CN101975936A - Rapid magnetic resonance imaging (MRI) method based on CS ( compressed sensing ) technique - Google Patents
Rapid magnetic resonance imaging (MRI) method based on CS ( compressed sensing ) technique Download PDFInfo
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Abstract
The invention discloses a rapid magnetic resonance imaging method based on a CS (compressed sensing) technique. The traditional imaging method has relatively low speed and high hardware cost. The method comprises the following steps of: firstly, acquiring variable-density random k spatial data; specifically, determining under sampling rate according to the structural sparsity of an image; carrying out sparse acquisition in a k-space central area and carrying out random sparse acquisition in a k-space peripheral area according to the under sampling rate by combining with the k-space energy distribution rule to generate a variable-density random data acquisition path; acquiring the data according to the determined data acquisition path; then carrying out sparse conversion on an MRI image; and finally, nonlinearly optimizing and reconstructing the image based on Li norm minimum. The method breaks through the limit of the classical Nyguist sampling theorem, accurately reconstructs the signal of the MRI image through randomly acquiring few data points by utilizing a nonlinear optimization algorithm and greatly shortens the data acquisition time.
Description
Technical field
The invention belongs to the magnetic resonance imaging field, relate to a kind of quick MR imaging method based on the compressed sensing technology.
Background technology
Magnetic resonance imaging MRI (Magnetic Resonance Imaging) is a kind of NMR signal generation intracorporeal organ physics of in-vitro measurements and faultage image imaging technique of chemical characteristic of utilizing.Because MRI does not have harmful effect to body, has higher advantages such as soft tissue resolution characteristic, in detecting, clinical disease is used widely at present.But MRI also often is subjected to the long restriction of data acquisition time in clinical practice, and the inspection that this has limited some patient has influenced the level of comfort when patient is checked.To each patient's long-time inspection, increase the weight of patient and accepted the financial burden that MRI checks, restricted the expensive MRI usage ratio of equipment of hospital, also influenced the economic benefit of hospital.
Image taking speed is the key factor during many kinds of MRI use, and the importance that image taking speed improves is to improve acquisition speed.The researchist shortens acquisition time by improving MRI hardware, research rapid serial and effective acquisition trajectories.The data acquisition of MRI is the round moving process of a multidimensional k-space (frequency space) curve, and mobile speed is subjected to physical condition such as gradient system Effect on Performance.Gradient system is subjected to the restriction of greatest gradient value and greatest gradient escalating rate (Slew-Rate), and high Grad and gradient switching fast can produce patient's peripheral nerve stimulation, and patient's physiology has limited the performance of gradient system performance.
The resolution of MRI image is relevant with the number of k-space data collection, and the data number of collection is many more, resolution is just high more, and the time cost that brings is also high more.Therefore, how reduce the data acquisition total amount under the picture quality condition and become further the key of magnetic resonance imaging fast not reducing.
The invention of the relevant MRI rapid data collection of having applied for at present has: utilize parallel MRI to be accelerated into the method and system (200410031404.3) of picture, propose to obtain the method and system that a plurality of magnetic resonance signals carry out parallel imaging by the target receiver coil array on every side that utilization is placed in the MRI system.Parallel imaging method and MRI equipment (200710128781.2) provide a kind of use a plurality of receiving coil image data, the method composograph of the sensitivity coefficient weighting by utilizing corresponding receiving coil.The fast generalized self calibration parallel collection image reconstruction of magnetic resonance imaging algorithm (200410082376.8) proposes the fast generalized self calibration parallel collection image reconstruction of a kind of magnetic resonance imaging algorithm, and this algorithm essence is the parallel image reconstruction algorithm of a kind of improved GRAPPA.More than three kinds of methods all be based on parallel image data clocklike, parallel data acquisition will be used the weighting coefficient that methods such as reference scan are calculated a plurality of data acquisition coils, but because the homogeneity of magnetic resonance magnetic field under different situations inconsistent (magnetic field that enters the front and back, magnetic field as human body will be inconsistent), therefore be difficult to calculate accurately the weighting coefficient of each coil, thereby influenced the precision of reconstructed image.
More than Shen Qing patent of invention shows, lacks a kind of active data acquisition mode, when shortening data acquisition time, need not to estimate that the weighting coefficient of a plurality of coils just can directly reconstruct high-quality image.
In recent years, CS compressed sensing (Compressed Sensing) technological breakthrough aromatic (Shannon) sampling thheorem must be higher than the limit of 2 times of signal bandwidths about sampling rate, become new research focus in a plurality of fields such as signal Processing at present.Briefly, the compression sensing technology is to utilize signal self or its sparse property in transform domain, only needs a spot of data point of random acquisition, just can recover original signal by non-linear reconstruction scheduling algorithm.
The patent of invention of the relevant compressed sensing technical elements of having applied for at present has: utilize compressed sensing to reduce the channel estimation methods (200910079441.4) of pilot tone number in the wide-band mobile communication, a kind of principle of utilizing the compressed sensing technology is proposed, required frequency pilot sign number and guarantee the method for channel estimating performance when reducing the system estimation channel.A kind of reconstructing method of sparse signal (200910023785.3) proposes a kind of reconstructing method of sparse signal, mainly solves from the low problem of observation vector reconstruct original sparse signal rate.Based on the method (200910242622.4) of the distributed source coding of compressed sensing technology, propose to utilize the advantage of compressed sensing technology and the sparse characteristic of video image, form a kind of new distributed source coding method.The signal detecting method with compressed sensing process (201010032485.4) based on orthogonal matching pursuit, propose a kind of signal detecting method, solved the problem that needs the wasting of resources that reconstruction signal brings when utilizing existing compressed sensing to realize input with compressed sensing process based on orthogonal matching pursuit.Sensor network physical signal collaborative compressed sensing system and cognitive method (200910198056.1) propose a kind of sensor network physical signal collaborative compressed sensing system and cognitive method.Above patent is mainly used in input and process field such as move in the broadband, radio.
More than Shen Qing patent of invention shows, does not also have a kind of special patent at MRI fast imaging compressed sensing technical elements.
Summary of the invention
The present invention is directed to the deficiencies in the prior art, from information-theoretical angle, provide a kind of new method to come magnetic resonance k-spatial data is gathered fast based on the CS compressed sensing, by data acquisition phase potential data are compressed collection, the number of samples of make gathering is far below the requirement of classical Nyquist (Nyquist) sampling theory.The invention provides three kinds of effective k-spaces that are applicable to hardware sparse data acquisition method at random: the variable density spiral fashion of owing to sample, add random perturbation at random based on the variable density of Cartesian coordinates owe to sample and add random perturbation radially owe sampling; Provide four kinds of sparse conversion: unit transformation, finite difference conversion, wavelet transformation and discrete cosine transform; Provide a kind of based on the minimized nonlinear images reconstruction algorithm of L1 norm.
The present invention includes three steps: variable density at random k space data collection, MRI image sparse conversion and based on the minimized nonlinear optimization image reconstruction of L1 norm.
Variable density k-space data collection at random comprises track, image data and four steps of gridding of determining to owe sampling rate, generating the collection of variable density random data:
1-1 determines to owe sampling rate, according to the sparse property of the structure of image, determines to owe sampling rate, i.e. the total amount of the data point that need gather.
1-2 generates variable density random data acquisition trajectories, according to the sampling rate of owing of step 1-1, in conjunction with k-dimensional energy distribution rule, in the dense collection in zone of k-space center, in the sparse at random collection of outer peripheral areas, generates the track that the variable density random data is gathered.The invention provides three kinds of data acquisition tracks:
(a) owe sample track at random based on the variable density of Cartesian coordinates, data on the frequency coding axle are carried out routine sampling, the data on phase encoding axle and the layer coding axle are carried out variable density owe sampling at random; Also can be that data on the frequency coding axle are carried out routine sampling, the data on phase encoding axle or the layer coding axle be carried out variable density owe sampling at random;
Described routine sampling is for gathering the total data point on this;
(b) the variable density spiral fashion that adds random perturbation is owed sample track, adds random perturbation and form the data acquisition track on the variable density spiral trajectory.
(c) the radial sample track of owing of adding random perturbation adds random perturbation and forms the data acquisition track on radial trajectories.
The 1-3 image data is according to the determined data acquisition track of step 1-2 image data.
For among the step 1-2 by (b) or (c) track data of gathering, need the data coordinates that will collect with the method gridding of interpolation to cartesian coordinate system.
The sparse conversion of MRI image can be adopted unit transformation, finite difference (Finite Difference) conversion, discrete cosine transform or wavelet transform:
(1) unit transformation: from being sparse image in pixel domain, the present invention adopts based on unit transformation one to one and carries out sparse conversion to some.
(2) finite difference conversion: some brain MRI image is piecewise smooth, and the image gradient of their correspondences is sparse, and the present invention adopts the finite difference conversion to carry out sparse conversion.
(3) discrete cosine transform: at the sparse MRI image of discrete cosine transform domain, the present invention adopts discrete cosine transform to carry out sparse conversion to some.
(4) wavelet transform: to most of MRI image, the present invention adopts wavelet transform to carry out sparse conversion.
Comprise establishment optimization aim and two steps of solving-optimizing target based on the minimized nonlinear optimization image reconstruction of L1 norm:
3-1 establishes optimization aim, need to suppose the image of reconstruction to be represented that by optimization variable m the sparse ψ that is transformed to supposes F
SThe Fourier transform of sampled data is owed in representative, and the k spatial data that the y representative is gathered the invention provides two class optimization aim:
(a) rebuild the following problem of solution that needs based on the nonlinear optimization of L1 norm minimum:
Minimize ‖ ψ m ‖
1S.t. ‖ F
SM-y ‖
2＜ε, formula (1)
Wherein, optimization aim be m in the L1 of ψ transform domain norm minimum, constraint condition is the continuity of m at k space and y, thresholding parameter ε is the noise level of expectation, the fidelity of rebuilding in order to control.
(b) rebuild the following problem of solution that needs based on the nonlinear optimization of L1 norm and weighting total variation minimum:
In formula (1), add total variation TV and optimize weighting, the hybrid optimization process can be expressed as:
Minimize ‖ ψ m ‖
1+ λ TV (m) s.t ‖ F
SM-y ‖
2＜ε, formula (2)
Wherein, λ is a weighting coefficient.
3-2 solving-optimizing target adopts the complex conjugate gradient method to be optimized finding the solution of target.
The inventive method can break through the limit of classical nyquist sampling theorem, by a spot of data point of random acquisition, utilizes nonlinear optimization algorithm accurate reconstruction MRI picture signal, has shortened data acquisition time significantly, and the present invention simultaneously has following characteristics:
(1) the desirable even stochastic sampling of frequency field does not consider that the most of concentration of energy in the MRI image is distributed in the k-central zone of space, energy to around be the state of quick decay.The present invention adopts the method for variable density stochastic sampling, in the dense collection in zone of k-space center, in the sparse collection of outer peripheral areas.
(2) establish the sparse data acquisition trajectories that is applicable to actual hardware, sample track is comply with level and smooth relatively line and curve, solves the contradiction that the completely random sampling is not suitable for actual hardware.
(3) provide four kinds of sparse conversion to satisfy the sparse property problem of most of MRI image, make the MRI image meet the precondition of applied compression cognition technology.
(4) provide the hybrid optimization target of a kind of L1 norm and total variation weighting, seek the sparse characteristic of image simultaneously in transform domain and finite difference territory.
Description of drawings
Fig. 1 owes the synoptic diagram of sampling in phase encoding or layer coding staff at random to carrying out variable density respectively;
Fig. 2 owes the synoptic diagram of sampling at phase encoding and layer coding staff at random to carrying out variable density simultaneously;
Fig. 3 does not add the preceding variable density spiral fashion of random perturbation to owe the sample track synoptic diagram;
Fig. 4 does not add the preceding radial sample track synoptic diagram of owing of random perturbation;
Fig. 5 (a) owes the synoptic diagram of sampled data after routine is rebuild;
Fig. 5 (b) owes the synoptic diagram of sampled data after the present invention rebuilds.
Embodiment
The invention will be further described below in conjunction with accompanying drawing.
A kind of quick MR imaging method based on CS compressed sensing technology comprises three steps: variable density at random k space data collection, MRI image sparse conversion and based on the minimized nonlinear optimization image reconstruction of L1 norm.
Variable density k-space data collection at random comprises track, image data and four steps of gridding of determining to owe sampling rate, generating the collection of variable density random data:
1-1 determines to owe sampling rate, according to the sparse property of the structure of image, determines to owe sampling rate, i.e. the total amount of the data point that need gather.
1-2 generates variable density random data acquisition trajectories, according to the sampling rate of owing of step 1-1, in conjunction with k-dimensional energy distribution rule, in the dense collection in zone of k-space center, in the sparse at random collection of outer peripheral areas, generates the track that the variable density random data is gathered.The invention provides three kinds of data acquisition tracks:
(a) owe sample track at random based on the variable density of Cartesian coordinates, as shown in Figure 1, frequency coding axle kx is gone up data carry out routine sampling, the data on phase encoding axle kx or the layer coding axle kz are carried out variable density owe sampling at random; Also can be frequency coding axle kx to be gone up data carry out routine sampling, as shown in Figure 2, the data on phase encoding axle ky and the layer coding axle kz be carried out variable density owe sampling at random;
Described routine sampling is for gathering the total data point on this;
(b) the variable density spiral fashion that adds random perturbation is owed sample track, as shown in Figure 3, adds random perturbation and form the data acquisition track on the variable density spiral trajectory.
(c) the radial sample track of owing of adding random perturbation as shown in Figure 4, adds random perturbation and forms the data acquisition track on radial trajectories.
The 1-3 image data is according to the determined data acquisition track of step 1-2 image data.
For among the step 1-2 by (b) or (c) track data of gathering, need the data coordinates that will collect with the method gridding of interpolation to cartesian coordinate system.
The sparse conversion of MRI image can be adopted unit transformation, finite difference (Finite Difference) conversion, discrete cosine transform or wavelet transform:
(1) unit transformation: from being sparse image in pixel domain, the present invention adopts based on unit transformation one to one and carries out sparse conversion to some.
(2) finite difference conversion: some brain MRI image is piecewise smooth, and the image gradient of their correspondences is sparse, and the present invention adopts the finite difference conversion to carry out sparse conversion.
(3) discrete cosine transform: at the sparse MRI image of discrete cosine transform domain, the present invention adopts discrete cosine transform to carry out sparse conversion to some.
(4) wavelet transform: to most of MRI image, the present invention adopts wavelet transform to carry out sparse conversion.
Comprise establishment optimization aim and two steps of solving-optimizing target based on the minimized nonlinear optimization image reconstruction of L1 norm:
3-1 establishes optimization aim, need to suppose the image of reconstruction to be represented that by optimization variable m the sparse ψ that is transformed to supposes F
SThe Fourier transform of sampled data is owed in representative, and the k spatial data that the y representative is gathered the invention provides two class optimization aim:
(a) rebuild the following problem of solution that needs based on the nonlinear optimization of L1 norm minimum:
Minimize ‖ ψ m ‖
1S.t. ‖ F
SM-y ‖
2＜ε, formula (1)
Wherein, optimization aim be m in the L1 of ψ transform domain norm minimum, constraint condition is the continuity of m at k space and y, thresholding parameter ε is the noise level of expectation, the fidelity of rebuilding in order to control.
(b) rebuild the following problem of solution that needs based on the nonlinear optimization of L1 norm and weighting total variation minimum:
In formula (1), add total variation TV and optimize weighting, the hybrid optimization process can be expressed as:
Minimize ‖ ψ m ‖
1+ λ TV (m) s.t. ‖ F
SM-y ‖
2＜ε, formula (2)
Wherein, λ is a weighting coefficient.
3-2 solving-optimizing target adopts the complex conjugate gradient method to be optimized finding the solution of target.
Below rebuild with the CS of blood vessel imaging image and to be illustrated.At first establishing and owing sampling rate is 32.8%; Establish then based on the variable density of Cartesian coordinates and owe sample track at random; Then by the selected sample track image data of owing; The data that collect are carried out wavelet transform; Then establish mixed optimization aim based on the TV weighting; Adopt the complex conjugate gradient method to be optimized finding the solution of target at last, obtain reconstructed image.Fig. 5 (a) and Fig. 5 (b) are that matrix is that 256 * 192 * 32 blood vessel imaging The data Cartesian coordinates variable density is owed sample track (track as shown in Figure 1) at random, in phase-encoding direction pairing non-linear reconstructed results after variable density is owed sampled data at random, wherein Fig. 5 (a) is to owing the conventional reconstructed results of the direct zero filling of sampled data, and Fig. 5 (b) is the result by method for reconstructing gained of the present invention.This shows that method of the present invention is being guaranteed under the prerequisite of picture quality, has significantly reduced the data volume of gathering, and has shortened the acquisition time of data.
Claims (6)
1. the quick MR imaging method based on CS compressed sensing technology is characterized in that this method comprises the steps:
Step (1) is gathered variable density k spatial data at random; Concrete grammar is:
1-1, according to the sparse property of the structure of image, determine to owe sampling rate;
1-2, basis are owed sampling rate, in conjunction with k-dimensional energy distribution rule, in the dense collection in zone of k-space center, in the sparse at random collection of k-space outer peripheral areas, generate variable density random data acquisition trajectories;
1-3, according to the determined data acquisition track of step 1-2 image data;
Step (2) is carried out sparse conversion to the magnetic resonance imaging image; Unit transformation, finite difference conversion, discrete cosine transform or wavelet transform are adopted in described sparse conversion;
Step (3) is based on the minimized nonlinear optimization reconstructed image of L1 norm; Concrete grammar is:
3-1, establish optimization aim, optimization aim be m in the L1 of ψ transform domain norm minimum, constraint condition is the continuity of m at k space and y, thresholding parameter ε is the noise level of expectation, in order to the fidelity of control reconstruction, i.e. minimize ‖ ψ m ‖
1S.t. ‖ F
SM-y ‖
2＜ε, wherein m is an optimization variable, ψ is sparse conversion, F
SFor owing the Fourier transform of sampled data, the k spatial data of y for gathering;
3-2, employing complex conjugate gradient method solving-optimizing target.
2. a kind of quick MR imaging method according to claim 1 based on CS compressed sensing technology, it is characterized in that: the method that generates variable density random data acquisition trajectories is that data on the frequency coding axle are carried out routine sampling, the data on phase encoding axle and the layer coding axle is carried out variable density owe sampling at random;
Described routine sampling is for gathering the total data point on this.
3. a kind of quick MR imaging method based on CS compressed sensing technology according to claim 1 is characterized in that: the method that generates variable density random data acquisition trajectories is to add random perturbation to form the data acquisition track on the variable density spiral trajectory.
4. a kind of quick MR imaging method based on CS compressed sensing technology according to claim 1 is characterized in that: the method that generates variable density random data acquisition trajectories is to add random perturbation to form the data acquisition track on radial trajectories.
5. according to claim 3 or 4 described a kind of quick MR imaging method based on CS compressed sensing technology, it is characterized in that: the data coordinates that collects arrives cartesian coordinate system with the method gridding of interpolation.
6. a kind of quick MR imaging method based on CS compressed sensing technology according to claim 1 is characterized in that: the establishment optimization aim described in the step 3-1 comprises that also adding total variation TV optimizes weighting, i.e. minimize ‖ ψ m ‖
1+ λ TV (m) s.t. ‖ F
SM-y ‖
2＜ε.
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