CN113808234A - Rapid magnetic particle imaging reconstruction method based on undersampling - Google Patents
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Abstract
The invention discloses a rapid magnetic particle imaging reconstruction method based on undersampling, which comprises the following steps: acquiring MPI under-sampling voltage signals, acquiring fully-sampled MPI images, performing nonlinear normalization on the signals and the images, training a neural network, and predicting the concentration distribution of magnetic particles. The method directly maps the voltage signals to the image domain and can reconstruct within a few milliseconds, and the wide evaluation of a large number of data sets shows that the method can reconstruct the undersampled voltage signals into the fully sampled high-resolution MPI images, and has better anti-noise capability and anti-artifact capability; the method has good generalization capability, higher quality of reconstructed images and higher reconstruction speed, improves the imaging potential of a magnetic particle imaging system, and solves the problem that MPI equipment introduces a large amount of noise due to overlong acquisition time.
Description
Technical Field
The invention belongs to the technical field of Magnetic Particle Imaging (MPI) Image reconstruction, and particularly relates to a rapid Magnetic Particle imaging reconstruction method based on undersampling.
Background
MPI is a novel, frontier tomography mode, performs concentration distribution imaging on superparamagnetic nanoparticles with biocompatibility, and has the characteristics of high sensitivity, high resolution, no radiation and the like. Generally, the ideal method of angiography is to see only the tracer but not the tissue, which is transparent to the low frequency magnetic field in MPI. Thus, MPI can detect nanoparticle contrast agents without any background and zero depth attenuation. MPI benefits from high temporal resolution and potentially high spatial resolution, which makes it suitable for a variety of in vivo applications such as blood flow imaging, long-term monitoring using circulating tracers, flow estimation, tracking/guiding medical devices, cancer detection, cancer treatment with hyperthermia. In addition, the potential medical applications for developing MPI are increasing.
In MPI, two important imaging features are resolution and sensitivity. During MPI imaging, a speed index is an important index, if the acquisition time is too slow, an imaging system can generate more noise, the thermal effect of the system can also generate thermal noise, the sensitivity of a reconstructed MPI image is reduced, and in addition, if an animal experiment is carried out, the breathing and slight movement of an animal can cause the artifact and the blur of the image, so the resolution of the reconstructed MPI image is reduced.
Disclosure of Invention
In order to solve the defects of the prior art, the invention provides an under-sampling-based rapid magnetic particle imaging reconstruction method, which takes image reconstruction as a data-driven supervised learning task, so that mapping is generated between a voltage signal and an image domain from a training data corpus, and a full-sampling high-resolution MPI image can be generated by using the under-sampling voltage signal. The specific technical scheme of the invention is as follows:
a rapid magnetic particle imaging reconstruction method based on undersampling comprises the following steps:
s1: acquiring MPI (multi-pulse amplification) undersampled voltage signals based on a Langmuir paramagnetic model, and converting time domain signals into frequency domain signals through Fourier transform;
s2: generating a full sampling MPI image according to an MPI system matrix reconstruction algorithm;
s3: normalizing the frequency domain signal obtained in the step S1 and the image obtained in the step S2 to obtain
Wherein the content of the first and second substances,
to the normalized MPI undersampled voltage signal,
the normalized fully sampled MPI image is obtained;
s4: generating a deep neural network;
to be provided with
As input to the network model to
Selecting a loss function as a target value of the network model, and training the network model;
s5: reconstructing an image;
and (4) reconstructing an image of any MPI undersampled voltage signal, performing Fourier transform on the voltage signal, and inputting the voltage signal into the deep neural network pre-trained in the step S4 to obtain a reconstruction result of unknown magnetic nanoparticle concentration.
Further, the specific process of step S1 is as follows:
s1-1: performing voltage simulation based on a paramagnetic Langewan model;
s1-2: gaussian noise is added into the simulated MPI undersampled voltage signal, so that a more real voltage signal is simulated;
s1-3: separating and vectorizing the real and imaginary parts of the voltage signal;
s1-4: and Fourier transform, converting the time domain signal into a frequency domain signal.
Further, the specific process of step S3 is as follows:
wherein SIG is MPI undersampled voltage signal,
min (SIG) represents the minimum gray value of the voltage signal, and max (SIG) represents the maximum gray value of the voltage signal;
wherein, IMG is a fully sampled MPI image,
in the normalized fully sampled MPI image, min (img) represents the minimum gray value of the fully sampled MPI image, and max (img) represents the maximum gray value of the fully sampled MPI image.
Further, the specific process of step S4 is as follows:
s4-1: obtaining an initial deep neural network model and a training data set, wherein the training data set is obtained in step S3
And corresponding
To be provided with
As an input to a network model;
s4-2: performing domain transformation through two full-connection layers to realize the mapping from the MPI under-sampling voltage signal to a full-sampling MPI image;
s4-3: image enhancement is carried out through a post-processing layer, and more accurate MPI image reconstruction is obtained;
s4-4: based on step S3
And step S2, determining the loss value loss of the deep neural network;
s4-5: and updating the parameters of the neural network based on the loss value loss of the neural network until the neural network generates an image with an error smaller than a set threshold value, thereby finishing training.
Further, the calculation of the loss value loss of the neural network is Mean Square Error (MSE), Structure Similarity (SSIM) or peak signal-to-noise ratio (PSN).
Further, the post-processing layer in step S4-3 includes two sub-convolution networks, one sub-convolution network includes a convolution layer, a pooling layer and a deconvolution layer, and the other sub-convolution network includes a convolution layer and a deconvolution layer.
The invention has the beneficial effects that:
1. compared with the traditional artificial reconstruction method, the method can effectively reduce the time for acquiring the MPI signals, directly map the voltage signals to the MPI image domain, and can reconstruct within a few milliseconds.
2. The extensive evaluation of a large number of data sets shows that the method can reconstruct the under-sampled voltage signals into the fully-sampled high-resolution MPI images, and has better anti-noise capability, robustness and anti-artifact capability. The method has good generalization capability, and the feedforward transmission is executed on the network in the test stage, so the calculation cost is very low, therefore, the method has higher reconstruction speed and higher precision, improves the imaging potential of the magnetic particle imaging system, and overcomes the problem that a large amount of noise is introduced due to overlong acquisition time of MPI equipment.
3. The method of the invention takes image reconstruction as a data-driven supervised learning task, so that mapping is generated between the induction voltage generated in the receiving coil and an image domain from a training data corpus, and a full-sampling high-resolution MPI image can be generated by using an undersampled voltage signal.
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In order to illustrate embodiments of the present invention or technical solutions in the prior art more clearly, the drawings which are needed in the embodiments will be briefly described below, so that the features and advantages of the present invention can be understood more clearly by referring to the drawings, which are schematic and should not be construed as limiting the present invention in any way, and for a person skilled in the art, other drawings can be obtained on the basis of these drawings without any inventive effort. Wherein:
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 is a flow chart of the present invention for training a deep neural network;
fig. 3 is a schematic structural diagram of the deep neural network of the present invention.
Detailed Description
In order that the above objects, features and advantages of the present invention can be more clearly understood, a more particular description of the invention will be rendered by reference to the appended drawings. It should be noted that the embodiments of the present invention and features of the embodiments may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, however, the present invention may be practiced in other ways than those specifically described herein, and therefore the scope of the present invention is not limited by the specific embodiments disclosed below.
As shown in fig. 1-2, a method for reconstructing fast magnetic particle imaging based on undersampling includes the following steps:
s1: acquiring MPI (multi-pulse amplification) undersampled voltage signals based on a Langmuir paramagnetic model, and converting time domain signals into frequency domain signals through Fourier transform;
s1-1: performing voltage simulation based on a paramagnetic Langewan model;
s1-2: gaussian noise is added into the simulated MPI undersampled voltage signal, so that a more real voltage signal is simulated;
s1-3: separating and vectorizing the real and imaginary parts of the voltage signal;
s1-4: fourier transform, converting the time domain signal into a frequency domain signal;
s2: generating a full sampling MPI image according to an MPI system matrix reconstruction algorithm;
s3: normalizing the frequency domain signal obtained in the step S1 and the image obtained in the step S2 to obtain
Wherein the content of the first and second substances,
to the normalized MPI undersampled voltage signal,
the normalized fully sampled MPI image is obtained;
the specific process is as follows:
wherein SIG is MPI undersampled voltage signal,
min (SIG) represents the minimum gray value of the voltage signal, and max (SIG) represents the maximum gray value of the voltage signal;
wherein, IMG is a fully sampled MPI image,
in the normalized fully sampled MPI image, min (IMG) represents the minimum gray value of the fully sampled MPI image, and max (IMG) represents the maximum gray value of the fully sampled MPI image;
s4: generating a deep neural network;
to be provided with
As input to the network model to
Selecting a loss function as a target value of the network model, and training the network model; in particular, as shown in figure 3,
s4-1: obtaining an initial deep neural network model and a training data set, wherein the training data set is obtained in step S3
And corresponding
To be provided with
As an input to a network model;
s4-2: performing domain transformation through two full-connection layers to realize the mapping from the MPI under-sampling voltage signal to a full-sampling MPI image;
s4-3: image enhancement is carried out through a post-processing layer, and more accurate MPI image reconstruction is obtained;
s4-4: based on step S3
And step S2, determining the loss value loss of the deep neural network;
s4-5: and updating the parameters of the neural network based on the loss value loss of the neural network until the neural network generates an image with an error smaller than a set threshold value, thereby finishing training.
S5: reconstructing an image;
and (4) reconstructing an image of any MPI undersampled voltage signal, performing Fourier transform on the voltage signal, and inputting the voltage signal into the deep neural network pre-trained in the step S4 to obtain a reconstruction result of unknown magnetic nanoparticle concentration.
In some embodiments, the neural network loss value loss is calculated as mean square error MSE, structural similarity SSIM or peak signal-to-noise ratio PSN.
In some embodiments, the post-processing layer in step S4-3 includes two sub-convolutional networks, one sub-convolutional network includes a convolutional layer, a pooling layer, and a deconvolution layer, and the other sub-convolutional network is composed of a convolutional layer and a deconvolution layer.
For the convenience of understanding the above technical aspects of the present invention, the following detailed description will be given of the above technical aspects of the present invention by way of specific examples.
In order to verify the effectiveness of MPI image reconstruction based on the multi-scale neural network, firstly, voltage signals are simulated in a simulation system, then, the deep neural network is used for image reconstruction, and a simulation experiment is carried out, wherein the specific process is as follows:
a simulation system: firstly, system parameters are defined, wherein the system parameters comprise a Boltzmann constant 1.3806488e-23, a vacuum magnetic conductivity 4 x pi x 1e-7, a particle diameter of 20nm, a two-dimensional field size of 20x20mm, a simulation of a voltage signal is based on a paramagnetic Langewan model, a field intensity gradient is set to be 3T/m, and a Cartesian track is simulated.
When the undersampled voltage signal is simulated, in order to reduce the acquisition time, the sampling frequency is reduced, so that the sampling frequency does not meet the Nyquist sampling theorem, and under the condition, the undersampled voltage signal is obtained.
In addition, system noise exists in the voltage signal which is actually acquired, in order to generate a simulation data set which has the same rule and property with the actual MPI image and illustrate the robustness of the network, 30dB of Gaussian white noise is added in the process of simulating the voltage signal.
When a target image of a corresponding image domain is obtained, the field intensity gradient is set to be 6T/m, the sampling frequency is improved, the sampling frequency meets the Nyquist sampling theorem, the full-sampling voltage signal is reconstructed into a clear image by using a system matrix reconstruction algorithm, and other parameters are kept unchanged.
Network architecture: the network consists of a full connection layer and a post-processing layer, wherein the full connection layer carries out domain transformation and converts from a signal domain to an image domain; the post-processing layer is mainly used for recovering the image quality, and comprises two sub-networks which both adopt convolution deconvolution structures.
The sub-network is followed by a convolutional layer to further improve the performance of the network in restoring the image quality.
In the aspect of model design, a network convolution layer, a deconvolution layer, a residual error learning layer, a linear unit and a pooling layer are integrated into a network, one sub-network does not contain the pooling layer and does not lose useful information of an MPI image, the other sub-network contains the pooling layer and extracts important information while deleting useless information, and the artifacts can be eliminated by adding the pooling layer because the output image of the full connection layer has a large number of artifacts. And after the sub-networks are processed by the convolutional layers, the two channels are fused into a single-channel network to improve the performance and obtain a clear MPI reconstructed image.
In the present invention, the terms "first", "second", "third" and "fourth" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. The term "plurality" means two or more unless expressly limited otherwise.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A rapid magnetic particle imaging reconstruction method based on undersampling is characterized by comprising the following steps:
s1: acquiring MPI (multi-pulse amplification) undersampled voltage signals based on a Langmuir paramagnetic model, and converting time domain signals into frequency domain signals through Fourier transform;
s2: generating a full sampling MPI image according to an MPI system matrix reconstruction algorithm;
s3: normalizing the frequency domain signal obtained in the step S1 and the image obtained in the step S2 to obtain
Wherein the content of the first and second substances,
to the normalized MPI undersampled voltage signal,
the normalized fully sampled MPI image is obtained;
s4: generating a deep neural network;
to be provided with
As input to the network model to
Selecting a loss function as a target value of the network model, and training the network model;
s5: reconstructing an image;
and (4) reconstructing an image of any MPI undersampled voltage signal, performing Fourier transform on the voltage signal, and inputting the voltage signal into the deep neural network pre-trained in the step S4 to obtain a reconstruction result of unknown magnetic nanoparticle concentration.
2. The undersampling-based fast magnetic particle imaging reconstruction method of claim 1, wherein the specific process of step S1 is as follows:
s1-1: performing voltage simulation based on a paramagnetic Langewan model;
s1-2: gaussian noise is added into the simulated MPI undersampled voltage signal, so that a more real voltage signal is simulated;
s1-3: separating and vectorizing the real and imaginary parts of the voltage signal;
s1-4: and Fourier transform, converting the time domain signal into a frequency domain signal.
3. The undersampling-based fast magnetic particle imaging reconstruction method according to claim 1 or 2, characterized in that the specific process of the step S3 is as follows:
wherein SIG is MPI undersampled voltage signal,
min (SIG) represents the minimum gray value of the voltage signal, and max (SIG) represents the maximum gray value of the voltage signal;
wherein, IMG is a fully sampled MPI image,
in the normalized fully sampled MPI image, min (img) represents the minimum gray value of the fully sampled MPI image, and max (img) represents the maximum gray value of the fully sampled MPI image.
4. The undersampling-based fast magnetic particle imaging reconstruction method according to claim 1 or 2, characterized in that the specific process of the step S4 is as follows:
s4-1: obtaining an initial deep neural network model and a training data set, wherein the training data set is obtained in step S3
And corresponding
To be provided with
As an input to a network model;
s4-2: performing domain transformation through two full-connection layers to realize the mapping from the MPI under-sampling voltage signal to a full-sampling MPI image;
s4-3: image enhancement is carried out through a post-processing layer, and more accurate MPI image reconstruction is obtained;
s4-4: based on step S3
And step S2, determining the loss value loss of the deep neural network;
s4-5: and updating the parameters of the neural network based on the loss value loss of the neural network until the neural network generates an image with an error smaller than a set threshold value, thereby finishing training.
5. The undersampling-based fast magnetic particle imaging reconstruction method of claim 4, characterized in that the calculation of the neural network loss value loss is Mean Square Error (MSE), Structural Similarity (SSIM) or peak signal-to-noise ratio (PSN).
6. The undersampled-based fast magnetic particle imaging reconstruction method according to claim 4 or 5, characterized in that the post-processing layer in step S4-3 includes two sub-convolution networks, one sub-convolution network includes a convolution layer, a pooling layer and a deconvolution layer, and the other sub-convolution network is composed of a convolution layer and a deconvolution layer.
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