A cardiac magnetic resonance undersampling reconstruction method, system, device and storage medium

Abstract

This application discloses a method, system, device, and storage medium for undersampled reconstruction of cardiac magnetic resonance imaging (MRI). The method includes: preprocessing the raw k-space data of multi-coil cardiac MRI and obtaining undersampled k-space data according to a preset undersampled rule; inputting the undersampled k-space data into a frequency domain reconstruction network to obtain a preliminary reconstructed k-space; performing an inverse Fourier transform on the k-space to obtain an intermediate reconstructed image; inputting the intermediate reconstructed image into an image domain reconstruction network; using parameterized quantum circuits to perform quantum encoding, quantum entanglement, and quantum measurement on the compressed features obtained from the intermediate reconstructed image; and predicting the image residual using the image domain reconstruction network; and fusing the image residual with the intermediate reconstructed image to obtain a reconstructed cardiac MRI image. This application provides an undersampled reconstruction method for cardiac MRI to address the problem that existing reconstruction methods cannot simultaneously fully utilize frequency domain sampling information, image domain structural priors, and complex nonlinear feature relationships.

Description

Technical Field

[0001] This application relates to a method, system, device, and storage medium for cardiac magnetic resonance undersampling reconstruction. Specifically, it relates to a method, system, device and storage medium for cardiac magnetic resonance undersampling reconstruction based on quantum-classical hybrid dual-domain networks, belonging to the field of magnetic resonance image reconstruction technology. Background Technology

[0002] Magnetic resonance imaging (MRI) is widely used in assessing cardiac structure and function due to its advantages such as high soft tissue contrast, no ionizing radiation, and the ability to perform multi-parameter imaging. Cardiac MRI requires acquiring a large amount of k-space data within a limited time. Complete sampling leads to excessively long scan times and increases the risk of artifacts caused by respiration, heartbeat, and patient movement. Undersampling to reduce the number of phase encoding lines can shorten acquisition time, but directly performing an inverse Fourier transform on the undersampling k-space data produces significant aliasing artifacts.

[0003] Traditional parallel imaging and compressed sensing reconstruction methods rely on coil sensitivity, sparse transformation, regularization parameters, and iterative optimization processes. Under conditions of complex cardiac structures, high undersampling rates, or noise, they are prone to problems such as long reconstruction times, overly smoothed details, or parameter sensitivity. Convolutional neural network-based reconstruction methods can learn image priors from data, but when processing only in the image domain, they tend to ignore sampled frequency domain information, while processing only in the frequency domain makes it difficult to fully recover tissue structure and local texture.

[0004] Dual-domain reconstruction networks, by processing continuously in the k-space domain and the image domain, to some extent balance frequency domain constraints and image structure. However, the feature transformation methods of classical convolution operations mainly consist of local linear combinations and nonlinear activations, and their ability to model the complex coupling relationships between high-dimensional features still has room for improvement. Parameterized quantum circuits can achieve feature mappings different from conventional convolutions through quantum superposition, entanglement, and measurement mechanisms, providing new possibilities for constructing quantum-classical hybrid reconstruction networks.

[0005] Therefore, there is an urgent need for a cardiac magnetic resonance undersampling reconstruction scheme that can jointly utilize k-space frequency domain information, image domain structural information, and parameterized quantum feature mapping to improve aliasing artifact suppression, reconstruction accuracy, and model expressive power. Summary of the Invention

[0006] This invention aims to provide a method for undersampling reconstruction of cardiac magnetic resonance imaging based on a quantum-classical hybrid dual-domain network, to address the problem that existing reconstruction methods struggle to simultaneously fully utilize frequency domain sampling information, image domain structural priors, and complex nonlinear feature relationships. Specifically: According to one aspect of this application, a method for undersampling reconstruction of cardiac magnetic resonance imaging is provided, the method comprising the following steps: S1, acquire the original k-space data of multi-coil cardiac magnetic resonance imaging, preprocess the original k-space data, and obtain undersampled k-space data according to the preset undersampling rule; S2, input the undersampled k-space data into the frequency domain reconstruction network to obtain the preliminary reconstructed k-space; S3, Perform an inverse Fourier transform on the initially reconstructed k-space to obtain the intermediate reconstructed image; S4, the intermediate reconstructed image is input into an image domain reconstruction network with a parameterized quantum circuit front end, and the compressed features obtained from the intermediate reconstructed image are quantum encoded, quantum entangled, and quantum measured using the parameterized quantum circuit, and the image domain reconstruction network predicts the image residual based on the quantum measurement results; S5, the image residual is fused with the intermediate reconstructed image to obtain a cardiac magnetic resonance reconstructed image.

[0007] Preferably, in S1, preprocessing the original k-space data and obtaining undersampled k-space data according to a preset undersampling rule specifically includes: By performing coil dimension synthesis on multi-coil images or multi-coil k-space data, a single-channel target image can be obtained; Normalize the target image or k-space data; Construct an undersampling mask, retain the data at the preset sampling positions in the k-space corresponding to the undersampling mask, and set the data at the remaining sampling positions to zero to obtain the undersampling k-space data; The aliased image is obtained by inverse Fourier transform of the undersampled k-space data; The undersampling mask is either an equally spaced undersampling mask that retains the sampling columns at fixed intervals along the phase encoding direction, or a variable density undersampling mask that retains the low-frequency region at the center of the k-space and performs random sampling in the outer high-frequency region.

[0008] Preferably, the frequency domain reconstruction network in S2 includes: a multi-level downsampling coding module, a multi-level upsampling decoding module, and skip connections between corresponding levels; Multi-level downsampling encoding module, multi-level upsampling decoding module, and jump connections between corresponding levels Used to extract local texture features and global frequency distribution features in k-space at different scales; The frequency domain reconstruction network is a U-shaped encoder-decoder network. The input of the frequency domain reconstruction network includes at least the real part channel and the imaginary part channel of the undersampled k-space, and the output includes the real part channel and the imaginary part channel of the reconstructed k-space.

[0009] Preferably, in S2, the specific process of obtaining the preliminary reconstructed k-space based on the frequency domain reconstruction network is as follows: The real and imaginary parts of the undersampled k-space data are used as independent input channels; The multi-level downsampling encoding module extracts local texture features and global frequency distribution features in the k-space; Spatial details are recovered through the multi-level upsampling decoding module, and features are transmitted between the encoding module and the corresponding level decoding module through skip connections; The output channels are the real and imaginary parts of the reconstructed k-space, and the initial reconstructed k-space is formed by combining the output real and imaginary channels.

[0010] Preferably, in S4, the parameterized quantum circuit front end includes: The classic feature compression module is used to compress the intermediate features of the image domain reconstruction network to a feature dimension corresponding to the number of qubits; A quantum coding module is used to encode compressed features into the rotation angle of each quantum bit; A quantum entanglement module is used to form entanglement relationships between qubits through a controlled NOT gate; The quantum measurement module is used to measure the Pauli Z expectation value of each qubit; A classical feature extension module is used to map quantum measurement results back to the image feature space; Preferably, the parameterized quantum circuit includes N qubits and L quantum layers, each quantum layer including a parameterized RY rotation gate acting on the N qubits respectively, and a controlled NOT gate connecting adjacent qubits to form a ring topology; Where N and L are positive integers, and their values ​​are determined based on a trade-off between experience and experimentation, and are adjusted according to computing resources and the complexity of the reconstruction task.

[0011] Preferably, in S5, the process of fusing the image residual with the intermediate reconstructed image to obtain the cardiac magnetic resonance reconstructed image specifically includes: The image domain reconstruction network receives the intermediate reconstructed image as input and predicts and outputs a residual image. The residual image is added element-wise to the intermediate reconstructed image to obtain the complete image; The clip function is used to truncate pixel values ​​in the complete image that are outside the preset display range to the preset range, thereby obtaining the cardiac magnetic resonance reconstruction image.

[0012] Preferably, in the method, the process of training the frequency domain reconstruction network and the image domain reconstruction network specifically includes: The reconstructed cardiac magnetic resonance image is used as the generator output, and the generator loss is calculated with the fully sampled target image. The generator loss includes at least the image mean square error loss and the generator adversarial loss. The reconstructed cardiac magnetic resonance image is input into the discriminator to obtain the authenticity discrimination result of local image patches, and the generator adversarial loss is calculated based on the discrimination result; The parameters of the frequency domain reconstruction network and the image domain reconstruction network are updated based on the generator loss, and the parameters of the discriminator are updated at a preset frequency lower than the generator update frequency. Preferably, the first set of loss weights is used in the first stage of training. After training reaches a preset number of rounds, the image mean square error loss weight is increased to the second weight, and the weights of at least one of the structural similarity loss, frequency domain consistency loss and adversarial loss are reduced to improve the peak signal-to-noise ratio of the reconstructed image. During training, exponential moving average parameters are used for validation and / or inference, and at least two checkpoints are selected from multiple checkpoints with the best validation performance for parameter averaging to obtain the output reconstructed model.

[0013] According to another aspect of this application, a cardiac magnetic resonance undersampling reconstruction system is provided, the system comprising: The data acquisition and undersampling module is used to acquire the raw k-space numbers from multi-coil cardiac magnetic resonance imaging. According to the above, the original k-space data is preprocessed, and undersampled k-space data is obtained according to the preset undersampling rules; The frequency domain reconstruction module is used to input the undersampled k-space data into the frequency domain reconstruction network to obtain a preliminary reconstructed k-space. The inverse Fourier transform module is used to perform an inverse Fourier transform on the initial reconstructed k-space to obtain an intermediate reconstructed image; The quantum-classical image domain reconstruction module is used to input the intermediate reconstructed image into an image domain reconstruction network with a parameterized quantum circuit front end. The parameterized quantum circuit is used to perform quantum encoding, quantum entanglement, and quantum measurement on the compressed features obtained from the intermediate reconstructed image. The image domain reconstruction network then predicts the image residual based on the quantum measurement results. An image fusion module is used to fuse the image residual with the intermediate reconstructed image to obtain a cardiac magnetic resonance reconstructed image.

[0014] According to another aspect of this application, an electronic device is provided, including a processor and a memory, the memory storing a computer program that, when executed by the processor, causes the processor to perform the aforementioned cardiac magnetic resonance undersampling reconstruction method.

[0015] According to another aspect of this application, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the aforementioned cardiac magnetic resonance undersampling reconstruction method.

[0016] Compared with the prior art, the beneficial effects of this application are as follows: This application reconstructs undersampled k-space data using a frequency domain reconstruction network, and then reconstructs it using the image domain. The reconstruction network restores the organizational structure and texture details, achieving continuous fusion of frequency domain sampling information and image domain structural priors, effectively suppressing aliasing artifacts and preserving high-frequency details; By introducing parameterized quantum circuits, compressed features are encoded as qubit rotation angles. Through quantum entanglement and quantum measurement, feature mappings different from classical convolution are obtained, which enhances the model's ability to express complex coupling relationships between high-dimensional features and achieves residual fusion with classical features, further improving the reconstruction quality. Among them, the image domain reconstruction network adopts the residual learning method, which only needs to predict the difference between the intermediate reconstructed image and the fully sampled target image, reducing the optimization difficulty of directly generating the complete image, accelerating convergence and improving reconstruction accuracy; through strategies such as multi-loss joint training, staged weight scheduling, exponential moving average verification and multi-checkpoint parameter averaging, the training stability and model generalization ability are significantly improved. The method can be deployed on magnetic resonance workstations, servers, or terminals with corresponding computing capabilities for offline or online reconstruction of cardiac magnetic resonance imaging, and has good versatility and practical value. Attached Figure Description

[0017] Figure 1 This invention relates to cardiac magnetic resonance undersampling reconstruction based on quantum-classical hybrid dual-domain networks. A schematic diagram of the overall process of the method; Figure 2 This is a flowchart illustrating the model training and inference process of the present invention; Figure 3 This is a schematic diagram of the structure of the frequency domain reconstruction network, quantum front end, and image domain reconstruction network of the present invention; Figure 4 This is a comparison chart of the reconstruction results of the present invention; Figure 5 The peak signal-to-noise ratio, structural similarity, and loss function variation curves during the training process of this invention are shown. Line chart. Detailed Implementation

[0018] According to a specific embodiment of this application, as shown in the appendix Figure 1 As shown, a method for undersampling reconstruction of cardiac magnetic resonance imaging based on a quantum-classical hybrid dual-domain network is provided, including: S1, acquire raw k-space data from multi-coil cardiac magnetic resonance imaging, preprocess the raw k-space data, and obtain undersampled k-space data according to a preset undersampling rule; The preprocessing process for the aforementioned original k-space data is as follows: A single-channel target image is obtained by synthesizing multi-coil images or multi-coil k-space data according to coil dimensions; the target image or k-space data is then normalized. Based on the undersampling mask, the preset sampling positions are retained and the remaining positions are set to zero; An aliased image is obtained by inverse Fourier transforming undersampled k-space data, and the aliased image and the fully sampled target image are used to construct a training sample pair; The preset undersampling rules include: Construct an undersampling mask, retain the data at the preset sampling positions in the k-space corresponding to the undersampling mask, and set the data at the remaining sampling positions to zero; The undersampling mask is either an equally spaced undersampling mask that retains the sampling columns at fixed intervals along the phase encoding direction, or a variable density undersampling mask that retains the low-frequency region at the center of the k-space and performs random sampling in the outer high-frequency region.

[0019] Furthermore, in one embodiment of this application, the coil dimension synthesis employs a sum of squares. Square root method, such as: I SoS =(Σc|Ic| 2 )^(1 / 2), where Ic represents the complex image corresponding to the c-th coil, I SoS This represents a composite image of coils.

[0020] S2, input the undersampled k-space data into the frequency domain reconstruction network to obtain the preliminary reconstructed k-space data. space; In some embodiments of the present invention, the frequency domain reconstruction network includes a multi-level downsampling coding module, a multi-level upsampling decoding module, and skip connections between corresponding levels, for extracting local texture features and global frequency distribution features in k-space at different scales.

[0021] The frequency domain reconstruction network is preferably a U-shaped encoder-decoder network. The input of the network includes at least the real and imaginary channels of the undersampled k-space, and the output includes the real and imaginary channels of the reconstructed k-space.

[0022] S3, Perform an inverse Fourier transform on the initially reconstructed k-space to obtain the intermediate reconstructed image; S4, input the intermediate reconstructed image into an image domain reconstruction network with a parameterized quantum circuit front end. The network utilizes the parameterized quantum circuits to perform quantum encoding, quantum entanglement, and quantum measurement on the compressed features obtained from the intermediate reconstructed image, and the image domain reconstruction network predicts the image residual based on the quantum measurement results; In some embodiments of the present invention, the parameterized quantum circuit front end includes: The classic feature compression module is used to compress the intermediate features of the image domain reconstruction network to a feature dimension corresponding to the number of qubits; A quantum coding module is used to encode compressed features into the rotation angle of each quantum bit; A quantum entanglement module is used to form entanglement relationships between qubits through a controlled NOT gate; The quantum measurement module is used to measure the Pauli Z expectation value of each qubit; A classical feature extension module is used to map quantum measurement results back to the image feature space; In some embodiments of the present invention, the parameterized quantum circuit includes N qubits and L quantum layers. Each quantum layer includes a parameterized RY rotation gate acting on the N qubits and a controlled NOT gate connecting adjacent qubits to form a ring topology. N and L are positive integers, and their values ​​are adjusted based on empirical and experimental trade-offs, according to computational resources and the complexity of the reconstruction task.

[0023] In some embodiments of the present invention, the preferred values ​​for N and L in the parameterized quantum circuit are N=8 and L=4, respectively.

[0024] S5, the image residual is fused with the intermediate reconstructed image to obtain a cardiac magnetic resonance reconstructed image.

[0025] The image domain reconstruction network receives the intermediate reconstructed image as input and predicts and outputs a residual image. The residual image is added element-wise to the intermediate reconstructed image to obtain the complete image; The `clip` function is used to truncate pixel values ​​in the complete image that exceed a preset display range to that range, thus obtaining the cardiac magnetic resonance reconstruction image. Specifically, in some embodiments of the present invention, the image domain reconstruction network predicts the residual image ΔI based on the intermediate reconstructed image, and according to I... rec =clip(I mid The final reconstructed image is obtained by adding ΔI,0,1), where I mid For the intermediate reconstructed image, I rec For the final image reconstruction, clip indicates that pixel values ​​will be truncated to a preset range.

[0026] Furthermore, in the method, the process of training the frequency domain reconstruction network and the image domain reconstruction network specifically includes: Raw k-space data from multi-coil cardiac magnetic resonance imaging was acquired, and preprocessed to obtain undersampled k-space data and fully sampled target images. The undersampled k-space data is input into the frequency domain reconstruction network to obtain a preliminary reconstructed k-space, and then an intermediate reconstructed image is obtained by inverse Fourier transform. The intermediate reconstructed image is input into an image domain reconstruction network with a parameterized quantum circuit front end to obtain the final reconstructed image; The generator loss is calculated based on the final reconstructed image and the fully sampled target image. The generator loss includes image mean square error loss and generator adversarial loss. The final reconstructed image is input into the discriminator to obtain the authenticity discrimination result of local image patches, and the generator adversarial loss is calculated based on the discrimination result; The parameters of the discriminator are updated at a preset frequency lower than the generator update frequency; The parameters of the frequency domain reconstruction network and the image domain reconstruction network are updated based on the generator loss.

[0027] In some embodiments of the present invention, the generator loss function used when training the frequency domain reconstruction network and the image domain reconstruction network is: LG=λ mse L mse +λ l1 L l1 +λ k L k +λ ssim L ssim +λ adv L adv ; Among them, L mse L represents the image mean square error loss. l1 L represents the image pixel difference loss. kL represents the frequency domain consistency loss. ssim L represents the structural similarity loss. adv This indicates that the generator suffers from adversarial loss, and the weights of each loss are scheduled according to the training phase.

[0028] In some embodiments of the present invention, a first set of loss weights is used in the first stage of training. After training reaches a preset number of rounds, the image mean square error loss weight is increased to a second weight, and the weights of at least one of structural similarity loss, frequency domain consistency loss and adversarial loss are reduced to improve the peak signal-to-noise ratio of the reconstructed image.

[0029] In some embodiments of the present invention, during the training process, exponential moving average parameters are used for verification and / or inference, and at least two checkpoints are selected from multiple model checkpoints with the best verification performance for parameter averaging to obtain the output reconstructed model.

[0030] In some embodiments of the present invention, the method further includes: inputting the final reconstructed image into a discriminator to obtain a local image patch authenticity discrimination result; calculating an adversarial loss based on the discrimination result; and updating the discriminator parameters at a preset frequency lower than the generator update frequency.

[0031] The present invention also provides a cardiac magnetic resonance undersampling reconstruction system, the system comprising: The data acquisition and undersampling module is used to acquire the raw k-space numbers from multi-coil cardiac magnetic resonance imaging. According to the above, the original k-space data is preprocessed, and undersampled k-space data is obtained according to the preset undersampling rules; The frequency domain reconstruction module is used to input the undersampled k-space data into the frequency domain reconstruction network to obtain a preliminary reconstructed k-space. The inverse Fourier transform module is used to perform an inverse Fourier transform on the initial reconstructed k-space to obtain an intermediate reconstructed image; The quantum-classical image domain reconstruction module is used to input the intermediate reconstructed image into an image domain reconstruction network with a parameterized quantum circuit front end. The parameterized quantum circuit is used to perform quantum encoding, quantum entanglement, and quantum measurement on the compressed features obtained from the intermediate reconstructed image. The image domain reconstruction network then predicts the image residual based on the quantum measurement results. An image fusion module is used to fuse the image residual with the intermediate reconstructed image to obtain a cardiac magnetic resonance reconstructed image.

[0032] like Figure 3The diagram illustrates the architecture of the reconstruction system described in this application. This architecture comprises an input processing module, a frequency domain reconstruction network (k-space-U-Net), an image domain reconstruction network (containing a quantum front-end), and a result fusion module. The structure and connections of each part are as follows: The input processing module is used to provide undersampled data to the system, including: multi-coil original k-space data and undersampled mask M; the two are combined to generate undersampled k-space data (containing real and imaginary parts), and optionally, the corresponding aliased image can also be generated as input to the subsequent frequency domain reconstruction network and image domain reconstruction network.

[0033] The k-space U-Net frequency domain reconstruction network employs a U-Net architecture with a 2C input channel configuration, corresponding to the real and imaginary parts of the undersampled k-space data. The network extracts and reconstructs features from the frequency domain data through a multi-layer encoder-decoder structure (including skip connections). The output channel is also 2C, and the reconstructed k-space data contains both real and imaginary parts. This reconstructed k-space data is then processed by an inverse Fourier transform (IFFT) to generate an amplitude map of the intermediate reconstructed image, which is then input into the subsequent image domain reconstruction network.

[0034] The image domain reconstruction network includes a quantum front-end and residual prediction. The image domain reconstruction network, with a residual prediction structure featuring a quantum front-end as its core, receives the intermediate reconstructed image and outputs a residual image ΔI. Its structure consists of the following parts: Classical feature extraction and compression: First, 32 channels of classic features are extracted from the reconstructed image through convolutional layers; then, global average pooling and 1×1 convolution are used to compress the feature channels to N (e.g., N=8) to adapt to the input dimension of subsequent quantum circuits.

[0035] Parameterized quantum circuit: The quantum circuit contains N qubits and L layers of ring entanglement structure; the circuit takes the compressed features as input and realizes the evolution of quantum state and feature transformation through a single-qubit rotation gate RY and a multi-qubit controlled entanglement gate.

[0036] Quantum measurement and feature expansion: Pauli-Z basis measurement is performed on the evolved quantum state to obtain the N-dimensional expectation value; then, through 1×1 convolution and upsampling operations, the quantum feature is expanded to 32 channels to restore the spatial size matching the input image and output the residual image ΔI.

[0037] The intermediate reconstructed image and the residual image ΔI output by the image domain reconstruction network are added pixel by pixel by the fusion module to obtain the final reconstructed image I. rec This completes the reconstruction process of undersampled magnetic resonance data.

[0038] This architecture directly achieves high-precision reconstruction of undersampled magnetic resonance data through two-stage reconstruction in the frequency and image domains and quantum-classical hybrid feature processing. It effectively suppresses aliasing artifacts caused by undersampling and improves the ability to restore image details.

[0039] The present invention also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the aforementioned cardiac magnetic resonance undersampling reconstruction method.

[0040] The present invention also provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, it implements the aforementioned method for cardiac magnetic resonance undersampling reconstruction. The storage medium may include a read-only memory, random access memory, solid-state drive, magnetic disk, optical disk, or other media capable of storing program code. The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments described are for illustrative purposes only and are not intended to limit the scope of protection of the invention. Parameters such as the number of network channels, layers, training epochs, and loss weights, which are not explicitly defined, can be adjusted according to the data scale, computing resources, and reconstruction task requirements.

[0041] Example 1: Data Acquisition and Preprocessing Acquire raw k-space data from multi-coil cardiac magnetic resonance imaging (MRI). Data can be sourced from publicly available cardiac MRI databases. The resonance dataset contains complex k-space data acquired by multiple coils, with dimensions including readout direction, phase encoding direction, coil dimension, and optional slice, time frame, or echo dimension.

[0042] Perform an inverse Fourier transform on the k-space data of each coil to obtain the corresponding complex coil image; synthesize the fully sampled target image using the square root of the sum of squares method, i.e.: I SoS =(Σc|Ic| 2 )^(1 / 2), where Ic is the complex image corresponding to the c-th coil, I SoS This is a synthesized image. The synthesized image is normalized according to the maximum value or a preset scale, and the image intensity is mapped to [0,1] or other preset ranges.

[0043] An undersampling mask M is generated based on a preset undersampling rule. Undersampling observations can be represented as: y = M⊙F(x)+n; Where x is the image to be reconstructed, F is the two-dimensional Fourier transform, M is the undersampling mask, ⊙ is the element-wise multiplication, y is the undersampling k-space data, and n is noise.

[0044] One example is to retain the sampling columns at fixed intervals along the phase encoding direction, achieving a speedup of approximately 3.3 times; another example is to retain the central low-frequency region and perform random sampling in the outer region.

[0045] The mask is multiplied element-wise with the original k-space data to obtain undersampled k-space data, and then an inverse Fourier transform is performed on it to obtain the aliased image.

[0046] Cropping or interpolating the aliased image and the fully sampled target image to a preset size (e.g., 256×256 pixels) constructs training, validation, and test sample sets, ensuring that there is no overlap between different subjects.

[0047] Example 2: This embodiment provides a specific example of the frequency domain reconstruction network.

[0048] The frequency domain reconstruction network in this embodiment adopts a U-shaped encoder-decoder structure. The frequency domain reconstruction network is constructed in the order of input layer, encoder, bottleneck layer, decoder, and output layer. First, the real and imaginary parts of the undersampled k-space data are input to the network as independent channels. Then, frequency domain features are extracted step-by-step through multiple cascaded coding units, each including a convolutional layer, a normalization layer, and a nonlinear activation layer. Downsampling operations are used to expand the network's receptive field, obtaining local frequency features and global frequency distribution features at different scales. The high-level frequency domain features output by the encoder are fused at the bottleneck layer. Next, the decoder recovers the feature resolution through step-by-step upsampling and passes the shallow features of the corresponding coding layer to the decoding layer through skip connections to fuse local detail information and high-level semantic information. Finally, two output channels are generated through the output convolutional layer, representing the real and imaginary parts of the initially reconstructed k-space, respectively. The two output channels are combined to form a complex initially reconstructed k-space. The undersampled input is converted into channels representing the real and imaginary parts of the complex k-space. When using multi-slice or multi-frame input, the real and imaginary parts corresponding to multiple adjacent slices or time frames can be spliced ​​along the channel dimension; in the single-slice implementation, the number of input channels is 2.

[0049] The encoder contains multiple convolutional blocks and downsampling operations. Each convolutional block consists of a convolutional layer, a normalization layer, and a nonlinear activation layer. The decoder uses upsampling or transposed convolution to restore spatial resolution and fuses features from the corresponding coding layers through skip connections. The network outputs two channels, representing the real and imaginary parts of the reconstructed k-space, respectively.

[0050] In one specific exemplary implementation, the frequency domain network has a base number of 32 channels, including 4 levels of downsampling encoding and 4 levels of upsampling decoding. The convolutional kernel size is 3×3, and the convolutional blocks are activated using BatchNorm2d and LeakyReLU(0.2). The upsampling method is bilinear interpolation. Convolutional networks, Transformers, or combinations thereof capable of outputting complex reconstructed k-space can all be used as frequency domain reconstruction networks.

[0051] Example 3: This embodiment provides a specific example of the quantum-classical image domain reconstruction network.

[0052] The quantum-classical image domain reconstruction network is constructed in the following order: classical feature extraction, classical feature compression, parameterized quantum feature transformation, quantum measurement result expansion, quantum-classical feature fusion, and image residual prediction. First, the complex preliminary reconstruction k-space output by the frequency domain reconstruction network is subjected to an inverse Fourier transform and its amplitude is taken to obtain an intermediate reconstructed image. Then, the intermediate reconstructed image is input into a classical convolutional feature extraction module to obtain image features with a preset number of channels. Through pooling operations and convolution mapping, the image features are compressed to N-dimensional features corresponding to the number of qubits, and each dimension of the feature is mapped to the rotation angle of the corresponding qubit. In the parameterized quantum circuit, the compressed features are sequentially quantum encoded and entangled through an RY rotation gate and a ring-connected controlled NOT gate, and an N-dimensional quantum expectation value is obtained through Pauli Z measurement. The quantum expectation value is expanded back to the classical image feature space through convolution mapping and upsampling, and then fused with the classical features before quantum processing. Finally, the fused quantum enhanced features are input into a U-shaped image domain reconstruction network to predict the single-channel residual image between the intermediate reconstructed image and the fully sampled target image.

[0053] Perform an inverse Fourier transform on the complex reconstructed k-space output of the frequency domain reconstruction network and take the amplitude. Obtain intermediate reconstructed image I mid The image domain reconstruction network adopts a U-shaped structure and sets up a quantum feature processing branch at its feature extraction front end.

[0054] The quantum feature processing branch first uses classical convolution to compress C-dimensional image features into N-dimensional features, and then obtains a feature tensor with a fixed spatial size through adaptive pooling. For each spatial location or feature block, the N-dimensional features are mapped to a rotation angle of N qubits, and angle encoding is completed through the RY gate.

[0055] The parameterized quantum circuit comprises L layers of quantum transformations. In each layer, an RY rotation gate with trainable parameters is first applied to each qubit, followed by a controlled NOT gate applied according to the adjacent connection pattern; the last qubit is connected to the first qubit, forming a ring entangled topology. After completing the L layers of transformations, a Pauli Z-measurement is performed on each qubit to obtain an N-dimensional expectation vector.

[0056] In this embodiment, the number of qubits N is 8, the number of quantum layers L is 4, and the number of trainable quantum rotation parameters is 32. The quantum measurement results are expanded back to the C dimension through linear layers or 1×1 convolutions and then residually fused with the classical features before quantum processing. The parameterized quantum circuit structure with 8 qubits and 4 quantum layers is shown in Table 1. Table 1. Schematic diagram of parameterized quantum circuit structure

[0057] In Table 1, odd-numbered steps represent parameterized RY rotations on each qubit, and even-numbered steps represent CNOT entanglement between adjacent qubits; the last pair of connections forms a head-to-tail ring topology.

[0058] The complex k-space output by the frequency domain network is denoted as K. rec Intermediate Reconstructed Image I mid Represented as: I mid = |F -1 (K rec )| The fused quantum enhancement features are fed into an image-domain U-shaped network, which outputs a single-channel residual image ΔI. The final reconstructed image is obtained using the following formula: I rec =clip(I mid +ΔI,0,1), where clip means truncating pixel values ​​to a preset range.

[0059] Let ΔI and I mid The pixels are added one by one, and the result is limited to [0,1] or other preset intensity ranges to obtain the final reconstructed image.

[0060] Example 4: like Figure 2 As shown, this embodiment provides a specific example of the training method for the frequency domain reconstruction network and the image domain reconstruction network in the cardiac magnetic resonance undersampling reconstruction method described in this application.

[0061] (1) Input configuration steps: Input training dataset, validation dataset and model initial parameters; wherein, the training dataset and validation dataset are pre-constructed cardiac magnetic resonance datasets, and the model initial parameters include the initial weights and hyperparameters of the frequency domain reconstruction network, image domain reconstruction network, quantum circuit module and discriminator.

[0062] (2) Data preprocessing steps: The input data is preprocessed, specifically including: performing SoS (sum-squared) synthesis processing on the original cardiac magnetic resonance signal; normalizing the synthesized data; generating an undersampled mask, and constructing an aliased target sample pair consisting of the undersampled data and the corresponding fully sampled target data based on the undersampled mask.

[0063] (3) Frequency domain reconstruction step: Input the preprocessed undersampled k-space data into the U-Net frequency domain reconstruction network, which predicts and outputs the reconstructed complete k-space data.

[0064] (4) Image domain reconstruction step: Perform inverse Fourier transform (IFFT) on the reconstructed k-space data output in step S103 to obtain an intermediate image; input the intermediate image into the image domain U-Net network equipped with a quantum front-end, and the network predicts and outputs the residual data between the intermediate image and the real full-sampled image.

[0065] (5) Result fusion step: The intermediate image is added pixel by pixel to the residual data output in step S104, and the addition result is truncated so that the pixel value is within a preset reasonable physical range to obtain the final reconstructed image.

[0066] (6) Loss calculation steps: Based on the final reconstructed image and the corresponding fully sampled target image, calculate the multi-dimensional loss function, including MSE (mean squared error) loss, SSIM (structural similarity) loss, k-space domain loss and adversarial loss; and sum the loss terms according to the preset weight coefficients to obtain the total loss value used for model optimization.

[0067] (7) Parameter update steps: Based on the backpropagation algorithm, the model parameters are updated according to the total loss value. The updated parameters include generator parameters (frequency domain reconstruction network parameters, image domain reconstruction network parameters), quantum circuit parameters, and discriminator parameters to achieve iterative optimization of the model.

[0068] (8) Stop condition judgment step: Determine whether the current training process has reached the preset stop condition; the stop condition includes but is not limited to: the validation set loss has not decreased for multiple consecutive rounds, the preset maximum number of iterations has been reached, and the model performance index has reached the preset threshold. If the stop condition has not been reached, return to step (3) to continue iterative training; if the stop condition has been reached, proceed to step (9).

[0069] (9) Output and inference steps: Output the reconstructed model after training; In the inference stage, input the cardiac magnetic resonance undersampled data to be reconstructed, and sequentially perform data preprocessing, frequency domain reconstruction, image domain reconstruction and result fusion steps to output the final reconstructed image and complete the reconstruction of cardiac magnetic resonance undersampled data.

[0070] During the training phase, undersampled data is used as the model input, and the fully sampled target image is used as the supervision signal. The generator includes a frequency domain reconstruction network, a parameterized quantum circuit front-end, and an image domain reconstruction network; the discriminator can use a local block discriminator network to determine the authenticity of the central region or the entire image in the final reconstructed image.

[0071] The loss function comprises several components: image mean square error loss L mse , represented as: L mse =||I rec -I gt || 2 2; Among them, I rec Represents the reconstructed image; I gt This represents the fully sampled target image corresponding to the reconstructed image; Image pixel difference loss can be achieved using methods such as L1 loss or Smooth L1 loss; Structural similarity loss L ssim From 1-SSIM(I rec ,I gt )get; Frequency domain uniformity loss L k Used to constrain the error between the Fourier transform of the reconstructed image and the target k-space or the sampled location; Generator Adversarial Loss L adv Used to make the reconstructed image have a local texture distribution that is closer to the target image; The total loss LG is expressed as: LG = λ mse L mse +λ l1 L l1 +λ k L k +λ ssim L ssim +λ adv L adv .

[0072] The generator loss weights can be changed with the training epochs.

[0073] Each loss weight is dynamically adjusted during the training phase: Initial weights from Table 2 are used in the early training stage, specifically λ. mse =1.5、λ l1 =0.003、λk =1×10 -5 , λ ssim =2×10 -5 , λ adv =5×10 -7 In the later stages of training, starting from round 65, a transition period of 15 rounds will be implemented to improve λ. mse Increased to 3.2, while also increasing λ l1 , λ k , λ ssim and λ adv Adjusted to 0.0012 and 5×10 respectively. -6 8×10 -6 and 1×10 -7 Classical networks, quantum circuits, and discriminators each employ independent optimizers or parameter sets; for example, classical networks use a learning rate of 1×10⁻⁶. -4 Quantum parameter learning rate 1×10 -5 Discriminator learning rate 5×10 -6 The total number of training rounds can be set to 100, the batch size to 2, and the undersampling factor to approximately 2 to 3.3.

[0074] Table 2 Training and Model Parameters (To be supplemented / verified)

[0075] During training, an exponential moving average parameter is used to evaluate the validation set. After a preset number of rounds, the multiple model checkpoints with the highest peak signal-to-noise ratio are saved, and their parameters are averaged to obtain the final model. The discriminator parameters are updated at a preset frequency lower than the generator's update frequency.

[0076] Verification experiment: To verify the effectiveness of the cardiac magnetic resonance undersampling reconstruction method described in this application, this experiment... The experiments compared the full-sampling target, undersampled zero-fill reconstruction, classical frequency domain network, classical dual-domain network, and the cardiac magnetic resonance undersampled reconstruction method described in this application. The comparisons were based on metrics including peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), normalized mean square error (NMSE), inference time, and the number of parameters in the final model.

[0077] In this experiment, the quantum-classical hybrid dual-domain reconstruction model described in this application achieved a Top-k average PSNR of approximately 42.22 dB and an SSIM of approximately 0.971 on the validation set, with approximately 8.64 M generator parameters and approximately 2.33 M discriminator parameters. Training curves show that the validation set PSNR and SSIM generally increase with training. Under the current OCMR paper-protocol experimental settings, the model's Top-k average PSNR on the validation set is approximately 42.22 dB, and the SSIM is approximately 0.971, demonstrating good reconstruction performance and stability.

[0078] The reconstruction results of the cardiac magnetic resonance undersampling reconstruction method described in this application are, for example, Figure 4 As shown, Figure 4 The image shows the comparison results of three different cardiac magnetic resonance images, arranged in rows. Each row, from left to right, consists of: the undersampled original image, the reconstruction result of the method in this application, and the fully sampled baseline image.

[0079] from Figure 4 The results show that: The undersampled images on the left exhibit significant aliasing artifacts, blurring, and loss of detail due to undersampling. The overall structural clarity is low, and the cardiac anatomy and edge details cannot be clearly presented. The reconstruction results in the middle (as per this application) demonstrate that after collaborative processing by a frequency domain reconstruction network and an image domain reconstruction network with a quantum front-end, the aliasing artifacts caused by undersampling are significantly suppressed, and the overall image clarity is greatly improved. Key anatomical details such as the cardiac chamber structure and myocardial edges are effectively restored, and the structural distortions caused by artifacts are significantly corrected.

[0080] Consistency between the middle and right columns and the baseline image: The reconstruction results of the method described in this application are highly consistent with the fully sampled baseline image (Ground Truth) in terms of overall anatomical structure, grayscale distribution, and edge details. There are no obvious structural deviations or artifact residues between the two, achieving high-precision restoration of undersampled cardiac magnetic resonance imaging data. Therefore, it can be concluded that the method described in this application can effectively overcome the image aliasing and blurring problems caused by undersampling, significantly improve the reconstruction quality of cardiac magnetic resonance imaging, and ensure that the reconstruction results are highly consistent with the fully sampled baseline image, meeting the requirements of clinical diagnosis for image clarity and detail fidelity.

[0081] Figure 5 This is a schematic diagram showing the performance and loss changes of the cardiac magnetic resonance undersampling reconstruction model based on a quantum-classical hybrid dual-domain network during 100 rounds of training in this experiment. Figure 5 It contains six sets of curves, which show the changes in key indicators during the training process. The content and direct results of each part are as follows: The blue curve in the upper right corner shows the trend of PSNR (Peak Signal-to-Noise Ratio) on the validation set as a function of training epochs. The horizontal axis represents the PSNR value, and the vertical axis represents the training epochs (0-100 epochs, increasing from top to bottom). The curve shows that the PSNR was approximately 40dB in the initial stage of the model. As training progressed, the PSNR remained at a high level overall, remaining stable in the later stages of training, and finally reaching its highest value in the 100th epoch, corresponding to the Top-k Avg marker. This indicates that the PSNR of the reconstructed image continuously optimizes with training, remaining at a high level overall, indicating high overall image fidelity, low noise level, and a stable improvement in reconstruction quality.

[0082] The cyan curve in the right represents the trend of SSIM on the validation set as a function of training epochs. The horizontal axis represents the SSIM value (0-1), and the vertical axis represents the number of training epochs. The curve shows that the SSIM was approximately 0.95 in the initial stage of the model. During training, the SSIM remained at a high level, finally reaching its highest value in the 100th epoch, corresponding to the Top-k Avg marker. This indicates that the reconstructed image has a high structural similarity to the fully sampled baseline image, and the restoration of cardiac anatomy and edge details continues to optimize with training, without significant overfitting or performance degradation.

[0083] The solid green line in the upper left corner represents the L1 loss curve in the image domain of the training set, and the dashed green line represents the L1 loss in the image domain of the validation set. The horizontal axis represents the loss value, and the vertical axis represents the number of training epochs. As shown in the curves, the loss decreases rapidly in the early stages of training, converges around 20 epochs, and shows no significant deviation between the training and validation set loss curves, eventually stabilizing at a very low level. This indicates that the model's error in the image domain continuously decreases, the training and validation set losses converge synchronously, no significant overfitting occurs, and the pixel-level image reconstruction error is effectively controlled.

[0084] The solid red line in the left-center represents the L2 loss curve in k-space for the training set, and the dashed orange line represents the L2 loss in k-space for the validation set. The horizontal axis represents the loss value, and the vertical axis represents the training epoch. The curve shows that the loss decreases rapidly in the early stages of training and then stabilizes. The trends of the training and validation set losses are consistent, with no significant divergence. This indicates that the model's reconstruction error in the frequency domain continuously decreases, the reconstruction accuracy of k-space data continuously improves with training, and the collaborative optimization of the frequency and image domains effectively suppresses undersampling artifacts.

[0085] The GAN adversarial loss curve (bottom left) shows the generator adversarial loss (purple curve) and the discriminator adversarial loss (yellow curve). The horizontal axis represents the loss value, and the vertical axis represents the training epochs. The curves show that the generator and discriminator losses change rapidly in the early stages of training, enter a stable adversarial phase in the middle stage, and then the discriminator loss fluctuates slightly while the generator loss stabilizes in the later stages, without pattern collapse or adversarial imbalance. This indicates that the model's adversarial training process is stable, the generator and discriminator maintain an effective game, and the dynamic balance of adversarial losses supports the realism and detail restoration of the reconstructed images.

[0086] The total loss curve (bottom right) shows the total loss on the training set (solid red line) and the total loss on the validation set (dashed purple line). The horizontal axis represents the loss value, and the vertical axis represents the number of training epochs. The curve shows that the total loss decreases rapidly in the early stages of training, converges around 20 epochs, and the training and validation loss curves highly overlap, eventually stabilizing at a very low level. This indicates that the model's overall loss function converges quickly, the training process is stable, and the validation and training loss decrease simultaneously, suggesting good generalization ability and no overfitting.

[0087] As can be seen from the above curves, the PSNR and SSIM indices of the model described in this application were continuously optimized and stabilized at a high level during 100 rounds of training. Various loss functions converged synchronously, the training process was stable and there was no obvious overfitting. In the end, it achieved cardiac magnetic resonance undersampling reconstruction with both high fidelity and structural consistency.

[0088] The above description is merely a few embodiments of this application and is not intended to limit this application in any way. Although this application discloses preferred embodiments as described above, it is not intended to limit this application. Any changes or modifications made by those skilled in the art without departing from the scope of the technical solution of this application using the disclosed technical content are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for undersampling reconstruction of cardiac magnetic resonance imaging, characterized in that, The method includes the following steps: S1, acquire the raw k-space data of multi-coil cardiac magnetic resonance imaging, preprocess the raw k-space data, and obtain undersampled k-space data according to the preset undersampling rule; S2, input the undersampled k-space data into the frequency domain reconstruction network to obtain the preliminary reconstructed k-space; S3, Perform an inverse Fourier transform on the initially reconstructed k-space to obtain the intermediate reconstructed image; S4, the intermediate reconstructed image is input into an image domain reconstruction network with a parameterized quantum circuit front end, and the compressed features obtained from the intermediate reconstructed image are quantum encoded, quantum entangled, and quantum measured using the parameterized quantum circuit, and the image domain reconstruction network predicts the image residual based on the quantum measurement results; S5, the image residual is fused with the intermediate reconstructed image to obtain a cardiac magnetic resonance reconstructed image.

2. The method according to claim 1, characterized in that, In S1, the preprocessing of the original k-space data and the obtaining of undersampled k-space data according to a preset undersampling rule specifically include: By performing coil dimension synthesis on multi-coil images or multi-coil k-space data, a single-channel target image can be obtained; Normalize the target image or k-space data; Construct an undersampling mask, retain the data at the preset sampling positions in the k-space corresponding to the undersampling mask, and set the data at the remaining sampling positions to zero to obtain the undersampling k-space data; The aliased image is obtained by inverse Fourier transform of the undersampled k-space data; The undersampling mask is either an equally spaced undersampling mask that retains the sampling columns at fixed intervals along the phase encoding direction, or a variable density undersampling mask that retains the low-frequency region at the center of the k-space and performs random sampling in the external high-frequency region.

3. The method according to claim 1, characterized in that, The frequency domain reconstruction network in S2 includes: a multi-level downsampling coding module, a multi-level upsampling decoding module, and skip connections between corresponding levels; Multi-level downsampling encoding module, multi-level upsampling decoding module, and jump connections between corresponding levels Used to extract local texture features and global frequency distribution features in k-space at different scales; The frequency domain reconstruction network is a U-shaped encoder-decoder network. The input of the frequency domain reconstruction network includes at least the real part channel and the imaginary part channel of the undersampled k-space, and the output includes the real part channel and the imaginary part channel of the reconstructed k-space.

4. The method according to claim 1, characterized in that, In S2, the specific process of obtaining the preliminary reconstructed k-space based on the frequency domain reconstruction network is as follows: The real and imaginary parts of the undersampled k-space data are used as independent input channels; The multi-level downsampling encoding module extracts local texture features and global frequency distribution features in the k-space; Spatial details are recovered through the multi-level upsampling decoding module, and features are transmitted between the encoding module and the corresponding level decoding module through skip connections; The output channels are the real and imaginary parts of the reconstructed k-space, and the initial reconstructed k-space is formed by combining the output real and imaginary channels.

5. The method according to claim 1, characterized in that, In S4, the parameterized quantum circuit front end includes: The classic feature compression module is used to compress the intermediate features of the image domain reconstruction network to a feature dimension corresponding to the number of qubits; A quantum coding module is used to encode compressed features into the rotation angle of each quantum bit; A quantum entanglement module is used to form entanglement relationships between qubits through a controlled NOT gate; The quantum measurement module is used to measure the Pauli Z expectation value of each qubit; A classical feature extension module is used to map quantum measurement results back to the image feature space; Preferably, the parameterized quantum circuit includes N qubits and L quantum layers, each quantum layer including a parameterized RY rotation gate acting on the N qubits respectively, and a controlled NOT gate connecting adjacent qubits to form a ring topology; Where N and L are positive integers, and their values ​​are determined based on a trade-off between experience and experimentation, and are adjusted according to computing resources and the complexity of the reconstruction task.

6. The method according to claim 1, characterized in that, In S5, the process of fusing the image residual with the intermediate reconstructed image to obtain the cardiac magnetic resonance reconstructed image is specifically as follows: The image domain reconstruction network receives the intermediate reconstructed image as input and predicts and outputs a residual image. The residual image is added element-wise to the intermediate reconstructed image to obtain the complete image; The clip function is used to truncate pixel values ​​in the complete image that are outside the preset display range to the preset range, thereby obtaining the cardiac magnetic resonance reconstruction image.

7. The method according to claim 1, characterized in that, In the method, the process of training the frequency domain reconstruction network and the image domain reconstruction network specifically includes: The reconstructed cardiac magnetic resonance image is used as the generator output, and the generator loss is calculated with the fully sampled target image. The generator loss includes at least the image mean square error loss and the generator adversarial loss. The reconstructed cardiac magnetic resonance image is input into the discriminator to obtain the authenticity discrimination result of local image patches, and the generator adversarial loss is calculated based on the discrimination result; The parameters of the frequency domain reconstruction network and the image domain reconstruction network are updated based on the generator loss, and the parameters of the discriminator are updated at a preset frequency lower than the generator update frequency. Preferably, the first set of loss weights is used in the first stage of training. After training reaches a preset number of rounds, the image mean square error loss weight is increased to the second weight, and the weights of at least one of the structural similarity loss, frequency domain consistency loss and adversarial loss are reduced to improve the peak signal-to-noise ratio of the reconstructed image. During training, exponential moving average parameters are used for validation and / or inference, and at least two checkpoints are selected from multiple checkpoints with the best validation performance for parameter averaging to obtain the output reconstructed model.

8. A cardiac magnetic resonance undersampling reconstruction system, characterized in that, The system includes: The data acquisition and undersampling module is used to acquire the raw k-space data from multi-coil cardiac magnetic resonance imaging. According to the above, the original k-space data is preprocessed, and undersampled k-space data is obtained according to the preset undersampling rules; The frequency domain reconstruction module is used to input the undersampled k-space data into the frequency domain reconstruction network to obtain a preliminary reconstructed k-space. The inverse Fourier transform module is used to perform an inverse Fourier transform on the initially reconstructed k-space to obtain an intermediate reconstructed image; The quantum-classical image domain reconstruction module is used to input the intermediate reconstructed image into an image domain reconstruction network with a parameterized quantum circuit front end. The parameterized quantum circuit is used to perform quantum encoding, quantum entanglement, and quantum measurement on the compressed features obtained from the intermediate reconstructed image. The image domain reconstruction network then predicts the image residual based on the quantum measurement results. An image fusion module is used to fuse the image residual with the intermediate reconstructed image to obtain a cardiac magnetic resonance reconstructed image.

9. An electronic device comprising a processor and a memory, characterized in that, The memory stores a computer program, which, when executed by the processor, causes the processor to perform the method described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method described in any one of claims 1 to 7.

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