Method, processing device and medium for analyzing imaging data

Abstract

A method for analyzing a multi-dimensional image tensor comprising a plurality of images, comprising: performing an imaging scan on an object to obtain imaging data; generating the multi-dimensional image tensor from the imaging data; based on the multi-dimensional image tensor, determining a space base tensor containing a base image; based on the multi-dimensional image tensor, determining a time base tensor containing a primary function for a time dimension; determining a kernel tensor that associates the spatial base tensor with the temporal base tensor; pre-multiplying the kernel tensor and the time base tensor to generate a modified time base tensor; storing the space base tensor and the modified time base tensor; and generating an image by multiplying at least (i) at least a portion of the spatial-based tensor and (ii) at least a portion of the modified temporal-based tensor.

Description

[0001] This application is a divisional application of patent application No. 201980060307.1, filed on September 18, 2019, with the invention name “Storage, display and analysis of decomposed multidimensional images”. Technical Field

[0002] The present disclosure relates to biomedical imaging and analysis. More specifically, the present disclosure relates to storing and analyzing multidimensional biomedical images using tensor decomposition, selective multiplication, and factor processing. Background Art

[0003] Many types of biomedical imaging (e.g., MRI (Magnetic Resonance Imaging), CT (Computed Tomography), CAT (Computerized Axial Tomography), etc.) can be used to measure multiple varying parameters of an object ("multidimensional imaging"). Multidimensional imaging generally involves many different factors that need to be considered, such as spatial factors (e.g., position within or on the object being imaged) that are time-varying parameters (e.g., cardiac motion, respiration). Capturing a full set of images of all the different factors would greatly increase storage requirements and computational analysis times. Aspects of the present disclosure are intended to address these and other difficulties described above. Summary of the invention

[0004] According to various aspects of the present disclosure, a method for analyzing a multidimensional image tensor is provided, wherein the multidimensional image tensor contains multiple images of a region of interest of an object, the method comprising: performing one or more imaging scans on the region of interest of the object to obtain imaging data; generating the multidimensional image tensor from the imaging data; based on the multidimensional image tensor, determining a spatial basis tensor containing one or more basis images; based on the multidimensional image tensor, determining one or more temporal basis tensors, each of which contains one or more basis functions for a corresponding one of multiple time dimensions; based on the multidimensional image tensor, determining a core tensor associating the spatial basis tensor with each of the one or more temporal basis tensors. tensor); premultiplying the core tensor and at least one of the one or more time basis tensors to produce a modified time basis tensor; storing the spatial basis tensor and the modified time basis tensor; and generating at least one of the multiple images by at least multiplying (i) at least a portion of the spatial basis tensor and (ii) at least a portion of the modified time basis tensor.

[0005] According to various aspects of the present disclosure, there is provided a system for analyzing a multidimensional image tensor containing multiple images of a region of interest of an object, the system comprising: a magnet operable to provide a magnetic field; a transmitter operable to transmit to a region within the magnetic field; a receiver operable to receive a magnetic resonance signal from the region using the magnetic field; and a processor operable to control the transmitter and the receiver. The processor is configured to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; generate the multidimensional image tensor from the imaging data; determine a spatial basis tensor containing one or more basis images based on the multidimensional image tensor; determine one or more time basis tensors based on the multidimensional image tensor, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; determine a core tensor that associates the spatial basis tensor with each of the one or more time basis tensors based on the multidimensional image tensor; premultiply the core tensor and at least one of the one or more time basis tensors to produce a modified time basis tensor; store the spatial basis tensor and the modified time basis tensor; and generate at least one of the multiple images by at least multiplying (i) at least a portion of the spatial basis tensor and (ii) at least a portion of the modified time basis tensor.

[0006] According to various aspects of the present disclosure, a non-transitory and machine-readable medium is provided, on which instructions for analyzing a multidimensional image tensor are stored, the multidimensional image tensor containing multiple images of a region of interest of an object, and when the instructions are executed by at least one processor, the instructions cause the at least one processor to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; generate the multidimensional image tensor from the imaging data; based on the multidimensional image tensor, determine a spatial basis tensor containing one or more basis images; based on the multidimensional image tensor, determine one or more time basis tensors, each of which is The time basis tensor includes one or more basis functions respectively for a corresponding one of multiple time dimensions; based on the multidimensional image tensor, determining a core tensor that associates the spatial basis tensor with each of the one or more time basis tensors; premultiplying the core tensor and at least one of the one or more time basis tensors to produce a modified time basis tensor; storing the spatial basis tensor and the modified time basis tensor; and generating at least one of the multiple images by at least multiplying (i) at least a portion of the spatial basis tensor and (ii) at least a portion of the modified time basis tensor.

[0007] According to various aspects of the present disclosure, a method for analyzing a multidimensional image tensor is provided, wherein the multidimensional image tensor contains multiple images of a region of interest of an object, the method comprising: performing one or more imaging scans on the region of interest of the object to obtain imaging data; generating the multidimensional image tensor from the imaging data; based on the multidimensional image tensor, determining a spatial basis tensor containing one or more basis images; based on the multidimensional image tensor, determining one or more time basis tensors, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; based on the multidimensional image tensor, determining a kernel tensor associating the spatial basis tensor with each of the one or more time basis tensors; and generating at least one of the multiple images by multiplying at least (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) at least a portion of at least one of the one or more time basis tensors.

[0008] According to various aspects of the present disclosure, there is provided a system for analyzing a multidimensional image tensor containing multiple images of a region of interest of an object, the system comprising: a magnet operable to provide a magnetic field; a transmitter operable to transmit to a region within the magnetic field; a receiver operable to receive a magnetic resonance signal from the region using the magnetic field; and a processor operable to control the transmitter and the receiver. The processor is configured to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; generate the multidimensional image tensor from the imaging data; determine a spatial basis tensor containing one or more basis images based on the multidimensional image tensor; determine one or more time basis tensors based on the multidimensional image tensor, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; determine a kernel tensor associating the spatial basis tensor with each of the one or more time basis tensors based on the multidimensional image tensor; and generate at least one of the multiple images by multiplying at least (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) at least a portion of at least one of the one or more time basis tensors.

[0009] According to various aspects of the present disclosure, a non-temporary and machine-readable medium is provided, on which instructions for analyzing a multidimensional image tensor are stored, the multidimensional image tensor containing multiple images of a region of interest of an object, and when the instructions are executed by at least one processor, the instructions cause the at least one processor to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; generate the multidimensional image tensor from the imaging data; based on the multidimensional image tensor, determine a spatial basis tensor containing one or more basis images; based on the multidimensional image tensor, determine one or more time basis tensors, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; based on the multidimensional image tensor, determine a kernel tensor associating the spatial basis tensor with each of the one or more time basis tensors; and generate at least one of the multiple images by multiplying at least (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) at least a portion of at least one of the one or more time basis tensors.

[0010] According to various aspects of the present disclosure, a method for analyzing a multidimensional image tensor is provided, wherein the multidimensional image tensor contains multiple images of a region of interest of an object, the method comprising: performing one or more imaging scans on the region of interest of the object to obtain imaging data; determining a spatial basis tensor containing one or more basis images based on the imaging data; determining one or more time basis tensors based on the imaging data, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; determining a core tensor associating the spatial basis tensor with each of the one or more time basis tensors based on the imaging data; premultiplying the core tensor and at least one of the one or more time basis tensors to produce a modified time basis tensor; storing the spatial basis tensor and the modified time basis tensor; and generating at least one of the multiple images by at least multiplying (i) at least a portion of the spatial basis tensor and (ii) at least a portion of the modified time basis tensor.

[0011] According to various aspects of the present disclosure, there is provided a system for analyzing a multidimensional image tensor containing multiple images of a region of interest of an object, the system comprising: a magnet operable to provide a magnetic field; a transmitter operable to transmit to a region within the magnetic field; a receiver operable to receive a magnetic resonance signal from the region using the magnetic field; and a processor operable to control the transmitter and the receiver. The processor is configured to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; determine a spatial basis tensor containing one or more basis images based on the imaging data; determine one or more time basis tensors based on the imaging data, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; determine a core tensor that associates the spatial basis tensor with each of the one or more time basis tensors based on the imaging data; premultiply the core tensor and at least one of the one or more time basis tensors to produce a modified time basis tensor; store the spatial basis tensor and the modified time basis tensor; and generate at least one of the multiple images by at least multiplying (i) at least a portion of the spatial basis tensor and (ii) at least a portion of the modified time basis tensor.

[0012] According to various aspects of the present disclosure, a non-temporary and machine-readable medium is provided, on which instructions for analyzing a multidimensional image tensor are stored, the multidimensional image tensor containing multiple images of a region of interest of an object, and when the instructions are executed by at least one processor, the instructions cause the at least one processor to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; based on the imaging data, determine a spatial basis tensor containing one or more basis images; based on the imaging data, determine one or more time basis tensors, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; based on the imaging data, determine a core tensor associating the spatial basis tensor with each of the one or more time basis tensors; premultiply the core tensor and at least one of the one or more time basis tensors to produce a modified time basis tensor; store the spatial basis tensor and the modified time basis tensor; and generate at least one of the multiple images by at least multiplying (i) at least a portion of the spatial basis tensor and (ii) at least a portion of the modified time basis tensor.

[0013] According to various aspects of the present disclosure, a method for analyzing multiple images of an area of ​​interest of an object is provided, comprising: performing one or more imaging scans on the area of ​​interest of the object to obtain imaging data; determining a spatial basis tensor containing one or more basis images based on the imaging data; determining one or more time basis tensors based on the imaging data, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; determining a kernel tensor associating the spatial basis tensor with each of the one or more time basis tensors based on the imaging data; and generating at least one of the multiple images by multiplying at least (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) at least a portion of at least one of the one or more time basis tensors.

[0014] According to various aspects of the present disclosure, a system for analyzing a multidimensional image tensor is provided, the multidimensional image tensor containing multiple images of a region of interest of an object, the system comprising: a magnet operable to provide a magnetic field; a transmitter operable to transmit to a region within the magnetic field; a receiver operable to receive a magnetic resonance signal from the region using the magnetic field; and a processor operable to control the transmitter and the receiver. The processor is configured to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; determine a spatial basis tensor containing one or more basis images based on the imaging data; determine one or more time basis tensors based on the imaging data, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; determine a kernel tensor associating the spatial basis tensor with each of the one or more time basis tensors based on the imaging data; and generate at least one of the multiple images by at least multiplying (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) at least a portion of at least one of the one or more time basis tensors.

[0015] According to various aspects of the present disclosure, a non-temporary and machine-readable medium is provided, on which instructions for analyzing a multidimensional image tensor are stored, the multidimensional image tensor containing multiple images of a region of interest of an object, and when the instructions are executed by at least one processor, the instructions cause the at least one processor to: perform one or more imaging scans on the region of interest of the object to obtain imaging data; based on the imaging data, determine a spatial basis tensor containing one or more basis images; based on the imaging data, determine one or more time basis tensors, each of the time basis tensors containing one or more basis functions for a corresponding one of multiple time dimensions; based on the imaging data, determine a kernel tensor associating the spatial basis tensor with each of the one or more time basis tensors; and generate at least one of the multiple images by multiplying at least (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) at least a portion of at least one of the one or more time basis tensors.

[0016] The foregoing and other various aspects and embodiments of the present disclosure will be readily apparent to those of ordinary skill in the art in view of the detailed description of various embodiments and / or implementations given with reference to the accompanying drawings, a brief description of which is provided below. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] The foregoing and other advantages of the present disclosure will become apparent by reading the following detailed description and by referring to the accompanying drawings.

[0018] Figure 1A shows a series of images over time constituting a video in accordance with various aspects of the present disclosure;

[0019] Figure 1B shows an array of images ordered along a time dimension according to various aspects of the present disclosure;

[0020] Figure 2 An image tensor showing a plurality of images containing a region of interest according to various aspects of the present disclosure;

[0021] Figure 3 Decomposing an image tensor of multiple images containing a region of interest into a spatial basis tensor, one or more temporal basis tensors, and a kernel tensor according to various aspects of the present disclosure is shown;

[0022] Figure 4A According to various aspects of the present disclosure, a method for Figure 3 The process of generating an image from the image tensor in;

[0023] Figure 4B According to various aspects of the present disclosure, a method for Figure 3 The process of generating multiple images from the image tensor in ;

[0024] Figure 4C According to various aspects of the present disclosure, a method for Figure 3 The process of generating a plurality of images from the image tensor in , wherein the plurality of images show an area smaller than the area of ​​interest;

[0025] Figure 5 The steps of a method for analyzing a multi-dimensional image tensor containing a plurality of images according to various aspects of the present disclosure are shown; and

[0026] Figure 6 A system for analyzing a multi-dimensional image tensor containing a plurality of images in accordance with various aspects of the present disclosure is shown. DETAILED DESCRIPTION

[0027] Although there are various variations and alternative forms of the present disclosure, some specific implementations and embodiments are shown in the drawings by way of example only, and they will be described in detail herein. However, it should be understood that the present disclosure is not intended to be limited to the specific form disclosed. On the contrary, the present disclosure should cover all variations, equivalents and alternatives falling within the spirit and scope of the present disclosure as defined by the appended claims.

[0028] Although the present disclosure is described with reference to one or more specific embodiments or implementations, it will be appreciated by those skilled in the art that various changes may be made to these embodiments or implementations without departing from the spirit and scope of the present disclosure. Each of these embodiments or implementations and their obvious variations are considered to fall within the spirit and scope of the present disclosure. It is also contemplated that other embodiments or implementations according to various aspects of the present disclosure may be combined with any number of features of any embodiment described herein.

[0029] Magnetic resonance-based imaging (MR imaging) is the most commonly used technique for imaging the human body and takes into account the principle of nuclear magnetic resonance. For example, doctors and other medical professionals often use MR imaging to observe tissues inside the human body. Nuclear magnetic resonance is a phenomenon in which atomic nuclei (for example, protons in human tissue) located in a magnetic field emit energy that can be detected. This detected energy can be used to create an image. MR imaging generally involves two main steps. First, the magnetic moments of the atomic nuclei (which are caused by the intrinsic spin properties of the elementary particles) are aligned (or polarized) due to the presence of an external magnetic field. In the presence of this external magnetic field, the magnetic moment of each atomic nucleus will generally precess about an axis parallel to the magnetic field. The rate of this precession, ω, is generally related to γB. 0 Proportional, here, B 0 is the magnitude of the external magnetic field, and γ is the gyromagnetic ratio of the nucleus, which is the ratio of the magnetic moment of the nucleus to the angular momentum of the nucleus. The rate of precession, ω, is considered to be the resonant frequency of the nucleus.

[0030] The second major step in MR imaging is the application of a sequence of electromagnetic pulses (usually radio frequency or RF pulses) to the nuclei. When the frequency of the RF pulse sequence is roughly equal to the resonant frequency of the nuclei, the nuclei absorb the energy of the RF pulses and the magnetic moments are rotated out of alignment with the magnetic field. The magnetic moments of the excited nuclei eventually realign in the presence of an external magnetic field in a process called relaxation, which has two components. 1 Relaxation describes how the component of the magnetic moment parallel to the external magnetic field returns to its initial value. 2 Relaxation describes how the component of the magnetic moment perpendicular to the external magnetic field returns to its initial value. Because the magnetic moment of the nucleus in the external magnetic field is usually parallel to the external magnetic field without the application of the RF pulse sequence, T 1 Relaxation generally describes how the parallel component of the magnetic moment returns to its maximum value, while T 2 Relaxation generally describes how the perpendicular component of the magnetic moment decays. Nuclei of different materials relax at different rates and therefore emit different signals that can be detected and used to form an image that can be used to identify different materials.

[0031] Quantitative MR imaging is an application of the principles of NMR (Nuclear Magnetic Resonance) that seeks to quantify certain characteristics of the tissue being imaged. For example, a practitioner may wish to quantify T 1 To detect abnormalities such as scar tissue, one may wish to quantify T 2 One may wish to quantify the value of a contrast agent to detect a tumor, one may wish to quantify the speed at which a contrast agent advances through tissue to detect ischemia, or one may wish to quantify diffusion-based features to detect abnormal fibrous structures. There are a variety of techniques that take all of these various parameters into account and are used to obtain images of a region of interest of a subject / patient.

[0032] In order to obtain an image, an MRI device is used to collect imaging data of an object / patient. In one example, the region of interest may be the abdomen or chest of an object. In other examples, the region of interest of an object is more specific, such as the liver, lungs or heart of an object. The imaging data is determined by one or more spatially-varying parameters such as voxel position, contrast agent kinetic parameters or diffusion parameters of the region of interest of the object or is related to the one or more spatially-varying parameters, and the imaging data generally indicates the value or size of the spatially-varying parameters. In some embodiments, the spatially-varying parameters can also be time-varying. In other embodiments, the spatially-varying parameters can be additionally or alternatively related to the physical movement of the region of interest of the object. Other types of biomedical imaging can also be used to obtain multidimensional images, such as CT scans or CAT scans.

[0033] Figure 1A The video 102 showing the heart of a subject from an MRI includes a series of images 104A-104E. The series of images 104A-104E represent cardiac motion and respiration over a period of time. Thus, the series of images 104A-104E show two different time-varying parameters: the phase of the subject's heart within the cardiac cycle; and the position of the subject's lungs within the respiratory cycle. Figure 1B An image tensor 106 (which is a matrix in this example) is shown, which includes multiple images from an MRI that have been separated into multiple time dimensions. The x-axis represents different phases of the heart during the cardiac cycle, while the y-axis represents different positions of the lungs during the respiratory cycle. Thus, each image in a given column has the same value in the time dimension representing cardiac motion, while each image in a given row has the same value in the time dimension representing respiration.

[0034] Figure 2A representation of an image tensor 202 is shown, which includes: an image representing cardiac motion along axis 204A (a time-varying parameter); and an image representing respiratory motion along axis 204B (another time-varying parameter). Thus, axis 204A and axis 204B represent the time dimension. Along axis 204C, the spatial dimension is represented. Each individual image of the region of interest of the object can be two-dimensional or three-dimensional. However, each two-dimensional or three-dimensional image can be reshaped into a vector that combines all of the spatial dimensions. This vector is then placed into a two-dimensional array (which includes cardiac motion on one axis and respiratory motion on another axis) at the appropriate time point. The spatial characteristics of each image in a single column are not necessarily the same as Figure 2 Instead, each column in the image tensor 202 may represent an entire two-dimensional or three-dimensional image of the region of interest at a given point in time (eg, at a given combination of cardiac motion value and respiratory motion value). Figure 2 Also shown are four images contained in image tensor 202. Image 206A corresponds to the image represented by vector 208A. Image 206B corresponds to the image represented by vector 208B. Image 206C corresponds to the image represented by vector 208C. Image 206D corresponds to the image represented by vector 208D.

[0035] This method of sorting images from multidimensional MRI can be extended to any number of different dimensions representing different time-varying parameters. The time-varying parameters may include, but are not limited to: the phase of the subject's heart during the cardiac cycle; the position of the subject's lungs, chest wall, or other organs during the respiratory cycle; the position of the liver's vault during respiration; T 1 Relaxation parameter; reversal time (or other time since magnetization preparation); T 2 Preparation duration (or duration of any magnetization preparation pulse); diffusion weighting intensity; diffusion weighting direction; echo time; dynamic contrast enhancement phase; flip angle; elapsed time since the start of the scan; phase offset of the elastic imaging excitation wave; frequency offset and duration of the saturation preparation pulse (e.g., for chemical exchange saturation transfer); duration of the magnetization transfer preparation pulse; spectral position (e.g., for spectroscopy); flow encoding intensity; or flow encoding direction. Therefore, all images from MRI can be stored in an image tensor having one or more space-varying dimensions and one or more time-varying dimensions. Any given image in the image tensor can show the value of the space-varying parameter on the region of interest that is the imaging target, and can indicate the time period used to collect imaging data and the value of one or more time-varying parameters in the time period.

[0036] As described in some examples, the images are arranged according to common attributes. In another example, the constructed image tensor can have three dimensions. If the image tensor is visualized, the first dimension can be along the x-axis and correspond to the spatial position of the voxels of the image (which is space-varying), and the second dimension can be along the y-axis and correspond to T 1 The third dimension may be along the z-axis and correspond to the position of the chest wall or liver vault during respiration (which is time-varying). In this example, a voxel along the x-axis at a given position along the y-axis and the z-axis will have the same value along both the y-axis and the z-axis, e.g., for each voxel, T 1 The relaxation parameters and the location of the chest wall or liver vault are the same. This is also true for each voxel spaced along the other two dimensions.

[0037] Typically, image tensors are low-rank rather than full-rank. A full-rank tensor is a tensor that produces a full-rank matrix when expanded or flattened along each of its dimensions. A full-rank matrix is ​​a matrix whose rows or columns (the smaller one in number) are linearly independent. A low-rank tensor is a tensor that produces a low-rank matrix when expanded or flattened along at least one of its dimensions. A low-rank matrix is ​​a matrix whose rows and columns are linearly dependent. Regarding image tensors, low-rank tensors are typically image tensors in which space-varying parameters and time-varying parameters can be accurately described with fewer data points than tensor elements. Images in low-rank tensors are usually always linearly independent, which is not necessarily the case for full-rank tensors. Therefore, compared to full-rank tensors, low-rank tensors can be decomposed into smaller factors without causing information loss.

[0038] Image tensors are useful for isolating time-varying properties of interest and ignoring other properties. By only needing to observe images where the time-varying property of interest has changed and other time-varying properties remain constant, a doctor or other healthcare professional can more easily analyze the images. Thus, a patient's cardiac motion can be analyzed at a fixed phase in the respiratory cycle, so that the motion of the lungs does not affect the image of the patient's heart. However, image tensors can easily become too bloated. The number of images in a given image tensor typically grows exponentially with the number of time dimensions, which increases the space required to store the image tensor and the computation time required to analyze the image tensor.

[0039] For example, Figure 1B The image tensor 106 of FIG. 1 only includes five cardiac phases and three respiratory phases, so the image tensor 106 only includes 15 images. However, the number of cardiac phases and respiratory phases is usually higher and often involves more time dimensions. Therefore, a typical image tensor may include images representing 20 cardiac phases, 6 respiratory phases, 200 inversion times, and 5 T2 Preparing images of duration, this would result in 120,000 images. This image tensor would likely require over 100GB of storage space. Furthermore, any image analysis operation on the entire set of images would typically take at least 120,000 times longer to execute than an image analysis operation on a single image.

[0040] Now refer to Figure 3 , image tensor 302 (which may be the same or similar to image tensor 202) can typically be decomposed into a number of tensor factors. Since the images in image tensor 302 are associated with each other, they can typically be modeled as linearly dependent. This makes image tensor 302 low-rank, which means that image tensor 302 can be decomposed or factored. Any number of low-rank tensor decompositions can be used. In some embodiments, Tucker decomposition is used.

[0041] Tucker decomposition decomposes the image tensor 302 into a kernel tensor 304, a spatial basis tensor 306, and the product of a plurality of time basis tensors 308A and 308B. In some embodiments, the spatial basis tensor 306 and the time basis tensors 308A and 308B can be matrices, such as two-dimensional arrays. However, any tensor discussed herein can generally have any number of dimensions, depending on the number of time-varying parameters being measured. Therefore, the image tensor 302 can be represented by the following equation:

[0042]

[0043] In this equation, X i The operator represents the i-th mode product, U X represents the spatial basis tensor 306, represents a time basis tensor 308A, 308B or other time basis tensors, 308B. The spatial basis tensor 306 contains one or more basis images (which are generally considered to be spatial basis functions), while each of the temporal basis tensors 308A, 308B contains one or more basis functions for the time dimension (e.g., for each time-varying parameter of the object). The kernel tensor 304 associates the spatial basis tensor 306 with each of the temporal basis tensors 308A and 308B. Depending on the complexity of the time-varying parameters of the object, the number of basis functions required to accurately describe all images may vary. For example, images from a patient with simple cardiac motion are likely to require fewer basis functions for the temporal basis tensor associated with the cardiac motion than images from a patient with complex cardiac motion.

[0044] Typically, the number of elements in the decomposed basis tensor is far less than the total number of elements in the image tensor itself. The number of elements typically grows linearly with the number of time dimensions, rather than exponentially. As a result, basis and core tensors require less memory space to store and less computation time to analyze.

[0045] In some embodiments, when a low-rank tensor model is used for image reconstruction, the basis tensors are known, and the basis tensors may never even be multiplied to form the image tensor. In this case, compression based on tensor decomposition is typically already performed, and such compression based on tensor decomposition may be lossless. In other embodiments, only the entire image tensor is known, in which case a tensor decomposition algorithm such as high-order singular value decomposition (HOSVD) can be applied, and the tensor decomposition algorithm can be truncated to produce a small tensor factor. In this case, compression may be lossy.

[0046] In one example of space savings obtained by decomposition, an image tensor may be stored as a 20×6×5×5 kernel tensor, a spatial basis tensor containing 50 basis images, a first time basis tensor containing 20 basis functions related to cardiac phase, a second time basis tensor containing 6 basis functions related to respiratory phase, a third time basis tensor containing 5 basis functions related to inversion time, and a fourth time basis tensor containing 10 basis functions related to T phase. 2 Prepare a fourth time basis tensor of 5 basis functions related to duration. If the time dimension generally has the same number of values ​​as discussed in the previous example, the first time basis tensor includes 20 basis functions × 20 cardiac positions = 400 elements; the second time basis tensor includes 6 basis functions × 6 respiratory positions = 36 elements; the third time basis tensor includes 5 basis functions × 200 inversion times = 500 elements; the fourth time basis tensor includes 5 basis functions × 5 T 2 Preparation duration = 25 elements. In this example, both the base tensor and the core tensor may have a storage requirement of only about 200MB. In addition, other established compression algorithms (e.g., JPEG, ZIP, or any other suitable compression algorithm) can also be used to compress the respective base tensors.

[0047] In some embodiments, the image tensor 302 is only partially decomposed, or is fully decomposed, and then more than two of the core tensor and the basis tensor are premultiplied. For example, premultiplying the core tensor with one or some of the time basis tensors in each time basis tensor may improve storage efficiency. It may also be preferred to premultiply the core tensor with all of the time basis tensors in each time basis tensor to save computation time during analysis, even if doing so does not save much storage space. In general, any combination of the core tensor, the spatial basis tensor, and the time basis tensor can be premultiplied to minimize storage requirements, minimize the computation time required during analysis, or minimize some combination of the two.

[0048] Now refer to Figure 4A-4C , the selective multiplication of a kernel tensor, a spatial basis tensor, and one or more temporal basis tensors can be used to generate an arbitrary image of a region of interest as part of a complete image tensor. Figure 4A The process for generating the desired image stored in the image tensor 402 is shown. The desired image is represented by the vector a 0 Indicates that the vector a 0 is a vector of spatial dimensions (e.g., an image of a region of interest) at a desired point in time. Image tensor 402 shows only two temporal dimensions, although image tensor 402 may also take into account any suitable number of temporal dimensions. By multiplying spatial basis tensor 404 by a single vector v of modified temporal basis tensor 406 0 , to generate the desired image. The modified time basis tensor 406 is determined by multiplying the kernel tensor with one or some or all of the time basis tensors. In other embodiments, one or some or all of such multiplications may be pre-multiplications, for example, performed when the image is initially generated during the MRI process, rather than later when the image is needed. In other embodiments, one or some or all of the multiplications used to obtain the modified time basis tensor 406 are performed in real time. The vector representation of the modified time basis tensor 406 used shows the image vector a 0 The result of this multiplication is a single image of the region of interest at the desired time point.

[0049] Figure 4B A process for generating multiple images of a region of interest that allows at least one temporal dimension to vary is shown. Figure 4B Overall, it shows Figure 4A A similar process. However, multiple images are represented by the matrix A 0 Represented by a single vector a 0 As shown in the figure, the matrix A 0The multiple images in the image tensor 402 represented by 404 all have the same value along one time dimension ("time 2"), but have different values ​​along another time dimension ("time 1"). The spatial basis tensor 404 is multiplied by a slice V of the modified temporal basis tensor 406. 0 . Slice V 0 The matrix A is composed of the image tensor 402 0 The images in are taken from the modified time basis tensor 406 at the same time points as the time points represented by the images in . In general, multiple images can be generated using any given subset of the modified time basis tensor 406. In one example, when any motion due to breathing remains constant, for example, when the chest is in the same position, the set of images can represent the changing phase of the subject's heart during the cardiac cycle.

[0050] Figure 4C A process for generating multiple images of an area smaller than the area of ​​interest is shown. Figure 4C The process and Figure 4B The process is similar to that of , except that only a subset of the spatial basis tensor 404 corresponding to the desired region is used. Although not shown, the subset of the spatial basis tensor 404 can be multiplied by a single vector of the modified temporal basis tensor 406 (e.g., Figure 4A Thus, in general, any single image or set of images can be generated from the kernel tensor, the spatial basis tensor, and the temporal basis tensor by multiplying the kernel tensor with the appropriate portion of the spatial basis tensor and the appropriate portion of the temporal basis tensor.

[0051] This selective multiplication can be used on demand to generate images at the request of the user. In one example, the user interface includes sliders for each time dimension. The user can move the sliders to generate and observe images for any combination of values ​​of the time dimensions. In some embodiments, each image is generated only when requested by the user. In other embodiments, multiple images along a single time dimension can be generated based on the user's first interaction with the corresponding slider to generate a single image, and can be generated based on the assumption that the user wants to continue observing images along the time dimension.

[0052] Other processes can be used to analyze the spatial basis tensor and the temporal basis tensor. These processes can directly analyze or process the basis tensor instead of directly analyzing or processing the entire set of images. In one example, multiplanar reconstruction can be used, which is the reconstruction of an image volume along arbitrarily oriented slices. Typically, this reconstruction would be performed for each image in the image tensor, or would be performed for each image selected for display. However, since this is purely spatial processing, the basis images in the spatial basis tensor can be directly reconstructed before the selective multiplication. Because there are far fewer images in the spatial basis tensor, this is much faster than performing multiplanar reconstruction on individual images.

[0053] In some embodiments, the basis images in the spatial basis tensor are pre-processed to modify spatial characteristics, such as the spatial orientation of the basis images. This enables reconstruction of images along arbitrarily oriented slices. Other types of spatial characteristics can also be modified. In other embodiments, the temporal basis functions of the temporal basis tensor can be directly temporally processed to modify the temporal characteristics of the temporal basis functions. In still other embodiments, machine learning-based analysis can be used directly on the basis tensors without having to fully multiply the tensors.

[0054] Now refer to Figure 5 , shows a method 500 for analyzing a multidimensional image tensor that includes multiple images of a region of interest of an object. In step 502, one or more imaging scans are performed to obtain a multidimensional image tensor. The imaging scans described above produce imaging data that are used to generate the multidimensional image tensor. The imaging scan is typically an MRI scan, although other scans such as CT scans and CAT scans may also be used. To collect the imaging data, a sequence of RF (radio frequency) pulses is applied to the region of interest of the object. The resulting signals are then measured. Thus, the multidimensional image tensor may be obtained by using a method for measuring T 1 Relaxation saturation recovery pulse, used to measure T 2 Relaxed T 2 The RF pulse sequence is designed to be a preparation pulse, or any other specific pulse sequence for measuring a specific space-varying parameter or a combination of space-varying parameters. There is usually a pause after each RF pulse in the RF pulse sequence to allow the generated signal to be measured. In some embodiments, imaging data is collected in a semi-continuous mode. In this semi-continuous mode, the RF pulse sequence also includes an additional time for T 1 The pause of signal recovery (because the measurement will make T 1 In other embodiments, imaging data is collected in a continuous mode in which the applied RF pulse sequence is not paused to allow T 1The signal is restored and only a pause is included to allow the measurement of the generated signal. In either embodiment, the applied RF pulse sequence is not paused to wait for any specific breathing position, but the subject is allowed to breathe freely.

[0055] At step 504, as part of the decomposition process, a spatial basis tensor is determined. The spatial basis tensor contains one or more basis images representing the spatial dimensions. The spatial basis tensor represents all possible values ​​of the spatial dimensions in the image. At step 506, one or more time basis tensors are determined. Each time basis tensor contains one or more basis functions for the corresponding time dimension. Therefore, one time basis tensor may contain one or more basis functions related to cardiac motion, while another time basis tensor contains one or more basis functions related to respiratory motion. The time basis tensor represents all possible values ​​of each time dimension in the image. The time dimension may include the phase of the subject's heart within the cardiac cycle, the position of the subject's lungs within the respiratory cycle, the inversion time of the MRI imaging sequence, and the T of the MRI imaging sequence. 2 Prepare for duration.

[0056] At step 508, a kernel tensor is determined. The kernel tensor associates a spatial basis tensor with each of one or more time basis tensors. At step 510, the kernel tensor is premultiplied with at least one time basis tensor to produce a modified time basis tensor. The premultiplication of the kernel tensor and at least one of the one or more time basis tensors is typically configured to minimize or reduce: (i) the computational time required to generate at least one of the multiple images, (ii) the amount of storage required to store the kernel tensor and at least one of the one or more time basis tensors, or (iii) both (i) and (ii). In some embodiments, the modified time basis tensor is generated by premultiplying the kernel tensor with all time basis tensors. In other embodiments, the modified time basis tensor is generated by premultiplying the kernel tensor with one or more time basis tensors.

[0057] At step 512, the spatial basis tensor and the modified time basis tensor are stored. At step 514, at least one of the multiple images from the image tensor is generated by multiplying at least a portion of the spatial basis tensor, at least a portion of the modified time basis tensor, and any other necessary tensors. In some embodiments, the modified time basis tensor is generated by premultiplying a core tensor with all time basis tensors. In this embodiment, the image is generated by multiplying only at least a portion of the spatial basis tensor with at least a portion of the modified time basis tensor. In other embodiments, the time basis tensor includes a first group and a second group, and the modified time basis tensor is generated by premultiplying the core tensor with the time basis tensor of only the first group. In this embodiment, the image is generated by multiplying at least a portion of the spatial basis tensor, at least a portion of the modified time basis tensor, and at least a portion of the second group of time basis tensors.

[0058] To generate a single image, the spatial basis tensor and the vector of the modified time basis tensor are multiplied. If the time basis tensor is created by pre-multiplying with fewer time basis tensors than all time basis tensors, the corresponding vectors of each of the remaining time basis tensors are also included in the selective multiplication. The vector represents the value of the time dimension at the time point of the desired image. To generate multiple images, the spatial basis tensor and a subset of the modified time basis tensor (and the corresponding subsets of any remaining time basis tensors) are multiplied. The modified time basis tensor and the subsets of any remaining time basis tensors represent the value of the time dimension for each time point covered by the multiple images. In any of these embodiments, it is possible to generate (one or more) images (and thereby collect data) that are smaller than the entire area of ​​interest of the imaged object by multiplying only a subset of the spatial basis tensor.

[0059] In some embodiments, a multidimensional image tensor is not generated or derived from the imaging data. Instead, a spatial basis tensor, a temporal basis tensor, and a kernel tensor are directly generated or derived from the imaging data. In other embodiments, no premultiplication of any basis tensor is performed, and instead, an image is generated by multiplying a kernel tensor, at least a portion of a spatial basis tensor, and at least a portion of one or more temporal basis tensors.

[0060] Various aspects of the present disclosure can be implemented using a variety of hardware. Figure 6Such an embodiment is shown in . A system 600 for performing magnetic resonance imaging on an object includes an imaging device 602 and a processing device 612. The imaging device 602 can be a device for standard magnetic resonance imaging, and can include a primary magnet 604, a gradient coil 606, an RF transmission system 608, and an RF receiving system 610. The primary magnet 604 can be a permanent magnet, an electromagnet (e.g., a coil), or any other suitable magnet. The primary magnet 604 is used to generate an external magnetic field applied to the sample during imaging. The gradient coil 606 generates a secondary magnetic field that distorts the above-mentioned external magnetic field and can cause the resonant frequency of the protons in the sample to vary with position. Therefore, the gradient coil 606 can be used to spatially encode the position of the protons in the entire sample, for example, it can be used to select which plane intersecting the sample will be used for imaging. The RF transmission system 608 is used to apply an RF pulse sequence that provides energy to the protons in the sample to rotate their magnetic moments so as to misalign with the external magnetic field and saturate the solute material with protons. The RF transmit system 608 typically includes a frequency generator (e.g., an RF synthesizer), a power amplifier, and a transmit coil. The RF receive system 610 receives signals emitted by the protons in the sample as they relax back to their standard alignment. The RF receive system 610 may include a receive coil that receives the emitted signals and a preamplifier that enhances the received signals and ensures that the signals are suitable for processing. In some embodiments, the RF receive system 610 may include a signal processing component that processes the received signals to provide data that can be used by a processing device 612. The various components of the imaging device can be disposed within a housing or within multiple housings.

[0061] The processing device 612 can be communicatively connected to the imaging device 602, and the processing device 612 can include a processor 614, a memory 616 that the processor can operate, a display 618, and a user input device 620. The processing device 612 is used to manage the operation of the imaging device 602, and can therefore be configured to cause the imaging device 602 to perform multi-dimensional imaging according to the principles disclosed herein. The system 600 can also include one or more additional processing devices so that various tasks required when performing multi-dimensional imaging can be performed by different processing devices. For example, the system 600 can include other processing devices or systems that analyze imaging data and reconstruct images from imaging data. The system 600 can also include one or more printers, one or more network interfaces, or one or more other types of hardware.

[0062] In some embodiments, a non-transitory machine-readable medium has instructions stored on the medium for implementing any method or any process discussed herein. The machine processor is configured to execute the instructions to implement these methods or processes.

[0063] Aspects of the present disclosure can be implemented on various types of processing devices, such as general purpose computer systems, microprocessors, digital signal processors, microcontrollers, application specific integrated circuits (ASICs), programmable logic devices (PLDs), field programmable logic devices (FPLDs), programmable gate arrays (PGAs), field programmable gate arrays (FPGAs), mobile devices (such as mobile phones, personal digital assistants (PDAs) or tablet computers, etc.), local servers, remote servers, or wearable computers, etc.

[0064] The memory storage device of one or more processing devices may include a machine-readable medium on which is stored one or more sets of instructions (e.g., software) that can embody any one or more of the methods or functions described herein. These instructions can also be transmitted or received over a network via a network transceiver. Although the machine-readable medium can be a single medium, the term "machine-readable medium" should be considered to include a single medium or multiple media (e.g., a centralized or distributed database; and / or associated caches and servers) storing one or more sets of instructions. The term "machine-readable medium" may also be considered to include any medium that can store, encode, or carry a set of instructions executed by a machine and cause the machine to perform any one or more methods of various embodiments, or it can store, encode, or carry a data structure used by or associated with the set of instructions. Thus, the term "machine-readable medium" may be considered to include, but is not limited to, solid-state memory, optical media, and magnetic media. As memory(s), various different types of memory storage devices may be used, such as: a random access memory (RAM) or a read-only memory (ROM) in the system; or a floppy disk, a hard disk, a CD ROM, a DVD ROM, a flash memory; or other computer-readable media that is read and / or written by a magnetic, optical or other form of reading and / or writing system connected to the processing device.

[0065] Although various aspects of the present disclosure have been described with reference to one or more specific embodiments, it will be appreciated by those skilled in the art that many changes may be made to the present disclosure without departing from the spirit and scope of the present disclosure. These embodiments and their obvious variations are considered to fall within the spirit and scope of the present disclosure. It is also contemplated that additional embodiments according to various aspects of the present disclosure may be combined with any number of features of any embodiment described herein.

[0066] References

[0067] The following documents are provided to explain various aspects of the present invention. The contents of each of these documents are incorporated herein by reference in their entirety.

[0068] 1. Christodoulou, AGet al. Magnetic resonance multitasking for motion-resolved quantitative cardiovascular imaging. Nature Biomed Eng 2, 215-226, doi:10.1038 / s41551-018-0217-y(2018).

[0069] 2.Feng,L.et al.XD-GRASP:Golden-angle radial MRI with reconstruction of extra motion-state dimensions using compressed sensing.Magn Reson Med 75,775-788(2016).

[0070] 3.Cheng,JYet al.Comprehensive multi-dimensional MRI for thesimultaneous assessment of cardiopulmonary anatomy and physiology.Sci Rep 7,5330(2017).

[0071] 4.Liang,Z.-P.in Proc IEEE Int Symp Biomed Imaging,988-991(2007)

[0072] 5.Tucker,L.R.Some mathematical notes on three-mode factoranalysis.Psychometrika 31,279-311(1966).

[0073] 6.De Lathauwer,L.,De Moor,B.&Vandewalle,J.A multilinear singularvalue decomposition.SIAM J Matrix Anal Appl 21,1253-1278(2000).

Claims

1. A method for analyzing imaging data associated with a region of interest of an object, the method comprising: Obtaining from the imaging data or the associated images: (i) a spatial basis tensor comprising one or more basis images; (ii) a plurality of time basis tensors, each of the time basis tensors comprising one or more basis functions for a respective one of a plurality of time dimensions; and (iii) a kernel tensor associating the spatial basis tensor with each of the one or more time basis tensors; and generating a plurality of images by multiplying (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) only a portion of the plurality of temporal basis tensors, Wherein, the portion of the multiple time basis tensors includes at least a first time basis tensor and does not include at least a second time basis tensor, the first time basis tensor includes the one or more basis functions for a first time dimension among the multiple time dimensions, and the second time basis tensor includes the one or more basis functions for a second time dimension among the multiple time dimensions, so that the multiple images display the region of interest when at least the first time dimension changes over time and at least the second time dimension remains unchanged.

2. The method according to claim 1, wherein: The spatial basis tensor, the multiple time basis tensors, and the core tensor are obtained in any order.

3. The method according to claim 1, wherein: The plurality of time basis tensors further include at least a third time basis tensor comprising the one or more basis functions for a third time dimension of the plurality of time dimensions.

4. The method according to claim 3, wherein: The portion of the multiple time dimensions used to multiply to generate the multiple images also includes the third time dimension, so that the multiple images display the region of interest when (i) the first time dimension and the third time dimension change over time and (ii) the second time dimension remains unchanged.

5. The method according to claim 3, wherein: The portion of the multiple time dimensions used for multiplication to generate the multiple images also does not include the third time dimension, so that the multiple images display the region of interest when (i) the first time dimension changes over time and (ii) the second time dimension and the third time dimension remain unchanged.

6. The method according to claim 1, wherein: Generating the plurality of images comprises: multiplying the core tensor and at least a portion of the plurality of time basis tensors to produce a modified time basis tensor; and multiplying at least the portion of the spatial basis tensor and at least a portion of the modified temporal basis tensor to generate the plurality of images, wherein: (i) the modified time basis tensor includes at least the first time basis tensor and the second time basis tensor, and the portion of the modified time basis tensor that includes only the first time basis tensor and does not include the second time basis tensor is used for multiplication to generate the plurality of images, or (ii) the modified time basis tensor includes at least the first time basis tensor and does not include at least the second time basis tensor, and only the portion of the modified time basis tensor that includes the first time basis tensor is used for multiplication to generate the plurality of images, or (iii) the modified time basis tensor includes at least the first time basis tensor and does not include at least the second time basis tensor, and all the modified time basis tensors are used for multiplication to generate the multiple images.

7. The method according to claim 1, wherein: Generating the image includes multiplying the kernel tensor, the portion of the plurality of time basis tensors, and one of: (i) all of the spatial basis tensors, such that the plurality of images display all of the regions of interest, or (ii) only a portion of the spatial basis tensor, such that the plurality of images only display a portion of the region of interest.

8. The method according to claim 1, wherein: The portion of the spatial basis tensor used for multiplication includes at least one basis image among the one or more basis images, and wherein the method further comprises: before generating the multiple images, preprocessing the spatial basis tensor to modify the at least one basis image among the one or more basis images so that the multiple images are reconstructed along a desired plane.

9. The method of claim 1, further comprising preprocessing at least the first time basis tensor to modify a temporal characteristic of the one or more basis functions of at least the first time basis tensor.

10. The method according to claim 1, wherein: The multiple time dimensions include the phase of the subject's heart within the cardiac cycle, the position of the subject's lungs within the respiratory cycle, the position of the liver's vault during respiration, inversion time, time since magnetization preparation, T2 preparation duration, duration of a magnetization preparation pulse, diffusion weighted intensity, diffusion weighted direction, echo time, dynamic contrast enhancement phase, flip angle, elapsed time since the start of the scan, phase offset of an elastic imaging excitation wave, frequency offset of a saturation preparation pulse, duration of a saturation preparation pulse, duration of a magnetization transfer preparation pulse, spectral position, flow encoding intensity, or flow encoding direction.

11. A processing device for analyzing imaging data related to a region of interest of an object, the processing device comprising: a processor-operable memory having instructions stored thereon; and A processor configured to execute the instructions to: Obtaining from the imaging data or associated images: (i) a spatial basis tensor comprising one or more basis images; (ii) a plurality of temporal basis tensors, each of the temporal basis tensors comprising one or more basis functions for a respective one of a plurality of temporal dimensions; and (iii) a kernel tensor associating the spatial basis tensor with each of the one or more temporal basis tensors; and generating a plurality of images by multiplying (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) only a portion of the plurality of temporal basis tensors, Wherein, the portion of the multiple time basis tensors includes at least a first time basis tensor and does not include at least a second time basis tensor, the first time basis tensor includes the one or more basis functions for a first time dimension among the multiple time dimensions, and the second time basis tensor includes the one or more basis functions for a second time dimension among the multiple time dimensions, so that the multiple images display the region of interest when at least the first time dimension changes over time and at least the second time dimension remains unchanged.

12. The processing device according to claim 11, wherein: The spatial basis tensor, the multiple time basis tensors, and the core tensor are obtained in any order.

13. The processing device according to claim 11, wherein: The plurality of time basis tensors further include at least a third time basis tensor comprising the one or more basis functions for a third time dimension of the plurality of time dimensions.

14. The processing device according to claim 13, wherein: The portion of the multiple time dimensions used to multiply to generate the multiple images also includes the third time dimension, so that the multiple images display the region of interest when (i) the first time dimension and the third time dimension change over time and (ii) the second time dimension remains unchanged.

15. The processing device according to claim 13, wherein: The portion of the multiple time dimensions used for multiplication to generate the multiple images also does not include the third time dimension, so that the multiple images display the region of interest when (i) the first time dimension changes over time and (ii) the second time dimension and the third time dimension remain unchanged.

16. A non-transitory, machine-readable medium having stored thereon instructions for analyzing imaging data associated with a region of interest of a subject, which instructions, when executed by at least one processor, cause the at least one processor to: Obtaining from the imaging data or associated images: (i) a spatial basis tensor comprising one or more basis images; (ii) a plurality of temporal basis tensors, each of the temporal basis tensors comprising one or more basis functions for a respective one of a plurality of temporal dimensions; and (iii) a kernel tensor associating the spatial basis tensor with each of the one or more temporal basis tensors; and generating a plurality of images by multiplying (i) the kernel tensor, (ii) at least a portion of the spatial basis tensor, and (iii) only a portion of the plurality of temporal basis tensors, in, The portion of the multiple time basis tensors includes at least a first time basis tensor and does not include at least a second time basis tensor, the first time basis tensor includes the one or more basis functions for a first time dimension among the multiple time dimensions, and the second time basis tensor includes the one or more basis functions for a second time dimension among the multiple time dimensions, so that the multiple images display the region of interest when at least the first time dimension changes over time and at least the second time dimension remains unchanged.

17. The non-transitory, machine-readable medium of claim 16, wherein: The spatial basis tensor, the multiple time basis tensors, and the core tensor are obtained in any order.

18. The non-transitory, machine-readable medium of claim 16, wherein: The plurality of time basis tensors further include at least a third time basis tensor comprising the one or more basis functions for a third time dimension of the plurality of time dimensions.

19. The non-transitory, machine-readable medium of claim 18, wherein: The portion of the multiple time dimensions used to multiply to generate the multiple images also includes the third time dimension, so that the multiple images display the region of interest when (i) the first time dimension and the third time dimension change over time and (ii) the second time dimension remains unchanged.

20. The non-transitory, machine-readable medium of claim 18, wherein: The portion of the multiple time dimensions used for multiplication to generate the multiple images also does not include the third time dimension, so that the multiple images display the region of interest when (i) the first time dimension changes over time and (ii) the second time dimension and the third time dimension remain unchanged.

Images