KR101826961B1 - Method and system for magnetic resonance imaging using compressive sensing - Google Patents

Abstract

The present invention provides a magnetic resonance imaging technique and system using compression sensing. According to the present invention, sampling is performed along one or more hyperbolic spiral trajectories using a compression sensing technique in k-space with respect to an input image, and 2 Dimensional inverse fast Fourier transform to obtain a reconstructed image. In this way, a reconstructed image of good quality can be obtained with a sampling rate lower than the Nyquist rate.

Description

TECHNICAL FIELD [0001] The present invention relates to a magnetic resonance imaging (MRI)

The present invention relates to a magnetic resonance imaging (MRI) system using compression sensing, and more particularly, to selection of a trajectory and a parameter optimization technique for increasing the efficiency of a magnetic resonance imaging system using compression sensing.

Magnetic resonance imaging (MRI) is a method of applying a strong external magnetic field to a human body, observing the electromagnetic waves emitted from the materials constituting each part of the human body, recognizing the magnetic properties of the materials, and reconstructing the image of the human body. However, due to the physical characteristics of magnetic resonance imaging, signal acquisition in magnetic resonance imaging is performed in the frequency domain rather than in the spatial domain. This frequency domain is called 'k-space'.

On the other hand, the compressive sensing technique is a technique for recovering the original signal while sampling at a rate much lower than the Nyquist rate using the sparsity inherent in the signal to be acquired. Therefore, by applying the compression sensing technique to magnetic resonance imaging, the original image can be reconstructed while taking fewer samples than the Nyquist rate in k-space. As a result, the time taken to take a magnetic resonance image can be shortened.

However, since the compression sensing technique restores the original image from a small number of samples compared to the sampling method that satisfies the Nyquist rate, the method of sampling data affects the quality of the reconstructed image. Generally, in the compression sensing technique, a random sampling method is used to randomly select and acquire a part of samples in k-space in order to restore incoherence between domains to restore an original image from a small sample. However, due to the physical characteristics of magnetic resonance imaging, data sampling in k-space must be performed along a continuous trajectory. Therefore, when compression sensing is applied to a MRI system, a random sampling method can not be used. For this reason, MRI techniques using conventional compression sensing use a k-space sampling trajectory consisting of continuous curves such as Cartesian and radial instead of random sampling. However, there is almost no research on how to optimize the parameters of each sampling trajectory according to various trajectories of k-space sampling trajectories and the medical trajectory of each part of human body . Korean Patent Laid-Open Publication No. 1020100004321 discloses a compression sensing based dynamic magnetic resonance imaging technique based on compression sensing theory.

A problem to be solved by the present invention is to find a k-space sampling trajectory suitable for a medical image and to optimize the parameters of the sampling trajectory, thereby reducing the number of k-space samples required for restoring an image in a compression sensing magnetic resonance imaging system And to reduce the total scan time of the MRI system.

According to an embodiment of the present invention, there is provided a method for acquiring a magnetic resonance image using compression sensing, the method comprising: generating one or more hyperbolic spiral trajectories using a compression sensing technique in k- And performing a two-dimensional inverse fast Fourier transform on the data obtained as a result of the sampling to obtain a reconstructed image.

According to an embodiment of the present invention, in a magnetic resonance imaging system using compression sensing, sampling is performed along one or more hyperbolic spiral trajectories using a compression sensing technique in a k-space with respect to an input image. And a reconstruction image acquiring unit for acquiring a reconstruction image by performing two-dimensional inverse fast Fourier transform on the data obtained as a result of the sampling.

According to an embodiment of the present invention, there is provided a method of optimizing the number of revolutions and radius parameters of the hyperbolic spiral trajectory in order to use the hyperbolic spiral trajectory for sampling a magnetic resonance imaging technique using compression sensing, Dimensional finite Fourier transform of I medical images sampled at a Nyquist rate, changing the number of rotations and radius parameters of the hyperbolic spiral locus to a predetermined interval within a predetermined range, A step of restoring an image by performing compression sensing on the 2D FFT-transformed image using a hyperbolic trajectory having a changed parameter value, calculating a prime function of the reconstructed image, and recording the parameter value And an arithmetic average value of parameter values recorded for the I images, It includes a step of determining a transfer parameter value as a radius.

According to the present invention, by using the hyperbolic spiral trajectory, a good quality image can be obtained when the same number of samples is obtained as compared with the existing Cartesian or radial trajectory. Therefore, since the image of the same quality can be acquired even with a relatively small sample, the scan time of the magnetic resonance imaging system can be reduced, and the amount of sampling data can be reduced, so that data transmission is also advantageous.

1 is a diagram showing an example of a hyperbolic spiral k-space trajectory according to an embodiment of the present invention;
FIG. 2 is a diagram showing a schematic configuration of a hyperbolic spiral k-space trajectory and parameter optimization technique for a compression-sensing MRI system according to an embodiment of the present invention.
FIG. 3 is a graph comparing the restored image and performance of a conventional Cartesian trajectory, a radial trajectory, and a hyperbolic spiral trajectory proposed in the present invention.
FIG. 4 is a graph comparing reconstructed images and performance obtained when samples are acquired using one of the hyperbolic spiral trajectories proposed in the present invention and when samples are acquired using several hyperbolic spiral trajectories
FIG. 5 is a graph comparing the performance of an image obtained using a hyperbolic spiral trajectory optimized for a brain image and an image obtained using an unsmoothed trajectory according to an embodiment of the present invention

Preferred embodiments according to the present invention will be described in detail with reference to the accompanying drawings. It should be noted that only the parts necessary for understanding the operation according to the present invention will be described in the following description, and the description of other parts will be omitted so as not to disturb the gist of the present invention.

The present invention is based on the fact that most medical image signals are concentrated in a low frequency region on a k-space, and thus a sparse hyperbolic spiral is dense in a low frequency region and relatively sparse in a high frequency region. We propose to use the trajectory as a k-space sampling trajectory.

FIG. 1 shows an example of a sparse hyperbolic spiral k-space trajectory in a low-frequency region and a sparse and relatively high-frequency region according to an embodiment of the present invention, where (a) Shows a case where the number of beams is eight.

The hyperbolic spiral trajectory is expressed by the following equation (1) according to the magnitude variable a and the time variable t.

와

는 각각 k-space에서의 x, y의 공간 주파수를 나타낸다. hyperbolic spiral 궤적을 영상의 중심에서부터 시작해서 반지름이

값을 가질 때까지 그리기 위하여 시간 변수 t는 하기의 수학식 2와 같은 값을 가진다.here

Wow

Represent the spatial frequencies of x and y in k-space, respectively. The hyperbolic spiral trajectory starts at the center of the image,

The time variable t has a value as shown in Equation 2 below. &Quot; (2) "

By setting the time variable t as shown in Equation (2), it can be seen that the hyperbolic spiral trajectory expressed by Equation (1) is determined through two parameters a and x. In this case, the parameter x is a value for adjusting the radius of the trajectory, and the maximum radius that the trajectory can have is one-half of the image size imgsize, so the range of the value that the parameter x can have is expressed by Equation 3 below.

The parameter a is a value for adjusting the number of revolutions of the hyperbolic spiral trajectory, and the range of the value that the parameter a can have is expressed by Equation 4 below.

와 자기 공명 영상 시스템에서 가하는 외부 자기장의 경사도(gradient)

가 하기의 수학식 5와 같은 관계를 가진다.On the other hand, in a magnetic resonance imaging system, spatial frequency in k-space

And the gradient of the external magnetic field applied in the MRI system,

(5) " (5) "

는 자기회전율(gyromagnetic ratio)로서 물질의 종류에 따라 정해지는 고유 상수이다. 따라서 자기 공명 영상 시스템에서 가하는 외부 자기장의 gradient

를 하기의 수학식 6과 같이 조절하여 k-space상에서 hyperbolic 궤적을 구현할 수 있다.here

Is a gyromagnetic ratio and is a unique constant determined by the type of material. Therefore, the gradient of the external magnetic field applied in the MRI system

Can be adjusted as shown in Equation (6) below to realize a hyperbolic trajectory on k-space.

In the above, a method of drawing a single hyperbolic spiral trajectory on k-space as shown in FIG. 1 (a) was examined. However, as shown in FIG. 1 (b), it is also possible to rotate one hyperbolic spiral trajectory at various angles and draw it several times for the convenience of implementation of the gradient magnetic field system. FIG. 1 (b) shows an example of a k-space sampling trajectory consisting of eight rotated hyperbolic spiral trajectories.

Next, the present invention proposes a price function for comparing the quality of the image obtained from the hyperbolic spiral trajectories having different parameters in the process of optimizing the parameters of the hyperbolic spiral trajectory to be used for k-space sampling.

FIG. 2 shows a schematic configuration of a parameter optimization technique of a hyperbolic spiral k-space trajectory in compression sensing of a magnetic resonance image.

First, I medical images sampled at the Nyquist rate are prepared as shown in Equation (7), and the first sampling medical images are prepared in the spatial frequency domain through two-dimensional fast Fourier transform (2D FFT) That is, expressed in k-space.

이다. here

to be.

In step 203, parameters a and x of the hyperbolic spiral k-space trajectory are changed within a predetermined range. The ranges of the parameters a and x are the same as those of Equations (3) and (4) described above, but parameters are selected within the range of Equation (9) below for practical implementation of the algorithm.

In step 204, compression sensing is performed using the hyperbolic spiral k-space trajectory defined by the parameters a and x, the image is reconstructed, and the reconstructed image is compared with the original image. At this time, a price function is used to compare the reconstructed image with the original image. In the present invention, a price function (c) as shown in Equation (10) is proposed. The larger the price function value, the better the efficiency.

Where PSNR is the peak signal to noise ratio (PSNR) of the reconstructed image, and T_PSNR is the minimum target PSNR value that the reconstructed image should guarantee. Also, SampleRatio is the ratio of the number of samples obtained when sampling along the trajectory to the total k-space sample.

The PSNR is defined by Equation (11) below.

은 각각 영상의 세로 가로의 픽셀의 수를 나타내고, I_xy는 압축 센싱을 적용하지 않은 영상의 x, y번째 픽셀의 값을 나타내고, R_xy는 압축 센싱을 수행하여 획득한 영상의 x, y번째의 픽셀의 값을 나타내며, maxval은 영상의 픽셀이 가질 수 있는 최대값을 나타낸다. In Equation (11)

Each represent the number of pixels vertically and horizontally in the image, I _xy represents the x, the value of the y th pixel in the image without applying a compressive sensing, R _xy is the second of the obtained by performing a compression-sensing image x, y And maxval represents a maximum value that a pixel of the image can have.

In step 205, if the currently obtained price function C value is larger than the recorded price function C value, the current parameters a and x are updated to the parameters a _i and x _i for the i-th medical image.

로 결정한다.In step 206, i is compared with the total number of samples I, and steps 202 to 206 are repeated for I medical images while i is increased by 1 in step 208 until i = I. In step 207, arithmetic mean values of the parameters a _i and x _i obtained for each of the I images are calculated according to equation (12), and the final parameters of the hyperbolic spiral k-space trajectory

.

FIG. 3 shows a case where a 5% sample is acquired using the Cartesian trajectory (a) and the radial trajectory (b) and the hyperbolic spiral trajectory (c) proposed in the present invention to perform compression sensing FIG. 2 is a block diagram illustrating a reconstructed image and a performance of the reconstructed image.

Referring to FIG. 3, it can be seen that the hyperbolic spiral trajectory (c) proposed in the present invention provides much better quality images from a similar number of samples compared to the Cartesian trajectory (a) and the radial trajectory (b).

FIG. 4 is a graph showing the relationship between (a) when a sample is acquired using one of the hyperbolic spiral trajectories proposed in the present invention and (b) when a sample is acquired using several hyperbolic spiral trajectories for convenience of implementation of a gradient magnetic field system And reconstructed images and performance. Referring to FIG. 4, it can be seen that similar performance is obtained for a similar number of samples without being greatly affected by the number of trajectories.

5 shows an image (a) obtained by using a hyperbolic spiral trajectory having an optimized parameter value according to an embodiment of the present invention, and the image (b) obtained by using a trajectory in which a parameter value is not optimized FIG. Referring to FIG. 5, it can be seen that the features such as the wrinkles of the brain are more clearly revealed when the hyperbolic spiral trajectory having optimized parameter values is used.

By using the hyperbolic spiral trajectory in the MRI system and optimizing the parameters, it is possible to obtain images of the same quality as the previous one with only a small sampling, so that the time required for the inspection can be shortened.

While the present invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not limited to the disclosed embodiments, but is capable of various modifications within the scope of the invention. Therefore, the scope of the present invention should not be limited by the illustrated embodiments, but should be determined by the scope of the appended claims and equivalents thereof.

Claims (8)

A method for obtaining a magnetic resonance image using compression sensing,
Performing sampling along one or more hyperbolic spiral trajectories using a compression sensing technique in k-space for an input image;
And performing 2D inverse fast Fourier transform on the data obtained as a result of the sampling to obtain a reconstructed image. The method according to claim 1,
Wherein the hyperbolic spiral trajectory has an optimized number of revolutions and a radius parameter value,
Wherein the step of optimizing the parameters of the hyperbolic spiral trajectory comprises:
Performing two-dimensional fast Fourier transform on I medical images sampled at a Nyquist rate,
Changing the number of revolutions of the hyperbolic spiral locus and the radius parameter value at a predetermined interval within a predetermined range;
Performing fast Fourier transform on the two-dimensional fast Fourier transformed image using a hyperbolic path having the changed parameter values to reconstruct an image;
Calculating a price function of the reconstructed image and recording the parameter value;
And determining an arithmetic mean value of the parameter values recorded for the I images as the optimized number of rotations and the radius parameter value. 3. The method of claim 2,
Wherein the price function is determined by the following equation.

Here, PSNR represents the peak signal to noise ratio (PSNR) of the reconstructed image, T_PSNR is the target PSNR value of the reconstructed image, SampleRatio represents the total number of samples obtained by sampling along the trajectory, Beam. In a magnetic resonance imaging system applying compression sensing,
A sampling unit for performing sampling along one or more hyperbolic spiral trajectories using a compression sensing technique in a k-space with respect to an input image;
And performing a two-dimensional inverse fast Fourier transform on the data obtained as a result of the sampling to obtain a reconstructed image. 5. The method of claim 4,
Wherein the hyperbolic spiral trajectory has an optimized number of revolutions and a radius parameter value,
The optimized number of revolutions and radius parameters of the hyperbolic spiral trajectory,
Performing two-dimensional fast Fourier transform on I medical images sampled at a Nyquist rate,
Changing the number of revolutions of the hyperbolic spiral locus and the radius parameter value at a predetermined interval within a predetermined range;
Performing fast Fourier transform on the two-dimensional fast Fourier transformed image using a hyperbolic path having the changed parameter values to reconstruct an image;
Calculating a price function of the reconstructed image and recording the parameter value;
And determining an arithmetic mean value of the parameter values recorded for the I images as the optimized number of rotations and the radius parameter value. 6. The method of claim 5,
Wherein the price function is determined by the following equation.

Here, PSNR represents the peak signal to noise ratio (PSNR) of the reconstructed image, T_PSNR is the target PSNR value of the reconstructed image, SampleRatio represents the total number of samples obtained by sampling along the trajectory, Beam. A method of optimizing the number of revolutions and radius parameters of a hyperbolic spiral trajectory in order to utilize the hyperbolic spiral trajectory in sampling of a magnetic resonance imaging technique using compression sensing,
Performing two-dimensional fast Fourier transform on I medical images sampled at a Nyquist rate,
Changing the number of revolutions of the hyperbolic spiral locus and the radius parameter value at a predetermined interval within a predetermined range;
Performing fast Fourier transform on the two-dimensional fast Fourier transformed image using a hyperbolic path having the changed parameter values to reconstruct an image;
Calculating a price function of the reconstructed image and recording the parameter value;
And determining an arithmetic average value of the parameter values recorded for the I images as the optimized number of rotations and the radius parameter value. 8. The method of claim 7,
Wherein the price function is determined by the following equation.

Here, PSNR represents the peak signal to noise ratio (PSNR) of the reconstructed image, T_PSNR is the target PSNR value of the reconstructed image, SampleRatio represents the total number of samples obtained by sampling along the trajectory, Beam.

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