A remote sensing image solid waste detection method based on improved YOLO11

CN122990344APending Publication Date: 2026-10-27CHINA UNIV OF PETROLEUM (EAST CHINA)
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Patent Information

Application Number
CN202611302784.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2026-08-26
Publication Date
2026-10-27

AI Technical Summary

Technical Problem

此外,部分固体废弃物区域存在视觉显著性弱、形态不规则以及边界过渡不明显等情况,对目标区域的特征提取和准确定位造成影响

Benefits of technology

[0047](1)本发明设计了通道傅里叶卷积模块CFCM,对不同层级特征进行频域建模,增强固体废弃物目标与复杂背景之间的特征区分能力。

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Abstract

The application discloses a kind of remote sensing image solid waste detection methods based on improved YOLO11, it is related to remote sensing image processing and computer vision technical field, including the following steps: constructing remote sensing image solid waste detection model based on improved YOLO11, designing channel Fourier convolution module and amplitude perception cross-stage attention module in backbone network, enhance the feature discrimination ability under complex background and the feature expression of weak significant target, and construct dynamic cross-scale feature pyramid network to carry out multi-scale feature fusion, strengthen the interaction of details and semantic information between different scale features;Remote sensing solid waste dataset is used to train the detection model;The remote sensing image to be detected is input into the trained model, and the solid waste detection result is output.The application can enhance the feature expression and multi-scale information fusion capability of solid waste under complex background, effectively improve the problem of solid waste missed detection and misdiagnosis.
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Description

Technical Field

[0001] This invention relates to the fields of intelligent interpretation of remote sensing images and computer vision technology, specifically to a method for detecting solid waste in remote sensing images based on an improved YOLO11. Background Technology

[0002] Remote sensing technology can quickly acquire large-scale surface images, providing data support for solid waste surveys, environmental monitoring, and pollution area investigations in cities and surrounding areas. With the development of computer vision and deep learning technologies, using target detection models to automatically identify and locate solid waste in remote sensing images can improve the automation level of solid waste surveys and monitoring.

[0003] Solid waste is typically formed by the irregular accumulation of various materials, and its color, texture, shape, and spatial distribution are influenced by material composition, stacking method, surrounding surface type, and remote sensing imaging conditions. Some solid waste areas share similar visual characteristics with bare land, building roofs, vegetation, and other surrounding features, making it difficult to distinguish solid waste targets from complex backgrounds. Solid waste in remote sensing images also exhibits significant scale differences, ranging from small, spatially dispersed accumulation areas to large, spatially continuous solid waste areas. Targets at different scales require different feature representations for both shallow spatial detail and deep semantic information. Furthermore, some solid waste areas exhibit weak visual saliency, irregular shapes, and indistinct boundary transitions, impacting feature extraction and accurate localization. Therefore, improvements are needed in hierarchical feature extraction, multi-scale feature fusion, and deep semantic feature processing methods in target detection models to achieve solid waste detection in complex remote sensing scenes. Summary of the Invention

[0004] To address the aforementioned problems, this invention provides a method for detecting solid waste in remote sensing images based on an improved YOLO11. By improving the backbone and neck networks of YOLO11, the method achieves automatic identification and localization of solid waste targets in remote sensing images.

[0005] The present invention adopts the following technical solution:

[0006] A method for detecting solid waste in remote sensing images based on an improved YOLO11 includes the following steps:

[0007] Step 1: Construct a remote sensing image solid waste detection model based on the improved YOLO11. The remote sensing image solid waste detection model includes a backbone network, a dynamic cross-scale feature pyramid network (DCFPN), and a detection head.

[0008] Step 2: Use the solid waste training set to train the remote sensing image solid waste detection model based on the improved YOLO11 described in Step 1, and obtain the trained remote sensing image solid waste detection model.

[0009] Step 3: Input the remote sensing image to be detected into the remote sensing image solid waste detection model trained in Step 2, and output the detection result of the solid waste target.

[0010] In the backbone network, a Channel-Wise Fourier Convolution Module (CFCM) is designed. Fourier transform and learnable channel complex spectral weights are used to adaptively model different channels and frequencies to obtain enhanced features that integrate global context information.

[0011] We designed a Magnitude-Aware Cross-Stage Attention (MACSA) module, which is based on magnitude-aware linear attention, to extract deep semantic features that enhance magnitude response.

[0012] The DCFPN network employs a two-dimensional perceptual selective fusion module and a high- and low-resolution feature fusion branch to perform cross-scale feature interaction, thereby obtaining multi-scale features that fuse detailed information and semantic information.

[0013] The detection head uses the original YOLO11 detection head, which consists of three scale detection branches, used to output the category, location and confidence level of solid waste targets;

[0014] The CFCM module retains the branch feature processing and splicing fusion structure of the original C3k2 module in YOLO11; at the same time, it introduces a Fourier bottleneck module, which includes two sequentially connected Fourier convolutional units with residual connections. The processing flow is as follows:

[0015] First, the input features are divided into two feature branches after channel adjustment. One branch is directly passed, and the other branch is processed by the Fourier bottleneck module. Finally, the features of each branch are concatenated and mapped by convolution to obtain the output features.

[0016] The Fourier convolutional unit first performs a two-dimensional real-valued Fast Fourier Transform on the input feature x:

[0017]

[0018] Where X represents the transformed complex frequency domain feature. The complex frequency domain characteristic X of the two-dimensional real fast Fourier transform function can be expressed as:

[0019]

[0020] in, Denotes the real part of X. Let represent the imaginary part of X, and j represent the imaginary unit;

[0021] A learnable complex weight W is set to adaptively modulate the frequency domain response at different channels and frequency positions:

[0022]

[0023] Among them, W r and W i Let represent the real and imaginary parts of the learnable complex weights, respectively;

[0024] Element-wise complex multiplication of the feature X and the weight W yields the real part Y of the modulated frequency domain feature. r And the imaginary part Y i :

[0025]

[0026]

[0027] in, This indicates element-wise multiplication between elements at corresponding positions;

[0028] Will As the actual part, As the imaginary part, construct the complex frequency domain feature Y:

[0029]

[0030] Subsequently, a two-dimensional inverse real fast Fourier transform is performed on the complex frequency domain feature Y to recover the spatial domain feature:

[0031]

[0032] in, Representing spatial domain characteristics, Represents the two-dimensional inverse real fast Fourier transform;

[0033] The recovered spatial domain features y are channel-mapped through a 1×1 convolution to obtain the output features of the Fourier convolution.

[0034] The MACSA module retains some channel processing structures from the original C2PSA module of YOLO11 and uses amplitude-aware linear attention MALA to enhance deep features. The processing flow is as follows:

[0035] The input features are channel-mapped by a 1×1 convolution and then divided into a first feature branch and a second feature branch. The first feature branch directly performs feature propagation, while the second feature branch inputs an amplitude-aware attention block for feature processing. The attention calculation for MALA is represented as follows:

[0036]

[0037] Where p represents the position index of query feature Q in the spatial feature sequence, and q represents the position index of key feature K in the spatial feature sequence; Represents a nonnegative eigenmap function. This represents the scaling factor obtained based on the response between the p-th query feature and all key features. This represents the offset corresponding to the p-th query position;

[0038] The amplitude-aware attention block uses MALA to calculate feature relationships and employs two-dimensional rotational position encoding (RoPE) to process the spatial location information of query features and key features. Simultaneously, it uses depthwise convolution to extract local location features from value features. The outputs of the first feature branch and the second feature branch are concatenated and channel-mapped using 1×1 convolution to obtain the output features of the MACSA module.

[0039] The DCFPN network includes a first-dimensional perceptual selective fusion module, an upsampled feature fusion branch, a downsampled feature fusion branch, and a second-dimensional perceptual selective fusion module. The processing flow is as follows:

[0040] The backbone network outputs three scale features: P3, P4, and P5. First, P3, P4, and P5 are input into the first-dimensional perceptual selective fusion module. In the first cross-scale feature fusion, P4 is used as the current layer feature, P5 as the deep semantic feature, and P3 as the shallow detail feature. The number of channels for P3, P4, and P5 is unified through convolutional mapping, and P3 is downsampled and P5 is interpolated and upsampled to the same spatial resolution as P4. Then, the aligned P3, P4, and P5 are evenly divided into four subgroups along the channel direction, and the sub-features of P4 are used as the basis for the fusion. Generate gate weights Complete selective fusion within the group:

[0041]

[0042] Where i represents the index of the channel subgroup, i = 1, 2, 3, 4; , and These represent the current layer feature, lower layer feature, and higher layer feature in the i-th subgroup, respectively; Indicates the current layer sub-features The generated gating weights; denoted as the fusion feature obtained after gated weighted fusion of the i-th subgroup, and σ represents the Sigmoid activation function; This indicates element-wise multiplication.

[0043] when When the module is large, it focuses more on preserving low-level details; when When the size is smaller, more emphasis is placed on introducing high-level semantic context. Finally, the four sets of fusion results are concatenated and mapped to obtain the intermediate fusion feature F4.

[0044] Subsequently, bidirectional feature transfer is performed centered on the intermediate fused feature F4. The intermediate fused feature is upsampled to the same spatial resolution as P3, concatenated with P3, and fused using the original C3k2 module of YOLO11 to obtain the updated high-resolution feature F3; at the same time, the intermediate fused feature F4 is downsampled to the same spatial resolution as P5, concatenated with P5, and fused using the C3k2 module to obtain the updated low-resolution feature F5.

[0045] Furthermore, the updated high-resolution feature F3, intermediate fusion feature F4, and updated low-resolution feature F5 are input into the second-dimensional perception selective fusion module for a second cross-scale feature fusion. The final multi-scale fusion feature is obtained through subsequent high- and low-resolution feature transfer and fusion, and finally input into the YOLO11 detection head for solid waste target detection.

[0046] Compared with the prior art, the advantages of the present invention are:

[0047] (1) The present invention designs a channel Fourier convolution module (CFCM) to perform frequency domain modeling of features at different levels, thereby enhancing the feature discrimination ability between solid waste targets and complex backgrounds.

[0048] (2) The present invention designs an amplitude-aware cross-stage attention module MACSA to enhance the expression of deep semantic features and improve the recognition ability of weakly salient solid waste targets.

[0049] (3) The present invention constructs a dynamic cross-scale feature pyramid network DCFPN to enhance information interaction between features at different scales and improve the detection capability of solid waste targets at different scales. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the process of the present invention.

[0051] Figure 2 This is a schematic diagram of the structure of the present invention.

[0052] Figure 3 This is a schematic diagram of the channel Fourier convolution module of the present invention.

[0053] Figure 4 This is a schematic diagram of the amplitude-sensing cross-stage attention module of the present invention.

[0054] Figure 5 This is a schematic diagram of the structure of the dynamic cross-scale feature pyramid network of the present invention. Detailed Implementation

[0055] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0056] It should be noted that the present invention will be further described below with reference to specific embodiments. These embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the scope of protection of the present invention. The terms "first," "second," etc., used in the specification and claims of the present invention are used to distinguish different objects, not to describe a specific order. Unless otherwise stated, the technical terms involved in the present invention shall have the meanings commonly understood by those skilled in the art.

[0057] The remote sensing image solid waste detection method proposed in this invention includes three steps. For example... Figure 1 and Figure 2 As shown, the method includes the following steps:

[0058] Step 1: Construct a remote sensing image solid waste detection model based on an improved YOLO11. The remote sensing image solid waste detection model includes a backbone network, a Dynamic Cross-Scale Feature Pyramid Network (DCFPN), and a detection head, wherein:

[0059] In the backbone network, the original Conv module and SPPF module of YOLO11 are retained. In the feature extraction stage, a Channel-Wise Fourier Convolution Module (CFCM) is designed. Fourier transform and learnable channel complex spectral weights are used to adaptively model different channels and frequencies to obtain enhanced features that integrate global context information.

[0060] We designed a Magnitude-Aware Cross-Stage Attention (MACSA) module, which is based on magnitude-aware linear attention, to extract deep semantic features that enhance magnitude response.

[0061] The DCFPN network employs a two-dimensional perceptual selective fusion module and high- and low-resolution feature fusion branches to perform cross-scale feature interaction, thereby obtaining multi-scale features that fuse detailed information and semantic information.

[0062] The detection head uses the original YOLO11 detection head, which consists of three scale detection branches, used to output the category, location and confidence level of solid waste targets;

[0063] like Figure 3 As shown, the CFCM module retains the branch feature processing and splicing fusion structure of the original YOLO11 C3k2 module; at the same time, it introduces the Fourier bottleneck module FB, which includes two sequentially connected Fourier convolutional units (FourierConv) with residual connections. The processing flow is as follows:

[0064] First, the input features are divided into two feature branches after channel adjustment. One branch is directly passed, and the other branch is processed by the Fourier bottleneck module. Finally, the features of each branch are concatenated and mapped by convolution to obtain the output features.

[0065] The Fourier bottleneck module processes the input features sequentially through two Fourier convolutional units, and adds the output of the second Fourier convolutional unit to the input features of the module as a residual to obtain the output features of the Fourier bottleneck module.

[0066] The Fourier convolutional unit first performs a two-dimensional real-valued Fast Fourier Transform on the input feature x:

[0067]

[0068] Where X represents the transformed complex frequency domain feature. The complex frequency domain characteristic X of the two-dimensional real fast Fourier transform function can be expressed as:

[0069]

[0070] in, Denotes the real part of X. Let represent the imaginary part of X, and j represent the imaginary unit;

[0071] A learnable complex weight W is set to adaptively modulate the frequency domain response at different channels and frequency positions:

[0072]

[0073] Among them, W r and W i Let represent the real and imaginary parts of the learnable complex weights, respectively;

[0074] Element-wise complex multiplication of the feature X and the weight W yields the real part Y of the modulated frequency domain feature. r And the imaginary part Y i :

[0075]

[0076]

[0077] in, This indicates element-wise multiplication between elements at corresponding positions;

[0078] Will As the actual part, As the imaginary part, construct the complex frequency domain feature Y:

[0079]

[0080] Subsequently, a two-dimensional inverse real fast Fourier transform is performed on the complex frequency domain feature Y to recover the spatial domain feature:

[0081]

[0082] in, Representing spatial domain characteristics, Represents the two-dimensional inverse real fast Fourier transform;

[0083] The recovered spatial domain features y are channel-mapped using a 1×1 convolution to obtain the output features of the Fourier convolution. Compared to feature extraction relying solely on local spatial convolution, this method can supplement the overall feature relationships between different spatial locations, thereby enhancing the feature discrimination ability between solid waste and similar backgrounds such as bare ground and rooftops.

[0084] In this embodiment, after processing by the last CFCM and SPPF modules, the feature space resolution input to the MACSA module is 20×20, and the number of channels is 512. The features are then mapped by a 1×1 convolution and divided into two 256-channel feature branches along the channel direction, with both branches maintaining a spatial resolution of 20×20. After attention processing, the two branches are reassembled and mapped by a 1×1 convolution, resulting in an output feature spatial resolution of 20×20 and a number of channels of 512.

[0085] like Figure 4 As shown, the MACSA module retains some channel processing structures of the original C2PSA module in YOLO11 and uses amplitude-aware linear attention MALA to enhance deep features. The processing flow is as follows:

[0086] The input features are channel-mapped by a 1×1 convolution and then divided into a first feature branch and a second feature branch. The first feature branch directly performs feature propagation, while the second feature branch inputs an amplitude-aware attention block for feature processing. The attention calculation for MALA is represented as follows:

[0087]

[0088] Where p represents the position index of query feature Q in the spatial feature sequence, and q represents the position index of key feature K in the spatial feature sequence; Represents a nonnegative eigenmap function. This represents the scaling factor obtained based on the response between the p-th query feature and all key features. This represents the offset corresponding to the p-th query position;

[0089] The amplitude-aware attention block uses MALA to calculate feature relationships and employs two-dimensional rotational position coding (RoPE) to process the spatial location information of query features and key features. Simultaneously, it uses 5×5 depth convolution to extract local location features from value features. The outputs of the first and second feature branches are concatenated and channel-mapped using 1×1 convolution to obtain the output features of the MACSA module.

[0090] Replace the original YOLO11 neck network with a DCFPN network. For example... Figure 5 As shown, the DCFPN network includes two dimension-aware selective fusion modules, two Upsample modules, two Conv modules, and four C3k2 modules, which are used to achieve two-stage cross-scale feature fusion.

[0091] The backbone network outputs three scale features, P3, P4, and P5, which correspond to downsampling rates of 1 / 8, 1 / 16, and 1 / 32 of the input image, respectively. For a 640×640 pixel input remote sensing image, the spatial resolutions of P3, P4, and P5 are 80×80, 40×40, and 20×20, respectively.

[0092] First, P3, P4, and P5 are input into the first-dimensional perceptual selective fusion module. In the first cross-scale feature fusion, P4 is used as the current layer feature, P5 as the deep semantic feature, and P3 as the shallow detail feature. The number of channels for P3, P4, and P5 is unified through convolutional mapping, and P3 is downsampled and P5 is interpolated and upsampled to the same spatial resolution as P4. Then, the aligned P3, P4, and P5 are evenly divided into four subgroups along the channel direction, and the sub-features of P4 are used as the basis for the fusion. Generate gate weights Complete selective fusion within the group:

[0093]

[0094] Where i represents the index of the channel subgroup, i = 1, 2, 3, 4; , and These represent the current layer feature, lower layer feature, and higher layer feature in the i-th subgroup, respectively; Indicates the current layer sub-features The generated gating weights; denoted as the fusion feature obtained after gated weighted fusion of the i-th subgroup, and σ represents the Sigmoid activation function; This indicates element-wise multiplication.

[0095] when When the module is large, it focuses more on preserving low-level details; when When the size is smaller, more emphasis is placed on introducing high-level semantic context. Finally, the four sets of fusion results are concatenated and mapped to obtain the intermediate fusion feature F4.

[0096] Subsequently, bidirectional feature transfer is performed centered on the intermediate fused feature F4. The intermediate fused feature is upsampled to the same spatial resolution as P3, concatenated with P3, and fused using the original C3k2 module of YOLO11 to obtain the updated high-resolution feature F3; at the same time, the intermediate fused feature F4 is downsampled to the same spatial resolution as P5, concatenated with P5, and fused using the C3k2 module to obtain the updated low-resolution feature F5.

[0097] Furthermore, the updated high-resolution feature F3, intermediate fusion feature F4, and updated low-resolution feature F5 are input into the second-dimensional perception selective fusion module for a second cross-scale feature fusion. The final multi-scale fusion feature is obtained through subsequent high- and low-resolution feature transfer and fusion, and finally input into the YOLO11 detection head for solid waste target detection.

[0098] Step 2: Train the remote sensing image solid waste detection model.

[0099] This embodiment uses the SWAD remote sensing solid waste dataset. The images are mainly from WorldView-2 and SPOT series satellites, with a spatial resolution of 1.8 meters. The training set, validation set, and test set contain 1197, 399, and 400 remote sensing images, respectively. The input image size is set to 640×640 pixels, the batch size is set to 16, the number of training epochs is set to 300, and a stochastic gradient descent optimizer is used. The initial learning rate is set to 0.01, the momentum is set to 0.937, and the weight decay is set to 0.0005.

[0100] The remote sensing images in the training set are input into the constructed detection model for iterative training. The detection loss is calculated based on the model prediction results and the real annotation results. The model parameters are updated through backpropagation to obtain the trained remote sensing image solid waste detection model.

[0101] Step 3: Perform solid waste detection in remote sensing images.

[0102] The remote sensing image to be detected is input into the trained detection model. The backbone network extracts image features at different scales step by step. The CFCM module performs channel frequency domain processing on the features at different stages of the backbone network. The MACSA module processes the deepest semantic features. The DCFPN network performs two-stage cross-scale feature fusion on P3, P4 and P5 output by the backbone network. The resulting multi-scale fused features are then input into the original YOLO11 detection head. The detection head outputs the category, location and confidence level of the solid waste target.

[0103] The remote sensing image solid waste detection model based on the improved YOLO11 of this invention was compared with a series of algorithms such as Faster RCNN, DINO, and YOLOv8 on the SWAD solid waste dataset. This invention uses Precision, Recall, mAP@50, and mAP@50:95 metrics to measure the detection results; the higher the metric, the better the model's detection performance. Precision represents the proportion of correctly detected targets in the detection results, reflecting the accuracy of the model's detection results; Recall represents the proportion of correctly detected targets among real targets, reflecting the model's ability to detect solid waste targets; mAP@50 represents the average precision of each category when the intersection-union ratio (IU / U) threshold is 0.50; mAP@50:95 represents the average precision calculated under the condition that the IU / U threshold ranges from 0.50 to 0.95, with an interval of 0.05, and is used to measure the overall detection performance of the model under different positioning requirements. The experimental results are shown in Table 1:

[0104] Table 1. Comparison results of different methods on the SWAD dataset.

[0105] Faster RCNN 72.2% 66.3% 72.9% 41.1% Cascade RCNN 70.9% 68.9% 73.8% 43.0% TOOD 69.2% 71.0% 74.1% 44.6% ATSS 76.3% 66.4% 75.1% 48.0% DINO 67.6% 62.3% 66.4% 37.0% YOLOv8 80.2% 68.7% 76.3% 52.0% YOLO11 81.0% 71.9% 77.4% 51.2% This invention 85.4% 72.8% 81.3% 56.4%

[0106] Experimental results show that the present invention achieves 85.4% precision, 72.8% recall, 81.3% mAP@50 and 56.4% mAP@50:95 on the SWAD solid waste dataset, respectively, which is better than other methods in terms of solid waste detection results.

[0107] It is understood that the execution order of each step in the above embodiments can be adjusted according to its function and actual needs. Without affecting the implementation of the technical solution, each step and technical feature can be selectively executed, combined, or replaced. The above embodiments are only used to illustrate the technical solution of the present invention and are not intended to limit the scope of protection of the present invention. Modifications, equivalent substitutions, or improvements made by those skilled in the art based on the technical concept of the present invention should all be included within the scope of protection of the present invention.

Claims

1. A method for detecting solid waste in remote sensing images based on an improved YOLOv11, characterized in that, The solid waste detection model used can detect solid waste targets in input remote sensing images, including the following steps: Step 1: Construct a remote sensing image solid waste detection model based on an improved YOLO11. This model includes a backbone network, a Dynamic Cross-Scale Feature Pyramid Network (DCFPN), and a detection head, wherein: In the backbone network, a Channel-Wise Fourier Convolution Module (CFCM) is designed. Fourier transform and learnable channel complex spectral weights are used to adaptively model different channels and frequencies to obtain enhanced features that integrate global context information. We designed a Magnitude-Aware Cross-Stage Attention (MACSA) module, which is based on magnitude-aware linear attention, to extract deep semantic features that enhance magnitude response. The DCFPN network employs a two-dimensional perceptual selective fusion module and a high- and low-resolution feature fusion branch to perform cross-scale feature interaction, thereby obtaining multi-scale features that fuse detailed information and semantic information. The detection head uses the original YOLO11 detection head, which consists of three scale detection branches, used to output the category, location and confidence level of solid waste targets; Step 2: Train the remote sensing image solid waste detection model based on the improved YOLO11 described in Step 1 using the publicly available solid waste training set to obtain the trained remote sensing image solid waste detection model. Step 3: Input the remote sensing image to be detected into the remote sensing image solid waste detection model trained in Step 2, and output the detection result of the solid waste target.

2. The method for detecting solid waste in remote sensing images based on improved YOLOv11 according to claim 1, characterized in that, In step 1, the CFCM module retains the branch feature processing and splicing fusion structure of the original C3k2 module of YOLO11; at the same time, a Fourier bottleneck module is introduced, which includes two sequentially connected Fourier convolutional units with residual connections. The processing flow is as follows: First, the input features are divided into two feature branches after channel adjustment. One branch is directly passed, and the other branch is processed by the Fourier bottleneck module. Finally, the features of each branch are concatenated and mapped by convolution to obtain the output features. The Fourier convolutional unit first performs a two-dimensional real-valued Fast Fourier Transform on the input feature x: Where X represents the transformed complex frequency domain feature. The complex frequency domain characteristic X of the two-dimensional real fast Fourier transform function can be expressed as: in, Denotes the real part of X. Let represent the imaginary part of X, and j represent the imaginary unit; A learnable complex weight W is set to adaptively modulate the frequency domain response at different channels and frequency positions: Among them, W r and W i Let represent the real and imaginary parts of the learnable complex weights, respectively; Element-wise complex multiplication of the feature X and the weight W yields the real part Y of the modulated frequency domain feature. r And the imaginary part Y i : in, This indicates element-wise multiplication between elements at corresponding positions; Will As the actual part, As the imaginary part, construct the complex frequency domain feature Y: Subsequently, a two-dimensional inverse real fast Fourier transform is performed on the complex frequency domain feature Y to recover the spatial domain feature: in, Representing spatial domain characteristics, Represents the two-dimensional inverse real fast Fourier transform; The recovered spatial domain features y are channel-mapped through a 1×1 convolution to obtain the output features of the Fourier convolution.

3. The method for detecting solid waste in remote sensing images based on improved YOLOv11 according to claim 1, characterized in that, In step 1, the MACSA module retains some channel processing structures of the original C2PSA module of YOLO11 and uses amplitude-aware linear attention MALA to enhance deep features. The processing flow is as follows: The input features are channel-mapped by a 1×1 convolution and then divided into a first feature branch and a second feature branch. The first feature branch directly performs feature propagation, while the second feature branch inputs an amplitude-aware attention block for feature processing. The attention calculation for MALA is represented as follows: Where p represents the position index of query feature Q in the spatial feature sequence, and q represents the position index of key feature K in the spatial feature sequence; Represents a nonnegative eigenmap function. This represents the scaling factor obtained based on the response between the p-th query feature and all key features. This represents the offset corresponding to the p-th query position; The amplitude-aware attention block uses MALA to calculate feature relationships and employs two-dimensional rotational position encoding (RoPE) to process the spatial location information of query features and key features. Simultaneously, it uses depthwise convolution to extract local location features from value features. The outputs of the first feature branch and the second feature branch are concatenated and channel-mapped using 1×1 convolution to obtain the output features of the MACSA module.

4. The method for detecting solid waste in remote sensing images based on improved YOLOv11 according to claim 1, characterized in that, In step 1, the DCFPN network includes a first-dimensional perceptual selective fusion module, an upsampled feature fusion branch, a downsampled feature fusion branch, and a second-dimensional perceptual selective fusion module. The processing flow is as follows: The backbone network outputs three scale features: P3, P4, and P5. First, P3, P4, and P5 are input into the first-dimensional perceptual selective fusion module. In the first cross-scale feature fusion, P4 is used as the current layer feature, P5 as the deep semantic feature, and P3 as the shallow detail feature. The number of channels of P3, P4, and P5 is unified through convolutional mapping, and P3 is downsampled and P5 is interpolated and upsampled to the same spatial resolution as P4. Then, the aligned P3, P4, and P5 are evenly divided into four subgroups along the channel direction, and the sub-features of P4 are used as the basis for the division. Generate gate weights Complete selective fusion within the group: Where i represents the index of the channel subgroup, i = 1, 2, 3, 4; , and These represent the current layer feature, lower layer feature, and higher layer feature in the i-th subgroup, respectively; Indicates the current layer sub-features The generated gating weights; denoted as the fusion feature obtained after gated weighted fusion of the i-th subgroup, and σ represents the Sigmoid activation function; This represents element-wise multiplication; when When the module is large, it focuses more on preserving low-level details; when When the size is smaller, more emphasis is placed on introducing high-level semantic context; finally, the four sets of fusion results are concatenated and mapped to obtain the intermediate fusion feature F4; Subsequently, bidirectional feature transfer is performed with the intermediate fused feature F4 as the center; the intermediate fused feature is upsampled to the same spatial resolution as P3, concatenated with P3, and fused with the original C3k2 module of YOLO11 to obtain the updated high-resolution feature F3; at the same time, the intermediate fused feature F4 is downsampled to the same spatial resolution as P5, concatenated with P5, and fused with the C3k2 module to obtain the updated low-resolution feature F5; Furthermore, the updated high-resolution feature F3, intermediate fusion feature F4, and updated low-resolution feature F5 are input into the second-dimensional perception selective fusion module for a second cross-scale feature fusion. The final multi-scale fusion feature is obtained through subsequent high- and low-resolution feature transfer and fusion, and finally input into the YOLO11 detection head for solid waste target detection.