Patent Publication Number: US-11035920-B2

Title: Sparse approximate encoding of Wave-CAIPI: preconditioner and noise reduction

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is based on, claims priority to, and incorporates herein by reference in its entirety U.S. Provisional Application Ser. No. 62/696,980, filed Jul. 12, 2018, and entitled “SPARSE APPROXIMATE ENCODING OF WAVE-CAIPI: PRECONDITIONER AND NOISE REDUCTION.” 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH 
     This invention was made with government support under EB019437, EB020613, MH106096, and EB015896 awarded by the National Institutes of Health. The government has certain rights in the invention. 
    
    
     BACKGROUND 
     Wave-CAIPI is an efficient MRI encoding technique that can be applied to many sequences. Wave-CAIPI is described, for example, in U.S. Pat. No. 8,981,776, which is herein incorporated by reference in its entirety. By utilizing sinusoidal gradients, the Wave-CAIPI method allows for high acceleration factors to be achieved with negligible g-factors. The iterative SENSE based reconstruction commonly used for Wave-CAIPI can be computationally costly given the high level of readout oversampling and large number of array coil elements utilized. In addition, when using Wave-CAIPI to achieve high acceleration factors, the intrinsic SNR penalty can cause the final images to be noisy. 
     SUMMARY OF THE DISCLOSURE 
     The present disclosure addresses the aforementioned drawbacks by providing a method for reconstructing an image of a subject using a magnetic resonance imaging (MRI) system. Data are accessed with a computer system. The data were acquired from a subject using an MRI system using an encoding scheme that distributes aliased spatial frequency information in three dimensions in k-space. An image of the subject is reconstructed from the data using the computer system. Reconstructing the image includes inputting the data to an iterative reconstruction algorithm that implements a sparse approximate encoding matrix, generating output as the reconstructed image. 
     The foregoing and other aspects and advantages of the present disclosure will appear from the following description. In the description, reference is made to the accompanying drawings that form a part hereof, and in which there is shown by way of illustration a preferred embodiment. This embodiment does not necessarily represent the full scope of the invention, however, and reference is therefore made to the claims and herein for interpreting the scope of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is an example illustration of k-space trajectories that can be used for a Wave-CAIPI encoding scheme. 
         FIG. 2  is a flowchart of an example method for generating images from magnetic resonance data acquired using a Wave-CAIPI encoding scheme and using a sparse approximate encoding matrix in the image reconstruction. 
         FIG. 3  is a block diagram of an example MRI system that can implement the methods described in the present disclosure. 
         FIG. 4  is a block diagram of an example computer system that can implement the methods described in the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Described here are systems and methods for producing images of a subject using magnetic resonance imaging (“MRI”) in which data are acquired using a sparse approximate encoding scheme for controlled aliasing techniques. As one example, the sparse approximate encoding can be used for a Wave-CAIPI encoding scheme, which can enable faster image reconstruction using fewer computational resources, in addition to reducing noise in the reconstructed images relative to those reconstructed from data acquired using a Wave-CAIPI encoding scheme without sparse approximate encoding. 
     The systems and methods described in the present disclosure thus use a sparse preconditioner for Wave-CAIPI encoding schemes, which allows for significant speed-up of iterative image reconstructions by removing the dependency on array coil channel count and over-sampling factors. The sparse approximate encoding of Wave-CAIPI also allows for the acquired data to be analyzed for dominate features, noisy features, or both. Based upon the number of cycles, the data can be binned and examined for low-rank structure. The low-rank property can be incorporated into the reconstruction as a penalty or used as a single denoising step. These properties are present for various different contrasts, and can be used for a joint reconstruction across SWI, MPRAGE, TSE, and so on. 
     The Wave-CAIPI encoding scheme improves imaging performance when undersampling is present in one or two directions, and provides good g-factor performance for three-dimensional imaging. In Wave-CAIPI, a k-space trajectory that effectively spreads aliasing patterns in all three spatial directions is used. This technique has the benefit of spreading the aliasing patterns throughout three dimensional space in a way that the aliasing patterns are spaced farther apart on average. As a result of this spreading out of the aliasing patterns, the aliased signals can be separated with less g-factor penalty than with previous methods. 
     The Wave-CAIPI encoding matrix can be accurately approximated by assuming an encoding sparsity pattern based upon the number of cycles played out by the imaging sequence. As one non-limiting example, it can be assumed that a given readout position is only coupled to voxels that are separated by an integer multiple of the number of cycles away from it. Given this fixed pattern, an encoding matrix with a sparse block Toeplitz matrix structure can be formed quickly. The size of each block is the number of readout voxels (no oversampling factor), and the number of blocks is based upon the acceleration factor. For instance, an acceleration factor of R=3×3 would couple nine readout lines. 
     This sparse encoding matrix can then be scaled by the sensitivity weights for a SENSE-based parallel imaging reconstruction. These sensitivity map based weights can be computed during the acquisition of the MRI data, allowing for efficient construction of the preconditioner. In the presence of field-of-view (“FOV”) tilting, gradient heterogeneity can cause additional spatially varying aliasing patterns. These aliasing patterns can be accurately modeled as a sparse tridiagonal matrix, which can then be applied to the sparse encoding matrix described above. 
     Given that both matrices are sparse, this multiplication is very efficient. Empirically, this preconditioner is accurate enough to result in 1×10 −3  relative error for the reconstruction of Wave-CAIPI data, which may be used as a convergence criteria. The sparse representation allows for significant speed-up as it does not depend on the number of receive channels or the over-sampling factor. 
     The sparse approximate encoding can also provide the advantage of reducing noise in the reconstructed images. By assuming that each voxel along the readout is only coupled to voxels that are separated by an integer multiple of the number of cycles away from it, the acquired data can be accurately binned. As one non-limiting example, if one assumes 30 cycles and an over-sampled readout length of 900, there will be 30 approximately separable encodings of size 30. The point spread function associated with Wave-CAIPI significantly blurs the data along the readout position to create a relatively incoherent pattern. This incoherency in the encoding process results in similarities in the data being binned. These similarities can be efficiently modeled using a low-rank representation, allowing for the removal of small differences. These small differences are often Gaussian noise. The low-rank modeling can be used directly to denoise the data or included as part of a constrained optimization using rank proxies. The low-rank modeling can be applied across similar channels, phase encode lines, slices, or contrasts to improve the compression. 
     The Wave-CAIPI encoding scheme can be described with reference to the following orthogonal spatial encoding directions common to magnetic resonance imaging (“MRI”): a partition-encoding, a phase-encoding direction, and a frequency-encoding direction. Alternatively, the partition-encoding direction may be simply referred to as a second phase-encoding direction. When two-dimensional images are acquired, the partition-encoding direction may be referred to as a slice-encoding direction. By way of example, as referred to herein, the partition-encoding direction corresponds to the z-direction in the image domain, which is aligned along the longitudinal axis of the bore of an MRI system, and the k z -direction in k-space. In this manner, the obtained images are transverse, or axial, images lying in the x-y plane. Accordingly, as referred to herein, the phase-encoding direction corresponds to the y-direction in the image domain, and the k y -direction in k-space; and the frequency-encoding direction corresponds to the x-direction in the image domain, and the k x -direction in k-space. It will be appreciated by those skilled in the art that any suitable permutation of these directions, or any set of orthogonal oblique directions, is possible and within the scope of the present invention. The choice of these directions is typically made depending on the desired imaging application, such as whether it is desirable to acquire axial, sagittal, coronal, or oblique images of a subject. 
     In Wave-CAIPI encoding scheme, additional differential encoding information is provided by applying alternating gradients along the two directions orthogonal to the readout direction. The result of these gradients being played out in the presence of a readout gradient is to more uniformly distribute aliasing patterns throughout k-space, thereby improving the ability to separate the aliased signals. In this manner, the so-called g-factor penalty for parallel image reconstruction can be reduced. The Wave-CAIPI encoding scheme can be implemented with rectilinear, radial, spiral, and other such sampling patterns. 
     An example of k-space trajectories that can be implemented in a Wave-CAIPI encoding scheme is shown in  FIG. 1 . Each k-space trajectory generally includes a corkscrew trajectory that is centered on and spirals around an axis extending along the readout direction (e.g., the k x  direction in this example). The starting point of each k-space trajectory is generally defined by the amplitude and polarity of phase-encoding and partition-encoding gradients, the selection of which can be made in different ways to achieve different samplings of k-space. In the example shown in  FIG. 1 , the starting positions of the k-space trajectories are staggered, or shifted, on a grid to distribute aliasing patterns in three spatial dimensions. In other examples, the starting points can be evenly and uniformly distributed on a grid. In still other examples, the starting points can be randomly distributed, pseudorandomly distributed, or distributed in otherwise non-uniform ways. 
     Referring now to  FIG. 2 , a flowchart is illustrated as setting forth the steps of an example of a method for reconstructing images from data acquired using the encoding schemes described in the present disclosure. Data acquired using the encoding schemes described in the present disclosure are provided to a computer system, as indicated at step  202 . Providing the data can include accessing previously acquired data from a memory or other data storage using the computer system, or can include acquiring the data with an MRI system and providing the acquired data to the computer system, which may be a part of the MRI system. As mentioned above, the data are preferably acquired using a Wave-CAIPI encoding scheme; however, other encoding schemes may also be implemented. Images are then reconstructed from the data using an image reconstruction techniques that incorporates a sparse approximate encoding into the reconstruction problem, as indicated at step  204 . The reconstructed images are then displayed to a user, can be stored for later use, or both, as indicated at step  206 . 
     Because the aliasing function of the alternating encoding gradients is known prior to the data acquisition, a generalized-SENSE reconstruction can be used to separate and reconstruct the aliased imaging slices. The generalized-SENSE formulation can be expressed as:
 
 k=E·i   (1);
 
     where k is the vector of acquired k-space data, E is an encoding matrix, and i is the image vector sought, usually via conjugate gradient. The encoding matrix, E, can often times be very large and, therefore, computationally burdensome to invert; however, in some instances various iterative techniques, such as the conjugate gradient method, may be used to find the target images, i. Thus, as described above, the Wave-CAIPI encoding matrix can be approximated by assuming an encoding sparsity pattern based upon the number of cycles played out by the imaging sequence. As one non-limiting example, it can be assumed that a given readout position is only coupled to voxels that are separated by an integer multiple of the number of cycles away from it. Given this fixed pattern, an encoding matrix with a sparse block Toeplitz matrix structure can be efficiently formed. The sparse encoding matrix, {tilde over (E)}, can be scaled by the sensitivity weights contained in coil sensitivity data. 
     Referring particularly now to  FIG. 3 , an example of an MRI system  300  that can implement the methods described here is illustrated. The MRI system  300  includes an operator workstation  302  that may include a display  304 , one or more input devices  306  (e.g., a keyboard, a mouse), and a processor  308 . The processor  308  may include a commercially available programmable machine running a commercially available operating system. The operator workstation  302  provides an operator interface that facilitates entering scan parameters into the MRI system  300 . The operator workstation  302  may be coupled to different servers, including, for example, a pulse sequence server  310 , a data acquisition server  312 , a data processing server  314 , and a data store server  316 . The operator workstation  302  and the servers  310 ,  312 ,  314 , and  316  may be connected via a communication system  340 , which may include wired or wireless network connections. 
     The pulse sequence server  310  functions in response to instructions provided by the operator workstation  302  to operate a gradient system  318  and a radiofrequency (“RF”) system  320 . Gradient waveforms for performing a prescribed scan are produced and applied to the gradient system  318 , which then excites gradient coils in an assembly  322  to produce the magnetic field gradients G x , G y , and G z  that are used for spatially encoding magnetic resonance signals. The gradient coil assembly  322  forms part of a magnet assembly  324  that includes a polarizing magnet  326  and a whole-body RF coil  328 . 
     RF waveforms are applied by the RF system  320  to the RF coil  328 , or a separate local coil to perform the prescribed magnetic resonance pulse sequence. Responsive magnetic resonance signals detected by the RF coil  328 , or a separate local coil, are received by the RF system  320 . The responsive magnetic resonance signals may be amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server  310 . The RF system  320  includes an RF transmitter for producing a wide variety of RF pulses used in MRI pulse sequences. The RF transmitter is responsive to the prescribed scan and direction from the pulse sequence server  310  to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole-body RF coil  328  or to one or more local coils or coil arrays. 
     The RF system  320  also includes one or more RF receiver channels. An RF receiver channel includes an RF preamplifier that amplifies the magnetic resonance signal received by the coil  328  to which it is connected, and a detector that detects and digitizes the I and Q quadrature components of the received magnetic resonance signal. The magnitude of the received magnetic resonance signal may, therefore, be determined at a sampled point by the square root of the sum of the squares of the I and Q components:
 
 M=I   2   +Q   2   (2);
 
     and the phase of the received magnetic resonance signal may also be determined according to the following relationship: 
     
       
         
           
             
               
                 
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     The pulse sequence server  310  may receive patient data from a physiological acquisition controller  330 . By way of example, the physiological acquisition controller  330  may receive signals from a number of different sensors connected to the patient, including electrocardiograph (“ECG”) signals from electrodes, or respiratory signals from a respiratory bellows or other respiratory monitoring devices. These signals may be used by the pulse sequence server  310  to synchronize, or “gate,” the performance of the scan with the subject&#39;s heart beat or respiration. 
     The pulse sequence server  310  may also connect to a scan room interface circuit  332  that receives signals from various sensors associated with the condition of the patient and the magnet system. Through the scan room interface circuit  332 , a patient positioning system  334  can receive commands to move the patient to desired positions during the scan. 
     The digitized magnetic resonance signal samples produced by the RF system  320  are received by the data acquisition server  312 . The data acquisition server  312  operates in response to instructions downloaded from the operator workstation  302  to receive the real-time magnetic resonance data and provide buffer storage, so that data is not lost by data overrun. In some scans, the data acquisition server  312  passes the acquired magnetic resonance data to the data processor server  314 . In scans that require information derived from acquired magnetic resonance data to control the further performance of the scan, the data acquisition server  312  may be programmed to produce such information and convey it to the pulse sequence server  310 . For example, during pre-scans, magnetic resonance data may be acquired and used to calibrate the pulse sequence performed by the pulse sequence server  310 . As another example, navigator signals may be acquired and used to adjust the operating parameters of the RF system  320  or the gradient system  318 , or to control the view order in which k-space is sampled. In still another example, the data acquisition server  312  may also process magnetic resonance signals used to detect the arrival of a contrast agent in a magnetic resonance angiography (“MRA”) scan. For example, the data acquisition server  312  may acquire magnetic resonance data and processes it in real-time to produce information that is used to control the scan. 
     The data processing server  314  receives magnetic resonance data from the data acquisition server  312  and processes the magnetic resonance data in accordance with instructions provided by the operator workstation  302 . Such processing may include, for example, reconstructing two-dimensional or three-dimensional images by performing a Fourier transformation of raw k-space data, performing other image reconstruction algorithms (e.g., iterative or backprojection reconstruction algorithms), applying filters to raw k-space data or to reconstructed images, generating functional magnetic resonance images, or calculating motion or flow images. 
     Images reconstructed by the data processing server  314  are conveyed back to the operator workstation  302  for storage. Real-time images may be stored in a data base memory cache, from which they may be output to operator display  302  or a display  336 . Batch mode images or selected real time images may be stored in a host database on disc storage  338 . When such images have been reconstructed and transferred to storage, the data processing server  314  may notify the data store server  316  on the operator workstation  302 . The operator workstation  302  may be used by an operator to archive the images, produce films, or send the images via a network to other facilities. 
     The MRI system  300  may also include one or more networked workstations  342 . For example, a networked workstation  342  may include a display  344 , one or more input devices  346  (e.g., a keyboard, a mouse), and a processor  348 . The networked workstation  342  may be located within the same facility as the operator workstation  302 , or in a different facility, such as a different healthcare institution or clinic. 
     The networked workstation  342  may gain remote access to the data processing server  314  or data store server  316  via the communication system  340 . Accordingly, multiple networked workstations  342  may have access to the data processing server  314  and the data store server  316 . In this manner, magnetic resonance data, reconstructed images, or other data may be exchanged between the data processing server  314  or the data store server  316  and the networked workstations  342 , such that the data or images may be remotely processed by a networked workstation  342 . 
     Referring now to  FIG. 4 , a block diagram of an example of a computer system  400  that can perform the methods described in the present disclosure is shown. The computer system  400  generally includes an input  402 , at least one hardware processor  404 , a memory  406 , and an output  408 . Thus, the computer system  400  is generally implemented with a hardware processor  404  and a memory  406 . 
     In some embodiments, the computer system  400  can be a workstation, a notebook computer, a tablet device, a mobile device, a multimedia device, a network server, a mainframe, one or more controllers, one or more microcontrollers, or any other general-purpose or application-specific computing device. 
     The computer system  400  may operate autonomously or semi-autonomously, or may read executable software instructions from the memory  406  or a computer-readable medium (e.g., a hard drive, a CD-ROM, flash memory), or may receive instructions via the input  402  from a user, or any another source logically connected to a computer or device, such as another networked computer or server. Thus, in some embodiments, the computer system  400  can also include any suitable device for reading computer-readable storage media. 
     In general, the computer system  400  is programmed or otherwise configured to implement the methods and algorithms described in the present disclosure. For instance, the computer system  400  can be programmed to reconstruct images from magnetic resonance data. 
     The input  402  may take any suitable shape or form, as desired, for operation of the computer system  400 , including the ability for selecting, entering, or otherwise specifying parameters consistent with performing tasks, processing data, or operating the computer system  400 . In some aspects, the input  402  may be configured to receive data, such as data acquired with an MRI system. Such data may be processed as described above to reconstruct images of a subject. In addition, the input  402  may also be configured to receive any other data or information considered useful for reconstructing images of a subject using the methods described above. As one example, such additional data may include coil sensitivity data. 
     Among the processing tasks for operating the computer system  400 , the one or more hardware processors  404  may also be configured to carry out any number of post-processing steps on data received by way of the input  402 . 
     The memory  406  may contain software  410  and data  412 , such as data acquired with an MRI system, and may be configured for storage and retrieval of processed information, instructions, and data to be processed by the one or more hardware processors  404 . In some aspects, the software  410  may contain instructions directed to reconstructing images as described in the present disclosure. 
     In addition, the output  408  may take any shape or form, as desired, and may be configured for displaying reconstructed images, in addition to other desired information. 
     In some embodiments, any suitable computer readable media can be used for storing instructions for performing the functions and/or processes described herein. For example, in some embodiments, computer readable media can be transitory or non-transitory. For example, non-transitory computer readable media can include media such as magnetic media (e.g., hard disks, floppy disks), optical media (e.g., compact discs, digital video discs, Blu-ray discs), semiconductor media (e.g., random access memory (“RAM”), flash memory, electrically programmable read only memory (“EPROM”), electrically erasable programmable read only memory (“EEPROM”)), any suitable media that is not fleeting or devoid of any semblance of permanence during transmission, and/or any suitable tangible media. As another example, transitory computer readable media can include signals on networks, in wires, conductors, optical fibers, circuits, or any suitable media that is fleeting and devoid of any semblance of permanence during transmission, and/or any suitable intangible media. 
     The present disclosure has described one or more preferred embodiments, and it should be appreciated that many equivalents, alternatives, variations, and modifications, aside from those expressly stated, are possible and within the scope of the invention.