noise pool and a sample label pool. Optionally, multiple data pairs are randomly selected from the sample noise pool and the sample label pool as training data.

[0074] Optionally, after inputting the training data into the neural network model to be trained, the neural network model is used to extract the predicted noise in the actual interferogram; then the sample noise pool is updated based on the predicted noise.

[0075] Step C3: Based on the predicted clean phase map and the sample label pool, iteratively train the neural network model to obtain the trained denoising model.

[0076] In this embodiment, the entire training process employs an iterative self-enhancing mechanism, enabling the model and dataset to co-evolve during training. Specifically, in each iteration, MSRD-Net is first applied to the real interferogram to estimate the clean phase and extract the corresponding noise; the extracted noise is then updated in the noise pool and used to generate new synthetic training sample pairs for fine-tuning MSRD-Net in the next round. As the iteration progresses, the model's denoising capability continuously improves, thereby enabling more accurate noise extraction.

[0077] In some embodiments, when iteratively training the neural network model based on the predicted clean phase map and the sample label pool to obtain the trained denoising model (i.e., step C3), the following steps can be specifically performed:

[0078] First, based on the predicted clean phase map and the sample label pool, the phase loss function and the magnitude loss function of the neural network model are determined. The phase loss function is used to represent the phase difference between the predicted clean phase map and the sample label map. The magnitude loss function is used to represent the difference between the magnitude corresponding to the predicted clean phase map and 1.

[0079] Secondly, the target loss function of the neural network model is determined based on the phase loss function and the magnitude loss function.

[0080] Next, the model parameters of the neural network model are adjusted according to the target loss function to obtain the denoising model.

[0081] In this embodiment, the phase loss function This can be expressed as the following formula:

[0082]

[0083] Magnitude loss function This can be expressed as the following formula:

[0084]

[0085] in, and These represent the first and second phases on the phase diagram, respectively. i The predicted complex phase value and the true complex phase value of each pixel. Indicates complex conjugation. Represents the phase angle of a complex value. Represents the magnitude of a complex value. Phase loss function. The goal is to recover the filtered phase angle, while the magnitude loss function... This is used to ensure that the signal maintains its normalized magnitude. The target loss function of the neural network model. This can be expressed as the sum of two losses, as shown in the following formula:

[0086]

[0087] In some embodiments, to evaluate denoising performance on real interferograms lacking true labels (i.e., noisy phase interferograms), multiple complementary metrics are used to evaluate model performance. Specifically, evaluation metrics for the denoising model are determined, and the model performance of the denoising model is evaluated based on these metrics.

[0088] The evaluation metrics include at least one of the following: LRCR (Log Residue Count Reduction), MNI (Mean Noise Intensity), MMCC (Mean Main Component Coherence), EPR (Edge Preservation Ratio), and data processing time. These evaluation metrics comprehensively assess different aspects of the model's denoising quality, including phase continuity, residual noise level, structural integrity, and computational efficiency. Each evaluation metric is described in detail below.

[0089] Residual points are phase discontinuities typically caused by noise or artifacts, which can lead to errors during phase unwrapping because they disrupt local phase continuity. Therefore, reducing residual points generally improves phase smoothness and unwrapping performance. To quantify this improvement, a percentage index, Logarithmic Residual Point Reduction (LRCR), is defined as follows:

[0090]

[0091] in, and These represent the number of residual points in the original phase interferogram and the denoised target phase interferogram, respectively. A higher LRCR value indicates a greater reduction in residual points compared to the original phase interferogram.

[0092] Mean Noise Intensity (MNI) is used to measure the average predicted noise level after denoising. It is a general indicator for measuring residual noise and is defined by the following formula:

[0093]

[0094] in, The noise intensity of the i-th pixel in the phase interferogram is represented by N, where N is the total number of pixels.

[0095] The average principal component coherence (MMCC) measures the structural similarity between the principal components of the denoised target phase interferogram and the original phase interferogram. A good denoising method should not only reduce noise but also maintain the integrity of the effective signal without introducing spurious fringes. Therefore, the average principal component coherence (MMCC) is defined as follows:

[0096]

[0097] in, and These represent the first and second phases on the phase interferogram, respectively. i The principal components of each pixel and the complex phase representation of the target phase interferogram are obtained. The principal components are obtained by applying a low-pass filter to the original phase interferogram. MMCC is the average coherence between the principal components and the denoised output; a higher value indicates better preservation of structural consistency.

[0098] Edge Preservation Ratio (EPR) suppresses noise, but excessive smoothing can remove meaningful structures such as fringes and architecturally relevant phase gradients. To evaluate the ability to preserve these structural features, EPR is introduced. This metric quantifies the proportion of phase edges that remain detectable after denoising in the original phase interferogram. Specifically, the phase edge proportion is identified by applying the Canny operator to the gradient magnitude map, and EPR is calculated as follows:

[0099]

[0100] in, The first phase interferogram represents the input phase interferogram. i The set of pixels of the strip. This represents the set of pixels corresponding to the edge in the denoised target phase interferogram. This indicates the amount of pixel overlap. A higher EPR value indicates better preservation of structural details and less oversmoothing.

[0101] Data processing time is used to measure the time required to denoise a single phase interferogram, reflecting the computational efficiency of the method and serving as an important reference for large-scale or near-real-time applications.

[0102] In some embodiments, MSRD-Net is scalable. By increasing the number of multi-scale structural layers, MSRD-Net effectively doubles the frequency domain filtering window size at each stage, thereby enabling the progressive extraction of cleaner principal components. This feature allows users to flexibly adjust the denoising intensity according to noise conditions. To demonstrate this capability, models with different scales and number of layers (from one to five layers) are applied to a real raw interferometric phase map, such as... Figure 4 As shown, deeper scale settings gradually improve denoising performance, with the noise phase becoming clearer while the effective phase structure is preserved.

[0103] To quantify this scalability, Figure 5 This visualization showcases the scalable phase reconstruction performance of MSRD-Net, including several denoising metrics such as data processing time, with the horizontal axis representing the number of layers. Data processing time (bar chart, left y-axis) monotonically increases with the number of layers. Denoising metrics—LRCR, MNI, MMCC, and EPR—are displayed as line graphs on the dual right y-axis to accommodate their different numerical ranges. With increasing multi-scale layers, LRCR steadily increases, MNI steadily decreases (indicating improved denoising), MMCC peaks at layer 4 and then slightly decreases at layer 5, while EPR gradually decreases, reflecting the trade-off between noise suppression and structure preservation. This visualization highlights the balance between computational cost and denoising performance, providing practical guidance for selecting the optimal layer under different noise conditions.

[0104] However, when the multi-scale levels are too large, an extremely large frequency domain window can produce unreasonable estimates in completely decoherent regions. For example, in the ROI (lake) shown in the figure, the results of layers 4 and 5 show spurious phase recovery on the water body. This phenomenon only occurs under the extreme parameter settings used here to illustrate scalability. In practical applications, such excessively large windows should be used with caution and are generally not recommended; decoherent regions are better suited for processing using masks in subsequent processing.

[0105] Furthermore, while MSRD-Net can adaptively adjust the denoising intensity through extended reconstruction and effectively handle moderate noise conditions, obtaining completely clean results in one pass under extreme noise remains challenging. To address this limitation, another inherent characteristic of this method—iterative properties—is utilized. Stable principal components are separated through frequency domain filtering, and lost details are recovered from the residual signal. MSRD-Net functions almost identically to a non-destructive filter: in the worst case, the result degenerates into principal components. This characteristic makes it naturally suitable for iterative denoising, gradually refining the phase through repeated iterations without compromising structural integrity.

[0106] For example, MSRD-Net is applied to the actual phase interferogram of an earthquake. The original phase interferogram is dominated by high-intensity noise, almost completely masking the deformation signal. The iterative reconstruction process of MSRD-Net is as follows: Figure 6As shown, after three iterations, the residual phase information is gradually recovered, ultimately yielding a clean and structurally reliable result. Experiments demonstrate that, compared to other methods, the interferometric phase denoising method presented in this application produces blocky artifacts in spatial domain methods (such as Boxcar, InSAR-BM3D, and NL-InSAR), while data-driven methods (such as PhiNet and MONet) generate spurious interference fringes. These artifacts disrupt phase continuity and reduce the reliability of the unwrapping results. In contrast, this method achieves smooth denoising and reliable unwrapping, exhibiting robustness in harsh real-world environments.

[0107] Therefore, MSRD-Net, as a hierarchical phase reconstruction method, can simultaneously achieve noise suppression, phase integrity preservation, and fine structure recovery in InSAR data. It combines the phase-preserving robustness of frequency-domain filtering with the nonlinear modeling capabilities of deep learning, and ensures good generalization ability across various sensors and Earth science environments through training under realistic noise conditions. Extensive evaluations in real-world scenarios demonstrate that this method effectively suppresses noise and preserves the true phase structure without introducing artifacts, thus achieving reliable phase unwrapping and deformation analysis. In addition to denoising accuracy, MSRD-Net has two unique advantages: its scalable multi-scale design allows for flexible adjustment of denoising intensity according to noise conditions, while its near-lossless iterative nature provides a practical solution for extreme noise. Overall, MSRD-Net provides a robust and flexible framework for InSAR phase denoising, supporting both large-scale operational monitoring and high-precision Earth science research needs, while improving the reliability of surface deformation measurement and interpretation.

[0108] Corresponding to the application scenarios and methods provided in the embodiments of this application, the embodiments of this application also provide an interference phase denoising device.

[0109] Figure 7 A block diagram of the interferometric phase denoising apparatus provided in an embodiment of this application is shown, as follows: Figure 7 As shown, the interferometric phase denoising device includes:

[0110] The decomposition module 71 is used to perform multi-scale frequency decomposition on the original interferometric phase map based on a preset frequency domain filtering window to obtain a hierarchical phase signal containing different frequency components; the size of the frequency domain filtering window increases layer by layer in order from low to high level.

[0111] The calculation module 72 is used to calculate the residual components of the adjacent levels based on the differences between the principal component signals of the adjacent levels, so as to obtain the residual domain signals corresponding to each level.

[0112] Processing module 73 is used to perform denoising processing on the residual domain signal using a pre-trained denoising model to obtain the denoised residual domain signal corresponding to each level.

[0113] Reconstruction module 74 is used to perform phase reconstruction on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map. In some embodiments, when decomposition module 71 performs multi-scale frequency decomposition on the original interferometric phase map based on a preset frequency domain filtering window to obtain the hierarchical phase signals containing different frequency components, it performs the following steps:

[0114] Determine multiple filtering windows corresponding to multiple levels; wherein the filtering window corresponding to each level is an integer multiple of the filtering window corresponding to its adjacent next level;

[0115] Based on the original interference phase signal, frequency decomposition is performed sequentially using the filtering window corresponding to each level, in order from low to high level, to obtain the phase signals of the multiple levels.

[0116] In some embodiments, the residual domain signal includes high-frequency signals and noise components of the corresponding level;

[0117] When the processing module 73 uses a pre-trained denoising model to denoise the residual domain signal and obtains the denoised residual domain signals corresponding to each level, it performs the following steps:

[0118] Using a pre-trained denoising model, the high-frequency signal in the residual domain signal is extracted to obtain the denoised residual domain signal.

[0119] In some embodiments, when the reconstruction module 74 performs phase reconstruction on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map, it performs the following steps:

[0120] Using the principal component signal at the lowest level as a reference, the denoised residual domain signal is superimposed layer by layer in ascending order of level to obtain the target interferometric phase map.

[0121] In some embodiments, the apparatus further includes:

[0122] The acquisition module is used to acquire a sample noise pool and a sample label pool; the sample noise pool includes multi-scale noise samples extracted from the noise residual components of the actual interferogram, and the sample label pool includes multi-scale label samples composed of the residual components of the label phase map.

[0123] The prediction module is used to input the trained data into the neural network model to be trained, and use the neural network model to predict the predicted clean phase map corresponding to the actual interferogram; the training data is determined based on the sample noise pool and the sample label pool;

[0124] The training module is used to iteratively train the neural network model based on the predicted clean phase map and the sample label pool to obtain the trained denoising model.

[0125] In some embodiments, the acquisition module performs the following steps when acquiring the sample noise pool and the sample label pool:

[0126] Obtain the actual interferogram, and extract the noise residual component from the actual interferogram to construct the sample noise pool;

[0127] Multiple phase components of the actual interferogram are simulated and combined to obtain a label phase map corresponding to the actual interferogram, and the sample label pool is constructed based on the label phase map;

[0128] The noise interferogram in the sample noise pool is decomposed into multi-scale frequency domain to obtain the multi-scale residual data; the label phase map in the sample label pool is decomposed into multi-scale frequency domain to obtain the multi-scale label samples.

[0129] In some embodiments, the apparatus further includes:

[0130] An extraction module is used to extract the prediction noise in the actual interferogram after the training samples are input into the neural network model to be trained;

[0131] An update module is used to update the sample noise pool based on the predicted noise.

[0132] In some embodiments, when the training module iteratively trains the neural network model based on the predicted clean phase map and the sample label pool to obtain the trained denoising model, it performs the following steps:

[0133] Based on the predicted clean phase map and the sample label pool, the phase loss function and the magnitude loss function of the neural network model are determined; the phase loss function is used to represent the phase difference between the predicted clean phase map and the sample label map; the magnitude loss function is used to represent the difference between the magnitude corresponding to the predicted clean phase map and 1.

[0134] The target loss function of the neural network model is determined based on the phase loss function and the magnitude loss function.

[0135] The model parameters of the neural network model are adjusted according to the target loss function to obtain the denoising model.

[0136] In some embodiments, the apparatus further includes:

[0137] The determination module is used to determine the evaluation index of the denoising model; the evaluation index includes at least one of the following: log residual point reduction, average noise intensity, average principal component coherence, edge preservation rate, and data processing time;

[0138] The evaluation module is used to evaluate the performance of the denoising model based on the evaluation metrics.

[0139] The functions of each module in each device in the embodiments of this application can be found in the corresponding description in the above method, and they have corresponding beneficial effects, which will not be repeated here.

[0140] Figure 8 This is a block diagram for implementing the electronic device provided in the embodiments of this application. Figure 8 As shown, the electronic device includes a memory 801 and a processor 802. The memory 801 stores a computer program that can run on the processor 802. When the processor 802 executes the computer program, it implements the method described in the above embodiments. The number of memories 801 and processors 802 can be one or more. In a specific implementation, the electronic device may also include a communication interface 803 for communicating with external devices and performing data exchange and transmission.

[0141] In practical implementation, if the memory 801, processor 802, and communication interface 803 are implemented independently, they can be interconnected via a bus to complete communication. This bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. This bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 8 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0142] Optionally, in a specific implementation, if the memory 801, the processor 802, and the communication interface 803 are integrated on a single chip, then the memory 801, the processor 802, and the communication interface 803 can communicate with each other through an internal interface.

[0143] This application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method provided in this application.

[0144] This application provides a computer program product, including a computer program that, when executed by a processor, implements the method provided in this application.

[0145] This application also provides a chip including a processor for calling and executing instructions stored in a memory, causing a communication device with the chip installed to perform the method provided in this application.

[0146] This application also provides a chip, including: an input interface, an output interface, a processor, and a memory. The input interface, output interface, processor, and memory are connected through an internal connection path. The processor is used to execute code in the memory. When the code is executed, the processor is used to execute the method provided in the application embodiment.

[0147] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. General-purpose processors can be microprocessors or any conventional processor. It is worth noting that the processor can be a processor supporting Advanced Reduced Instruction Set Machines (ARM) architecture.

[0148] Further, optionally, the aforementioned memory may include read-only memory and random access memory. The memory may be volatile memory or non-volatile memory, or may include both. Non-volatile memory may include read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory may include random access memory (RAM), which serves as an external cache. By way of example, but not limitation, many forms of RAM are available. Examples include Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), Synchronous DRAM (SDRAM), Double Data Rate SDRAM (DDR SDRAM), Enhanced Synchronous DRAM (ESDRAM), Sync Link DRAM (SLDRAM), and Direct Rambus RAM (DR RAM).

[0149] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions according to this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another.

[0150] In the description of this specification, the 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 this application. 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.

[0151] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified.

[0152] Any process or method described 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. Furthermore, the scope of the preferred embodiments of this application 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 functionality involved.

[0153] The logic and / or steps described in the flowchart or otherwise herein, for example, can be considered as a sequenced 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-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0154] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. All or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware, the program being stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiments.

[0155] Furthermore, the functional units in the various embodiments of this application 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. This storage medium can be a read-only memory, a disk, or an optical disk, etc.

[0156] The above description is merely an exemplary embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope described in this application, and these should all be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An interferometric phase denoising method, characterized in that, include: The original interferometric phase map is decomposed into multiple scales based on a preset frequency domain filtering window to obtain a hierarchical phase signal containing different frequency components. The size of the frequency domain filtering window increases progressively in order of increasing hierarchy; Based on the differences between the principal component signals of adjacent levels, the residual components of the adjacent levels are calculated to obtain the residual domain signals corresponding to each level. The residual domain signal is denoised using a pre-trained denoising model to obtain the denoised residual domain signal corresponding to each level. Phase reconstruction is performed on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map.

2. The method according to claim 1, characterized in that, The process of performing multi-scale frequency decomposition on the original interferometric phase map based on a preset frequency domain filtering window to obtain hierarchical phase signals containing different frequency components includes: Determine multiple filtering windows corresponding to multiple levels; wherein the filtering window corresponding to each level is an integer multiple of the filtering window corresponding to its adjacent next level; Based on the original interferometric phase diagram, frequency decomposition is performed sequentially using the filtering window corresponding to each level, in order from low to high, to obtain the phase signals of the multiple levels.

3. The method according to claim 1, characterized in that, The residual domain signal includes high-frequency signals and noise components of the corresponding level; The step of using a pre-trained denoising model to denoise the residual domain signal to obtain the denoised residual domain signal corresponding to each level includes: Using a pre-trained denoising model, the high-frequency signal in the residual domain signal is extracted to obtain the denoised residual domain signal.

4. The method according to claim 1, characterized in that, The step of performing phase reconstruction on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map includes: Using the principal component signal at the lowest level as a reference, the denoised residual domain signal is superimposed layer by layer in ascending order of level to obtain the target interferometric phase map.

5. The method according to claim 1, characterized in that, The method further includes: Obtain a sample noise pool and a sample label pool; the sample noise pool includes multi-scale noise samples extracted from the noise residual components of the actual interferogram, and the sample label pool includes multi-scale label samples composed of the residual components of the label phase map. Training data is input into a neural network model to be trained, and the neural network model is used to predict the predicted clean phase map corresponding to the actual interferogram; the training data is determined based on the sample noise pool and the sample label pool; wherein, the training data is obtained by randomly selecting multiple data pairs from the sample noise pool and the sample label pool; Based on the predicted clean phase map and the sample label pool, the neural network model is iteratively trained to obtain the trained denoising model.

6. The method according to claim 5, characterized in that, The acquisition of the sample noise pool and sample label pool includes: Obtain the actual interferogram, and extract the noise residual component from the actual interferogram to construct the sample noise pool; Multiple phase components of the actual interferogram are simulated and combined to obtain a label phase map corresponding to the actual interferogram, and the sample label pool is constructed based on the label phase map; Multi-scale frequency domain decomposition is performed on the noise interferogram in the sample noise pool to obtain the multi-scale noise sample; multi-scale frequency domain decomposition is performed on the tag phase map in the sample tag pool to obtain the multi-scale tag sample.

7. The method according to claim 5, characterized in that, After inputting the training data into the neural network model to be trained, the method further includes: Using the neural network model, the predicted noise in the actual interferogram is extracted; The sample noise pool is updated based on the predicted noise.

8. The method according to claim 5, characterized in that, The step of iteratively training the neural network model based on the predicted clean phase map and the sample label pool to obtain the trained denoising model includes: Based on the predicted clean phase map and the sample label pool, the phase loss function and the magnitude loss function of the neural network model are determined; the phase loss function is used to represent the phase difference between the predicted clean phase map and the multi-scale labeled samples; the magnitude loss function is used to represent the difference between the magnitude corresponding to the predicted clean phase map and 1. The target loss function of the neural network model is determined based on the phase loss function and the magnitude loss function. The model parameters of the neural network model are adjusted according to the target loss function to obtain the denoising model.

9. The method according to claim 1, characterized in that, The method further includes: Determine the evaluation metrics for the denoising model; the evaluation metrics include at least one of the following: logarithmic residual point reduction, average noise intensity, average principal component coherence, edge preservation rate, and data processing time; The performance of the denoising model is evaluated based on the evaluation metrics.

10. An interferometric phase denoising device, characterized in that, include: The decomposition module is used to perform multi-scale frequency decomposition on the original interferometric phase map based on a preset frequency domain filtering window to obtain a hierarchical phase signal containing different frequency components. The size of the frequency domain filtering window increases progressively in order of increasing hierarchy; The calculation module is used to calculate the residual components of adjacent levels based on the differences between the principal component signals of adjacent levels, so as to obtain the residual domain signals corresponding to each level. The processing module is used to denoise the residual domain signal using a pre-trained denoising model to obtain the denoised residual domain signal corresponding to each level. The reconstruction module is used to perform phase reconstruction on the denoised residual domain signals corresponding to each level to obtain the target interferometric phase map.

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