Blind image super-resolution reconstruction method based on bicubic down-sampling image space alignment

Abstract

The application provides a blind image super-resolution reconstruction method based on bicubic down-sampling image space alignment, and the provided super-resolution reconstruction network is composed of three sub-networks, namely, a kernel estimation sub-network, a bicubic down-sampling image space alignment sub-network and an image reconstruction sub-network. Traditional blind image super-resolution reconstruction networks generally comprise two sub-networks, namely, a kernel estimation sub-network and an image reconstruction sub-network. This kind of method obtains the estimation of blur kernel through the kernel estimation sub-network, and then directly inputs the blur kernel information into the image reconstruction sub-network, so that the estimation error of the blur kernel is directly transmitted to the image reconstruction process, thereby affecting the quality of the reconstructed image. However, the application inputs the estimated kernel information into the bicubic down-sampling image space alignment sub-network, maps the low-resolution image into the bicubic down-sampling image space first, and obtains the bicubic down-sampling LR image, so that the image reconstruction sub-network can adopt any non-blind super-resolution reconstruction network.

Description

Technical Field

[0001] This invention relates to the field of image processing technology, and in particular to a blind image super-resolution reconstruction method based on spatial alignment of Bicubic downsampled images. Background Technology

[0002] Single-image super-resolution (SISR) is a fundamental problem in computer vision, referring to resolution enhancement techniques that construct high-resolution (HR) images from low-resolution (LR) observations. In recent years, with the rapid development of deep learning, convolutional neural networks (CNNs) have demonstrated powerful learning capabilities, making CNNs the most popular method for solving SR problems. Blind super-resolution involves solving for the blur kernel and reconstructing the SR image using the blur kernel. Many past research methods typically decompose this into two consecutive steps, each a separate research task. Therefore, inaccurate estimation of blur kernel information can lead to poor SR model performance. To address this issue, researchers have proposed single-stage blind SR. By incorporating kernel estimation into the SR reconstruction network, stronger reconstruction performance is achieved. Gu et al. proposed an Iterative Kernel Correction (IKC) method for blur kernel estimation when the blur kernel is unknown. This method addresses the regularity artifacts (oversharpening or oversmoothing) that may arise from kernel mismatch by correcting inaccurate blur kernels. The estimated kernel is used in its Spatial Feature Transform (SFT) layer, which combines degradation information and LR input. Luo et al. used an alternating optimization algorithm in a single model to estimate the blur kernel and reconstruct the SR image. This model uses an expanded end-to-end trainable model to predict the blur kernel and the SR image. In this model, a series of restorer and estimator modules are stacked alternately, with each module reconstructing the SR image or estimating the blur kernel based on the output of the previous module. Zheng et al. proposed UDKE based on USRNet, decomposing the single-stage blind SR objective function based on explicit kernel estimation into two sub-problems through HQ decomposition. They designed the kernel estimation sub-network and the blind SR reconstruction sub-network using an iterative optimization method of alternating direction multipliers (ADMM), achieving better reconstruction results than IKC and DAN. Therefore, solving the problem of inaccurate estimation of blur kernel information is a hot topic and an important research direction in the field of blind image super-resolution. Summary of the Invention

[0003] The purpose of this invention is to provide a blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment, which is beneficial for reconstructing clearer high-resolution images.

[0004] The provided super-resolution reconstruction network consists of three subnetworks: a kernel estimation subnetwork, a bicubic downsampling image space alignment subnetwork, and an image reconstruction subnetwork. Traditional blind image super-resolution reconstruction networks typically include two subnetworks: a kernel estimation subnetwork and an image reconstruction subnetwork. These methods obtain an estimate of the blur kernel through the kernel estimation subnetwork and directly input this blur kernel information into the image reconstruction subnetwork. This causes the estimation error of the blur kernel to be directly propagated into the image reconstruction process, affecting the quality of the reconstructed image. In contrast, this invention inputs the estimated kernel information into the bicubic downsampling image space alignment subnetwork, allowing the low-resolution image to be mapped into the bicubic downsampling image space to obtain a bicubic downsampling LR image. Therefore, the image reconstruction subnetwork can employ any non-blind super-resolution reconstruction network. Extensive experimental results demonstrate that the blind image super-resolution network of this invention achieves a significant improvement in the quality of the reconstructed image.

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

[0006] A blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment is characterized by the following: the blind image super-resolution reconstruction network consists of three sub-networks: kernel estimation sub-network KNet, Bicubic downsampling image spatial alignment sub-network BNet, and image reconstruction sub-network SRNet; by inputting the estimation kernel information into the Bicubic downsampling image spatial alignment sub-network, the blind low-resolution image is first mapped into the Bicubic downsampling image space to obtain a low-resolution Bicubic downsampling LR image; the image reconstruction sub-network SRNet adopts a non-blind super-resolution reconstruction network.

[0007] Low-resolution image I LR The input is fed into the blind image super-resolution reconstruction network, and the output is the reconstructed high-resolution image I. SR .

[0008] In other words, compared to traditional methods, this invention adds a mapping network BNet between the kernel estimation subnetwork and the SR reconstruction subnetwork. The estimated fuzzy kernel information is introduced to guide the mapping of the LR image (with unknown degradation process) into a Bicubic downsampled LR image. Finally, the Bicubic downsampled LR image is input into a trained non-blind SR network to output the reconstructed high-resolution image.

[0009] Furthermore, the blind image super-resolution reconstruction network first accurately estimates the information of the blur kernel through the kernel estimation sub-network KNet. Then, the Bicubic downsampling image space alignment sub-network BNet maps the LR image domain to the Bicubic downsampling image space under the guidance of the blur kernel. Finally, the image reconstruction sub-network SRNet uses the Bicubic downsampling LR image generated by BNet to reconstruct the high-resolution (HR) image.

[0010] Furthermore, ResNet is used as the kernel estimation subnetwork KNet; the Bicubic downsampled image spatial alignment subnetwork BNet uses the dense residual network RRDB and spatial feature transformation SFT to map low-resolution images generated by different degradation processes to Bicubic downsampled LR images.

[0011] Specifically, the kernel estimation network ResNet is primarily responsible for estimating the blur kernel K. It takes the LR image as input and outputs the estimated blur kernel K. BNet is responsible for mapping the LR image domain to the Bicubic downsampled image domain and incorporating degradation information into the mapping process to guide the network in reconstructing the Bicubic downsampled LR image. SRNet is a non-blind super-resolution network that uses the Bicubic downsampled LR image generated by BNet to reconstruct the HR image.

[0012] Furthermore, the kernel estimation sub-network KNet uses ResNet as the kernel estimation network, extracts image features through multiple deep residual modules, and uses multiple skip connections to connect the input to the network output: first, shallow features are extracted through a 3×3 convolutional layer, then deep features are extracted by feeding them into multiple residual blocks, and skip connections are used to accelerate model training and improve model accuracy. Finally, the output feature map of the subject is converted into a fuzzy kernel matrix through two convolutional layers, average pooling, and Softmax.

[0013] Furthermore, the Bicubic downsampled image spatial alignment sub-network BNet consists of two convolutional layers and two RRDB-SFTs; wherein, the first 3×3 convolutional layer is used to extract shallow features of the LR image, and then the shallow features are further utilized through RRDB-SFT; in addition to receiving the shallow features from the previous layer, the SFT layer also takes the estimated blur kernel K as input.

[0014] The Bicubic Downsampled Image Spatial Alignment Network (BNet) consists of two SFT layers, two RRDB layers, and two convolutional layers. The first convolutional layer extracts shallow features from the LR image. The SFT layer, in addition to receiving the output of the previous layer, also takes a blur kernel as input to modulate the input LR image features. The RRDB layer further extracts the input features to obtain deeper features. The final convolutional layer maps the extracted features to the Bicubic downsampled LR image.

[0015] Furthermore, the image reconstruction subnetwork SRNet can be any non-blind super-resolution network.

[0016] Furthermore, the blind image super-resolution reconstruction network converts LR images generated by different degradation processes to the Bicubic downsampled image space, and then uses the trained image reconstruction sub-network SRNet for reconstruction, so that the network has a certain tolerance for the error caused by the blur kernel estimation, so as to reconstruct a clearer high-resolution image.

[0017] Furthermore, the training process of the super-resolution reconstruction network is divided into three stages:

[0018] The first stage involves pre-training three sub-networks. Specifically, the kernel estimation sub-network KNet is supervised using real kernels to predict blur kernels for the input LR image; the Bicubic downsampled image spatial alignment sub-network BNet is a supervised network trained using real LR images, real blur kernels K, and corresponding Bicubic downsampled LR images; and the image reconstruction sub-network SRNet is also a supervised network trained using HR images and corresponding Bicubic downsampled LR images.

[0019] In the second stage, the estimation kernel generated by the kernel estimation subnetwork KNet is used to fine-tune the spatial alignment subnetwork BNet of the Bicubic downsampled image, and the LR is mapped to the Bicubic downsampled LR image.

[0020] The third stage uses the estimated Bicubic downsampled LR image to fine-tune the SRNet network and obtain the final SR result.

[0021] Furthermore, when a training dataset is provided, the loss function is expressed as:

[0022]

[0023] Where N represents the number of training samples, and ||·||1 represents the L1 norm; K represents the estimated fuzzy kernel. i A fuzzy kernel representing reality; This represents the generated Bicubic downsampled LR image, B i Represents a true Bicubic downsampled LR image. SR images reconstructed from the network The network parameters are obtained from real HR images after training and can be directly used for image super-resolution reconstruction.

[0024] Since it is necessary not only to estimate the blur kernel and the super-resolution (SR) reconstructed image, but also to map the LR image to the bicubic downsampled LR image, the loss function consists of three parts: kernel estimation loss, bicubic downsampled image spatial alignment loss, and SR image reconstruction loss.

[0025] Furthermore, a blind image super-resolution reconstruction system based on Bicubic downsampling image spatial alignment includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the method described above.

[0026] Compared with existing technologies, this invention and its preferred embodiment add a Bicubic downsampling image spatial alignment subnetwork (BNet) between the kernel estimation subnetwork and the SR reconstruction subnetwork. This introduces the estimated blur kernel information to guide the mapping of LR images with unknown degradation processes into Bicubic downsampling LR images, thus mitigating the impact of inaccurate estimated blur kernel information and improving the performance of blind SR. This invention can achieve complex super-resolution reconstruction functions, thereby obtaining high-quality, high-resolution images. Attached Figure Description

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0028] Figure 1 This is a schematic diagram of the structure of a blind image super-resolution reconstruction network based on Bicubic downsampling image spatial alignment in an embodiment of the present invention.

[0029] Figure 2 This is a schematic diagram of the kernel estimation network in an embodiment of the present invention.

[0030] Figure 3 This is a schematic diagram of the structure of the Bicubic downsampling image spatial alignment network in an embodiment of the present invention.

[0031] Figure 4 This is a schematic diagram of the SR reconstruction network in an embodiment of the present invention.

[0032] Figure 5 This is a comparison chart of the kernel estimation results of this method and two other methods in this embodiment of the invention.

[0033] Figure 6 This is a comparison chart of the reconstruction results of this method with three other methods in this embodiment of the invention. Detailed Implementation

[0034] To make the features and advantages of this patent more apparent and understandable, specific embodiments are provided below, along with accompanying drawings, for detailed explanation:

[0035] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0036] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0037] This embodiment provides a blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment. The blind super-resolution task is decomposed into three sub-tasks: kernel estimation, Bicubic downsampling image spatial alignment, and SR reconstruction. Each sub-task has its specific objectives and constraints, and specific network structures and loss functions can be designed for each sub-task. The low-resolution image I... LR The input is fed into a blind image super-resolution reconstruction network based on Bicubic downsampling image spatial alignment, and the network outputs a reconstructed high-resolution image I. SR .

[0038] like Figure 1 As shown, in this embodiment, the Blind Image Super-Resolution Reconstruction Network (BMSR) based on Bicubic Downsampled Image Spatial Alignment includes a kernel estimation network (KNet), a Bicubic Downsampled Image Spatial Alignment sub-network (BNet), and an SR reconstruction network (SRNet). First, the kernel estimation network (KNet) accurately estimates the information of the blur kernel. Then, the Bicubic Downsampled Image Spatial Alignment sub-network (BNet) maps the LR image domain to the Bicubic downsampled image space under the guidance of the blur kernel. Finally, the SR reconstruction network (SRNet) uses the Bicubic downsampled LR image generated by BNet to reconstruct the HR image.

[0039] like Figure 2As shown in this embodiment, the kernel estimation network part of the Blind Image Super-Resolution Reconstruction Network (BMSR) based on Bicubic downsampled image spatial alignment is used. ResNet (Residual Network) is employed as the kernel estimation network, extracting image features through multiple deep residual modules. Multiple skip connections are used to connect the input to the network output: first, a 3×3 convolutional layer extracts shallow features, then multiple residual blocks are fed in to extract deep features. Skip connections are used to accelerate model training and improve model accuracy. Finally, two convolutional layers, average pooling, and Softmax are used to convert the main body's output feature map into a blurred kernel matrix.

[0040] like Figure 3 As shown in this embodiment, the Bicubic Downsampled Image Spatial Alignment Network (BNet) of the Blind Image Super-Resolution Reconstruction Network (BMSR) consists of two convolutional layers and two RRDB-SFT layers. The first 3×3 convolutional layer is used to extract shallow features from the LR image, and then the RRDB-SFT further utilizes these shallow features. The SFT layer, in addition to receiving the shallow features from the previous layer, also takes the estimated blur kernel K as input. This means that the input to BNet includes not only the LR image but also additional information related to the LR image. By inputting this additional information into the network, BNet can better learn how to convert the LR image into a higher-quality Bicubic downsampled LR image.

[0041] like Figure 4 As shown, in this embodiment, as an optional approach, the SR reconstruction part of the Blind Image Super-Resolution Reconstruction Network (BMSR) based on Bicubic downsampled image spatial alignment uses RCAN (Residual Channel Attention Network) as the non-blind SR network. Feature extraction is performed using multiple residual blocks, each containing a sub-module called the Residual Channel Attention Module. The Residual Channel Attention Module performs two key steps to enhance feature representation: First, it performs feature recalibration in the channel orientation, learning the importance of each channel and assigning weights to it. This helps the network better capture different features in the input image for better super-resolution reconstruction. Second, the Residual Channel Attention Module performs feature recalibration in the spatial orientation, learning the importance of each spatial location and updating the feature map accordingly. This helps the network better handle spatial variations in the input image and adapt it better to different super-resolution reconstruction tasks.

[0042] The blind image super-resolution reconstruction network based on bicubic downsampling image spatial alignment transforms LR images generated by different degradation processes into the LR image domain of bicubic downsampling, and then uses a trained non-blind SR network for reconstruction. This makes the network more tolerant of errors caused by blur kernel estimation, and can better reconstruct clearer high-resolution images.

[0043] Furthermore, the blind image super-resolution reconstruction method based on Bicubic downsampled image spatial alignment provided in this embodiment not only needs to estimate the blur kernel and the super-resolution (SR) reconstructed image, but also needs to map the LR image to the Bicubic downsampled LR image. Therefore, the loss function includes three parts: kernel estimation loss, Bicubic downsampled image spatial alignment loss, and SR image reconstruction loss.

[0044]

[0045] Where N represents the number of training samples, and ||·||1 represents the L1 norm. This indicates the generated Bicubic downsampling, B i Represents true Bicubic downsampling. HR images reconstructed from the network The images used are real HR (High-Resolution Earth) images. After training, the trained network parameters are obtained and directly used for image super-resolution reconstruction.

[0046] This embodiment also provides a blind image super-resolution reconstruction network system based on Bicubic downsampling image spatial alignment, including a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the above-described method steps.

[0047] In one application example, a BMSR was trained using DIV2K (800 images) and Flickr2K (2650 images). For testing, three benchmark datasets were used: Set5, Set14, and DIV2KRK. Peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) were used to measure the quality of the SR images. For each training mini-batch, eight 64×64 patches were randomly cropped from the LR images as input. The BMSR of this method was trained using a cosine annealing optimizer for 8×10 training iterations. 5 Second-rate.

[0048] To demonstrate the effectiveness of the method of this invention, a horizontal comparison is made with the bicubic method and three existing representative deep learning-based single-image super-resolution reconstruction methods: IKC, DANv1, and DANv2.

[0049] The quantitative comparison of the method of this invention with the above three methods is shown in Table 1. The evaluation indexes are peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), and the values ​​are the mean values ​​of the reconstruction results of the test dataset. The unit of PSNR is dB.

[0050] Table 1

[0051]

[0052] Experimental data show that the BMSR method of this invention achieves better reconstruction results than DANv2 on the Set5 and DIV2KRK datasets, and obtains similar results on the Set14 dataset.

[0053] In terms of visual reconstruction, the super-resolution reconstruction effects of the two comparative methods and the method of this invention are compared as follows: Figure 5 As shown. By Figure 5 It can be seen that the blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment of the present invention can reconstruct more accurate detail information.

[0054] Regarding fuzzy kernel estimation, the kernel estimation performance of the two comparative methods and the method of this invention is compared as follows: Figure 6 As shown. By Figure 6 It can be seen that the blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment of the present invention can accurately estimate the blur kernel information.

[0055] As can be seen, the BMSR of this invention, by adding a Bicubic downsampling image spatial alignment module between the kernel estimation and SR reconstruction networks, maps the LR image to Bicubic downsampling under the guidance of the estimated degradation information, thus mitigating the error introduced by the kernel estimation network and better solving the single-image super-resolution reconstruction problem. BMSR decomposes the difficult super-resolution reconstruction task into three sub-tasks, which can more effectively solve the blind SR task and obtain high-quality high-resolution images.

[0056] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0057] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0058] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0059] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0060] This patent is not limited to the above-described preferred embodiments. Anyone can derive other forms of blind image super-resolution reconstruction methods based on Bicubic downsampling image spatial alignment under the guidance of this patent. All equivalent changes and modifications made within the scope of this patent application shall fall within the scope of this patent.

Claims

1. A blind image super-resolution reconstruction method based on spatial alignment of bicubic downsampled images, characterized in that: The blind image super-resolution reconstruction network consists of three sub-networks: kernel estimation sub-network KNet, bicubic downsampled image space alignment sub-network BNet, and image reconstruction sub-network SRNet. By inputting the estimation kernel information into the bicubic downsampled image space alignment sub-network, the blind low-resolution image is first mapped to the bicubic downsampled image space to obtain the bicubic downsampled LR image. The image reconstruction sub-network SRNet is a non-blind super-resolution reconstruction network. low-resolution images The input is fed into the blind image super-resolution reconstruction network, and the output is a reconstructed high-resolution image. ; ResNet is used as the kernel estimation subnetwork KNet; the Bicubic downsampled image spatial alignment subnetwork BNet uses dense residual network RRDB and spatial feature transformation SFT to map low-resolution images generated by different degradation processes to Bicubic downsampled LR images; The Bicubic downsampled image spatial alignment subnetwork BNet consists of two convolutional layers and two RRDB-SFT layers. The first 3×3 convolutional layer is used to extract shallow features of the LR image, and then the shallow features are further utilized by RRDB-SFT. In addition to receiving the shallow features from the previous layer, the SFT layer also takes the estimated blur kernel K as input.

2. The blind image super-resolution reconstruction method based on bicubic down-sampled image space alignment according to claim 1, characterized in that: The kernel estimation sub-network KNet uses ResNet as the kernel estimation network. It extracts image features through multiple deep residual modules and uses multiple skip connections to connect the input to the network output: first, a 3×3 convolutional layer is used to extract shallow features, and then multiple residual blocks are fed in to extract deep features. At the same time, skip connections are used to accelerate the training of the model and improve the accuracy of the model. Finally, the output feature map of the subject is converted into a blurred kernel matrix through two convolutional layers, average pooling, and Softmax.

3. The blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment according to claim 1, characterized in that: The blind image super-resolution reconstruction network converts blind LR images generated by different degradation processes to the Bicubic downsampled image spatial domain, and then uses the trained image reconstruction sub-network SRNet for reconstruction. This allows the network to have a certain tolerance for the errors caused by blur kernel estimation, so as to reconstruct a clearer high-resolution image.

4. The blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment according to claim 1, characterized in that: The training process of the super-resolution reconstruction network is divided into three stages: The first stage involves pre-training three sub-networks. Specifically, the kernel estimation sub-network KNet is supervised using real kernels to predict blur kernels for the input LR image. The Bicubic downsampled image spatial alignment sub-network BNet is a supervised network trained using real LR images, real blur kernels, and corresponding Bicubic downsampled LR images. The image reconstruction sub-network SRNet is also a supervised network trained using HR images and corresponding Bicubic downsampled LR images. In the second stage, the estimation kernel generated by the kernel estimation subnetwork KNet is used to fine-tune the spatial alignment subnetwork BNet of the Bicubic downsampled image, and the LR is mapped to the Bicubic downsampled image. The third stage uses the estimated B image to fine-tune the SRNet network and obtains the final SR result.

5. The blind image super-resolution reconstruction method based on Bicubic downsampling image spatial alignment according to claim 4, characterized in that: When a training dataset is provided, the loss function is expressed as: in, Indicates the number of training samples. Represents the L1 norm; This indicates the estimation of the fuzzy kernel. A fuzzy kernel representing reality; This represents the generated Bicubic downsampled LR image. Represents a true Bicubic downsampled LR image. SR images reconstructed from the network The network parameters are obtained from real HR images after training and can be directly used for image super-resolution reconstruction.

6. A blind image super-resolution reconstruction system based on Bicubic downsampling image spatial alignment, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor, wherein when the processor executes the computer program instructions, it can implement the method as described in any one of claims 1-5.

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