CN103399285A - Magnetic resonance non-Descartes sampling quick rebuilding method - Google Patents

Magnetic resonance non-Descartes sampling quick rebuilding method Download PDF

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CN103399285A
CN103399285A CN2013103114781A CN201310311478A CN103399285A CN 103399285 A CN103399285 A CN 103399285A CN 2013103114781 A CN2013103114781 A CN 2013103114781A CN 201310311478 A CN201310311478 A CN 201310311478A CN 103399285 A CN103399285 A CN 103399285A
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郭红宇
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Shenyang University of Technology
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Abstract

The invention discloses a magnetic resonance non-Descartes sampling quick rebuilding method. The magnetic resonance non-Descartes sampling quick rebuilding method is provided through utilizing the characteristics of the symmetry of sampling tracks and a back compensation grid algorithm, and belongs to the technical field of magnetic resonance imaging. According to the magnetic resonance non-Descartes sampling quick rebuilding method, a back compensation gridding rebuilding algorithm is effective on samples without severe sampling track variation, and additionally, a density compensating function in the back compensating algorithm is only related to the sampling point distribution (i.e. sampling tracks) and is not related to sampling values. The characteristics are combined together, so that the computing speed of the provided new non-Descartes sampling quick rebuilding method is greatly increased than that of a conventional grid rebuilding algorithm, and the rebuilding image quality is not obviously changed.

Description

A kind of fast reconstructing method of magnetic resonance non-Cartesian sampling
Technical field
The invention belongs to the mr imaging technique field, particularly relate to a kind of fast reconstructing method of magnetic resonance non-Cartesian sampling.
Background technology
Magnetic resonance imaging is due to radiationless, and resolution is high, and the advantage such as multi-faceted, multiparameter, be used widely clinically.Compare traditional Descartes sampling, the non-Cartesian sampling has many advantages, and is as fast as image taking speed, to motion with flow insensitive etc.Especially in heart dynamic imaging, cerebral function imaging and magnetic resonance spectrum imaging, the advantage of non-Cartesian sampling is more obvious.In addition, many motion correction technology based on non-Cartesian sampling, take full advantage of self gather in integrated motion correction navigation information, very effective to the motion artifacts of eliminating in magnetic resonance imaging.
Yet, the non-Cartesian sampling but delays to obtain widespread adoption and popularization in clinical, one of them chief reason is because the non-Cartesian sampled point not drops on cartesian grid points, therefore the reconstruction algorithm of traditional fast fourier transform can not be applied directly in the reconstruction of non-Cartesian sampling, but must use some more senior reconstruction algorithm.But the general computation process complexity of these algorithms, carry out efficiency low, causes the reconstruction speed of non-Cartesian sampling very slow.Wherein Gridding Reconstruction Method is the most frequently used method in non-Cartesian sampling reconstruction method, and in mesh reconstruction, must use the density compensation function to carry out density compensation to the distribution of sampled point.The sampling density compensation process has a great impact for reconstructed image quality.But the calculating of Sampling density compensation function is often very consuming time, and very the time, this situation is more obvious when the sampled point number, has had a strong impact on non-Cartesian and has rebuild the real-time of calculating.The present invention is directed to the symmetric sampling track, propose a kind of method of the penalty function of bulk density fast.
Summary of the invention
Goal of the invention:
The invention provides the fast reconstructing method of a kind of magnetic resonance non-Cartesian sampling, it is very consuming time that its fundamental purpose is to solve the calculating of density compensation function in the sampling of magnetic resonance non-Cartesian, affects the problem that the process of reconstruction real-time is difficult to realize.
Technical scheme:
The present invention is achieved through the following technical solutions:
A kind of fast reconstructing method of magnetic resonance non-Cartesian sampling, the method follows these steps to carry out:
The quick calculating of a, density compensation function:
With the procedural representation of the post-compensation mesh reconstruction of Jackson density compensation function, be formula (1):
M swcs ( k x , k y ) = [ M s ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) [ S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) - - - ( 1 )
By formula (1), obtained, the density compensation function in the post-compensation method is formula (2),
W ( k x , k y ) = 1 [ S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) - - - ( 2 )
From the molecular moiety of formula (2), find out, in the post-compensation mesh reconstruction, density compensation is actually and sampled value is all equaled to 1 sampled data carries out gridding and rebuild and calculate; In mesh reconstruction, each sampled point is calculated to it for the contribution that is in the net point in convolution window, that is to say that the density compensation function of this moment is only that sample track is relevant with the distribution of collection point;
B, according to the quick calculating sampling density function of symmetry:
In the non-Cartesian sampling, the distribution of a lot of sample track is symmetrical; Net point (k in first quartile x, k y) density compensation function W (k x, k y) with other quadrants in identical with the sampling density function of the net point of its symmetry, namely suc as formula (3):
W(k x,k y)＝W(-k x,k y)＝W(-k x,-k y)＝W(k x,-k y) （3），
When the bulk density penalty function, only need to calculate the density compensation function of the sampled point that is positioned at the rectangular coordinate system first quartile, consider the impact of convolution window width, the sampled point that needs the bulk density penalty function in actual implementation procedure is that the point of first quartile adds the convolution window width half;
C, carry out gridding calculating:
Utilize the density compensation function that completes as calculated, sampled data carried out to the gridding reconstruction according to formula (4),
M SWCS ( k x , k y ) = [ M S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) W ( k x , k y ) - - - ( 4 ) .
Advantage and effect:
In order to improve the calculating of the density compensation function in magnetic resonance non-Cartesian sampled data process of reconstruction, the invention provides the fast reconstructing method of a kind of magnetic resonance non-Cartesian sampling, the calculating that the method is utilized the density compensation function is only relevant to sampling point position and do not rely on the occurrence of sampled point.Therefore the distribution for those sampled points has very large symmetric non-Cartesian sample track, and method provided by the invention can improve the sampled point quantity that minimizing need to be calculated greatly.If the sampling number of non-cartesian trajectories is N, for classic method, need to calculate the distance of any two sampled points in all sampled points, need altogether N*N/2 calculating.And method provided by the invention only needs the distance of the net point in convolution window around calculating section sampled point and its get final product, and therefore needing altogether calculation times is (N/4+L) * L, and L is the convolution window width, is generally about 20-50.The calculation times of Traditional calculating methods is N*N/2 calculating.
The accompanying drawing explanation:
Fig. 1 is gridding reconstruction algorithm schematic diagram;
Fig. 2 is the quick calculation method schematic diagram of Radial sample track density compensation function in the inventive method;
Fig. 3 (a) uses conventional mesh method for reconstructing reconstructed image for the Radial sampled data, and Fig. 3 (b) is row intensity profile curve and ideal curve comparison diagram in the middle of image;
Fig. 4 (a) uses the inventive method reconstructed image for the Radial sampled data, and Fig. 4 (b) is row intensity profile curve and ideal curve comparison diagram in the middle of image;
Fig. 5 is the human brain data that the PROPELLER track gathers, the comparison diagram as a result that utilizes classic method and the inventive method to rebuild; Fig. 5 (a) is the image of rebuilding with classic method, the image of Fig. 5 (b) for adopting the inventive method to rebuild, and Fig. 5 (c) is the difference image of Fig. 5 (a) and Fig. 5 (b).
Table 1 classic method and the inventive method are to Radial and the error of calculation of PROPELLER sampled data image reconstruction and the comparative result of computing time.
Embodiment:
Below in conjunction with accompanying drawing, the present invention is added and is described further:
Traditional Descartes's sampling is compared in the sampling of the non-Cartesian of magnetic resonance a lot of advantages, under high-field magnetic resonance the non-Cartesian Sampling techniques more and more be applied in clinical in.the present invention is from the principle of density compensation process, a kind of quick calculation method based on symmetric sampling track density compensation function is proposed, for the slower non-Cartesian sampling of sample track conversion, its mesh reconstruction can use the method for rear density compensation, and in this method, the calculating of penalty function is actually the mesh reconstruction method that all sampled values equal 1, therefore for the non-Cartesian sample track of symmetry, during calculating sampling density, need only and calculate wherein very little a part of sampled point, and other sampled point is without direct calculating, as long as it is just passable that utilization has calculated according to symmetry density compensation function carries out assignment, greatly reduce the computing time of density compensation function.
The fast reconstructing method of this magnetic resonance non-Cartesian of the present invention sampling, speed is rebuild in the density compensation function and the gridding that are mainly used in improving symmetrical non-Cartesian sample track.
A kind of fast reconstructing method of magnetic resonance non-Cartesian sampling, it is characterized in that: the method follows these steps to carry out:
The quick calculating of a, density compensation function
Adopt the density compensation function of post-compensation method calculating sampling point, with the process of the post-compensation mesh reconstruction of Jackson density compensation function, can be expressed as formula (1):
M swcs ( k x , k y ) = [ M s ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) [ S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) - - - ( 1 )
By formula (1), obtained, the density compensation function in the post-compensation method is formula (2),
W ( k x , k y ) = 1 [ S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) - - - ( 2 )
From the molecular moiety of formula (2), find out, in the post-compensation mesh reconstruction, density compensation is actually and sampled value is all equaled to 1 sampled data carries out gridding and rebuild and calculate; In mesh reconstruction, each sampled point is calculated to it for the contribution that is in the net point in convolution window, that is to say that the density compensation function of this moment is only that sample track is relevant with the distribution of collection point.
B, according to the quick calculating sampling density function of symmetry, the density compensation function of calculating section sampled point, to the density compensation function indirect assignment of other left points:
In the non-Cartesian sampling, the distribution of actual a lot of sample track (as RADIL, PROPELLER etc.) of using is symmetrical; Net point (k in first quartile x, k y) density compensation function W (k x, k y) with other quadrants in identical with the sampling density function of the net point of its symmetry, namely suc as formula (3):
W(k x,k y)＝W(-k x,k y)＝W(-k x,-k y)＝W(k x,-k y) （3），
The distribution of sampled point has good coordinate symmetry, and sees from density compensation function calculating formula (2), and its calculating is only that sample track is relevant with sampling point position, and it doesn't matter with the value of sampled point; Therefore, when the bulk density penalty function, symmetrical according to sampled point, the density compensation function that only needs to calculate the sampled point that is positioned at the rectangular coordinate system first quartile gets final product, consider the impact of convolution window width, the sampled point that needs the bulk density penalty function in actual implementation procedure is that the point of first quartile adds the convolution window width half.
C, carry out gridding calculating:
Utilize the density compensation function that completes as calculated, sampled data carried out to the gridding reconstruction according to formula (4),
M SWCS ( k x , k y ) = [ M S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) W ( k x , k y ) - - - ( 4 ) .
The present invention will be further described below by embodiment:
Embodiment 1:
For the validity of verification portion post-compensation algorithm, we use respectively the Radial sampled data to verify.The emulated data that data use Shepp-Logan Digital Simulation water mould to generate, the Radial sample track is comprised of 576 Spoke, and each Spoke comprises 128 sampled points, and the reconstructed image size is 256 * 256.The technical essential that this invention relates generally to has:
1, the calculating of partial density penalty function:
Utilize formula (1), the density compensation function of grey and light gray areas sampled point in calculating chart 1.Wherein gray area is the first quartile of rectangular axes, and wherein the width of light gray areas is the width of the convolution window while calculating convolution in formula (1).
2, the density compensation function that utilizes symmetry will remain sampled point carries out assignment; White portion in Fig. 1.
3, utilize the density compensation function of trying to achieve to carry out gridding calculating.
Fig. 3 be utilize image that part post-compensation method that we propose and precompensation method rebuild the Radial sampled data respectively and correspondence image in the middle of the comparative result of row intensity profile curve.From the emulated data result, this paper method is compared with the precompensation method, and reconstructed image does not have significant difference, and the mean square deviation error of two kinds of method reconstructed images and ideal image is very approaching.Fig. 4 is the human brain data that gather for the PROPELLER track, the result of utilizing classic method and the method that the invention provides to rebuild compares, and from the difference image of reconstructed image, finds out, normalization inequality error is 0.0161, the difference image maximal value is less than 1 under 255 grades of gray scales, and the image difference is very little.
Table 1 mean square deviation error and computing time are relatively
Figure BDA00003552043300061
Table 1 is that RADIAL and PROPELLER sampled data are used classic method and the error of calculation of the inventive method reconstructed image and the comparative result of computing time, the partial density compensation method computing velocity that proposes of the present invention is compared previous method and has been improved more than 470 times as can be seen from the table, shortened in 0.2 second computing time from tens seconds, what make the density compensation process becomes possibility in real time, particularly for the track that resembles PROPELLER and have so a large amount of sampled points, the method has the practical application meaning more.

Claims (1)

1. the fast reconstructing method of magnetic resonance non-Cartesian sampling, it is characterized in that: the method follows these steps to carry out:
The quick calculating of a, density compensation function:
With the procedural representation of the post-compensation mesh reconstruction of Jackson density compensation function, be formula (1):
M swcs ( k x , k y ) = [ M s ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) [ S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) - - - ( 1 )
By formula (1), obtained, the density compensation function in the post-compensation method is formula (2),
W ( k x , k y ) = 1 [ S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) - - - ( 2 )
From the molecular moiety of formula (2), find out, in the post-compensation mesh reconstruction, density compensation is actually and sampled value is all equaled to 1 sampled data carries out gridding and rebuild and calculate; In mesh reconstruction, each sampled point is calculated to it for the contribution that is in the net point in convolution window, that is to say that the density compensation function of this moment is only that sample track is relevant with the distribution of collection point;
B, according to the quick calculating sampling density function of symmetry:
In the non-Cartesian sampling, the distribution of a lot of sample track is symmetrical; Net point (k in first quartile x, k y) density compensation function W (k x, k y) with other quadrants in identical with the sampling density function of the net point of its symmetry, namely suc as formula (3):
W(k x,k y)＝W(-k x,k y)＝W(-k x,-k y)＝W(k x,-k y) （3），
When the bulk density penalty function, only need to calculate the density compensation function of the sampled point that is positioned at the rectangular coordinate system first quartile, consider the impact of convolution window width, the sampled point that needs the bulk density penalty function in actual implementation procedure is that the point of first quartile adds the convolution window width half;
C, carry out gridding calculating:
Utilize the density compensation function that completes as calculated, sampled data carried out to the gridding reconstruction according to formula (4),
M SWCS ( k x , k y ) = [ M S ( k x , k y ) * C ( k x , k y ) ] · III ( k x , k y ) W ( k x , k y ) - - - ( 4 ) .
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Cited By (5)

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CN105607020A (en) * 2014-11-13 2016-05-25 西门子公司 Method and system for generating magnetic resonance image
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WO2021184350A1 (en) * 2020-03-20 2021-09-23 中国科学院深圳先进技术研究院 Neural network-based method and device for gridded magnetic resonance image reconstruction

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