WO2005026765A1 - Imagerie par rm dynamique a reconstruction contrainte a l'aide d'un algorithme pocs - Google Patents

Imagerie par rm dynamique a reconstruction contrainte a l'aide d'un algorithme pocs Download PDF

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Publication number
WO2005026765A1
WO2005026765A1 PCT/GB2004/003998 GB2004003998W WO2005026765A1 WO 2005026765 A1 WO2005026765 A1 WO 2005026765A1 GB 2004003998 W GB2004003998 W GB 2004003998W WO 2005026765 A1 WO2005026765 A1 WO 2005026765A1
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image data
image
data items
space
fourier
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PCT/GB2004/003998
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English (en)
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Andreas Degenhard
Mark James White
Martin Osmund Leach
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The Institute Of Cancer Research; Royal Cancer Hospital
The Royal Marsden Nhs Foundation Trust
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Publication of WO2005026765A1 publication Critical patent/WO2005026765A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
    • G01R33/48—NMR imaging systems
    • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
    • G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution
    • G01R33/561—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution by reduction of the scanning time, i.e. fast acquiring systems, e.g. using echo-planar pulse sequences
    • G01R33/5619—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution by reduction of the scanning time, i.e. fast acquiring systems, e.g. using echo-planar pulse sequences by temporal sharing of data, e.g. keyhole, block regional interpolation scheme for k-Space [BRISK]
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R33/00—Arrangements or instruments for measuring magnetic variables
    • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
    • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
    • G01R33/48—NMR imaging systems
    • G01R33/54—Signal processing systems, e.g. using pulse sequences ; Generation or control of pulse sequences; Operator console
    • G01R33/56—Image enhancement or correction, e.g. subtraction or averaging techniques, e.g. improvement of signal-to-noise ratio and resolution

Definitions

  • the present invention relates to methods and apparatus 5 for the processing of image data in the reconstruction of images and particularly, though not exclusively, to the reconstruction of Nuclear Magnetic Resonance (NMR) images for use in a series of such images representing changes or dynamics within an imaged object or article.
  • NMR Nuclear Magnetic Resonance
  • 10 Nuclear Magnetic Resonance (NMR) imaging enables internal portions of a human or animal body to be imaged non- invasively.
  • the phenomenon of NMR occurs when a magnetic field B is applied to an object to be imaged. In the 15 presence of the applied magnetic field B, the intrinsic nuclear spin of atomic nuclei of the material of the object are caused to precess around the direction of the magnetic field B.
  • the frequency of nuclear spin precession is known as the Larmor frequency ( ⁇ )and is given by ⁇ — ⁇ B where the constant of proportionality ( ⁇ ) is the gyromagnetic ratio of the nucleus and is distinctive of each atomic nucleus type. Because those nuclear spins aligned with 25 components of spin parallel to the direction of the magnetic field B reside in a lower energy state than those nuclei aligned with components of spin anti- parallel to B, the result is that marginally more nuclei will align in a direction parallel to that of B. Thus, 30 the nuclei of the material of the object become partially spin polarised and therefore the material exhibits a net spin density per unit volume, p(x,y, z), pointing in the direction of the magnetic field B.
  • the Larmor frequency (cy)of a given nucleus is typically shifted from the expected value ⁇ - ⁇ B due to the influence of the electron cloud of the atom or molecule within which the precessing nucleus resides.
  • the effect of the electron cloud is to partially shield the precessing nucleus from the applied magnetic field B.
  • These properties are applied in NMR imaging by causing the nuclei of the material of an imaged object to precess about an applied magnetic field B. This precession is detected, at various parts of the imaged object, as a varying magnetic field signal which oscillates at the shifted Larmor frequency ( ⁇ ) oi the portion of the object being imaged.
  • gradient fields vary linearly in the x, y and z directions of space and cause the precession frequency of the imaged object to vary from its already shifted Larmor frequency ( ⁇ )as a function of the position of a precessing nucleus within the object. It can be shown that, if we denote the derivatives of the gradient fields in the x, y and z directions as G x , G y and G 2 respectively, then the modulated signal A(t) received at the detector of the NMR device will be given by:
  • k — (k x ,k y ,k z ) is the spatial frequency vector of the spin density function in Fourier-Space.
  • NMR imaging methods while often providing adequate spatial resolution and contrast when imaging a static or unvarying object typically have image data acquisition procedures insufficiently rapid to enable a series of images to be taken in rapid succession.
  • spatial image resolution may be adequate
  • temporal image resolution is inadequate in accurately representing changes or dynamics within an imaged object over a period of time.
  • NMR imaging applications such as cardiac imaging
  • cardiac imaging involve a collection of a time series of 2D images or 3D images (volumes) to monitor the dynamic process/changes occurring within an imaged object.
  • 3D images volumes
  • sampling schemes which differ from one another principally in the distribution of the data sampled in Fourier-Space. Such sampling schemes commonly fall into one of two categories of sampling strategy being: asymmetric sampling; or, symmetric sampling.
  • Asymmetric sampling techniques include "half Fourier" sampling techniques in which only image data residing in one half of Fourier-Space are sampled, the data residing in the other half of Fourier-Space being regarded as redundant due to the Hermitian symmetry exhibited within this representation.
  • asymmetric sampling techniques provide a resulting image of higher quality than that provided by symmetric sampling techniques. This is because asymmetric techniques do intrinsically contain additional sampled data apart from the central portion.
  • symmetric data sampling techniques typically permit a much greater reduction of sampling because the bulk of the data resides in the central region of Fourier-Space, and can achieve much higher temporal resolution than is generally to be expected from asymmetric sampling methods.
  • the present invention aims to overcome at least some of the deficiencies inherent in existing asymmetric and symmetric sampling techniques so as to provide an efficient sampling strategy which permits increased temporal image resolution while at least to some extent reversing the reduction in spatial image resolution that would otherwise be expected.
  • the invention proposed is to employ image reconstruction for estimating high spatial resolution data for an image sampled only at low spatial resolution, by the aligned incorporation of high resolution data from a reference image obtained separately.
  • Aligned incorporation of high resolution data means that not only is high resolution data incorporated, but that it is also adjusted or modified during incorporation using information regarding the image data into which it is being incorporated to make predetermined properties of the former data more closely match or approximate the corresponding properties of the latter data.
  • the present invention in any of its aspects, is not limited in its application to the processing of image data for Magnetic Resonance Imaging, but may be applied to any image data derived in any way representing any article/object or measurement, such as images resulting from spectroscopic or crystallographic measurements or the like.
  • the present invention may provide a method of processing image data for use in the reconstruction of an image (e . g. representing an object or otherwise) , the image data comprising complex-valued data items possessing an amplitude component and a phase component, the method comprising the steps of: (a) generating image data items for a first image of the object including only low spatial resolution image data items which represent the object at low image resolution; (b) generating image data items for a second image of the object including low spatial resolution image data items which represent the object at low spatial image resolution and high spatial resolution image data items which represent the object at high image resolution; (c) modifying said phase component or said amplitude component of image data items generated in step (b) according to low spatial resolution image data items generated in step (a) thereby to estimate high spatial resolution image data for use in reconstructing said first image at high spatial resolution.
  • Such modification could involve replacing the phase or amplitude component with a replacement phase/amplitude component, or it could involve modifying (e.g. by addition/subtraction/
  • step (c) may comprise modifying image data items generated in step (b) by replacing (or adding to, subtracting from, or multiplying/scaling) said phase component or said amplitude component thereof with a replacement (or modification) phase component or a replacement (or modification) amplitude component respectively derived from low spatial resolution image data ite s ⁇ generated in step (a) .
  • Possible modifications to image data include truncation, where amplitude components greater than a predetermined or calculated threshold value are made equal to that threshold value; another modification includes phase unwrapping, wherein a variable multiple of 2 ⁇ is added to the phase image to produce smooth rather than cyclic changes.
  • the completely sampled amplitude data of a high resolution reference image is caused to be forced or aligned towards a phase value or an amplitude value estimated from or corresponding to the phase or amplitude of the low spatial resolution image acquired by a reduced sampling method.
  • This estimation procedure may be used at least as a first step in a series of processing steps used to reconstruct the low resolution image to high spatial resolution as will be described further below.
  • phase or amplitude modification may take place at step (c)
  • both phase and amplitude modification may take place at step (c) .
  • Replacement of image data components may take place in such "modification” e.g. phase and/or amplitude component replacement. Modification may be made to all or only some of the image data items generated in step (b) .
  • Spatial resolution of an image refers to the degree of discernible detail within the image, that is to say, the degree of
  • references to “high or low spatial resolution image data items” are references to data (whether in Real-Space or in another space such as Fourier-Space) which, when used in the formation of an image in Real-Space, produce features within that image at correspondingly "high” or “low” spatial resolution.
  • low spatial resolution image data is acquired by sampling image data items from within a range of spatial frequency values which resides inside the range of spatial frequency values from which the high spatial resolution reference image data items are sampled.
  • the spatial frequency (k) of each image data element generated in step (b) each resides within a first range of values
  • the spatial frequency (k) of each image data element generated in step (a) each resides within a second range of values which is smaller than and is included within the first range of values.
  • the smaller range of values is preferably a sub-range arranged in the centre of the larger first range of values.
  • the first range of values and the second range of values are each substantially centred upon a common spatial frequency (k) value.
  • the image data items corresponding to the low spatial resolution image are preferably sampled centrally from a sub-range of values centred around the larger range of spatial frequency values from which the high spatial resolution reference image data items are sampled.
  • the smaller sub-region need not be centred upon the middle of the larger range enclosing it.
  • the invention in its first aspect may at least represent the first step or series of steps in a larger image reconstruction method according to the present invention.
  • steps (b) and (c) are preferably to be repeated a number of times wherein each repetition of the two consecutive steps occurs alternately in Image Space and in Fourier-Space. It has been found that through this procedure the alignment of the phase component (or the approximation of the amplitude component) of image data items being processed converges towards the phase (or amplitude) components of image data items generated in step (a) .
  • spaces other than Fourier-Space may be employed in the present invention in any of its aspects.
  • wavelet transformations or nonlinear embeddings could be employed in place of the Fourier transformations referred to herein.
  • the image data items generated in step (b) may represent the second image in: Image Space wherein the phase component or amplitude component is modified (e.g. replaced) in Image Space; or, Fourier-Space wherein the phase component or amplitude component is modified (e . g. replaced) in Fourier-Space.
  • image data items generated in step (a) represent the first image in Fourier-Space.
  • the method preferably involves the procedure whereby the image data items are data items previously generated in steps (b) and (c) and represent the second image in Image Space, the method may then comprise the steps of: (I) performing step (b) by transforming the image data items from Image Space to Fourier-Space; and, in respect of image data items so generated; (II) performing step (c) by modifying (e.g. replacing) the phase or amplitude component of the image data items in Fourier-Space according to low resolution image data items generated in step (a) .
  • the modifying step may involve replacing the phase component or the amplitude component of step (b) image data items with a replacement phase/amplitude component derived from low resolution step (a) image data items.
  • one cycle of steps (b) and (c) may take the Image Space results of previous steps (b) and (c) , transform those results into Fourier-Space and effect phase modification or amplitude modification (e.g. replacement! in that space to produce image data items which may subsequently be employed in a further repetition of steps (b) and (c) .
  • phase modification or amplitude modification e.g. replacement! in that space to produce image data items which may subsequently be employed in a further repetition of steps (b) and (c) .
  • the resultant image data items may then be transformed back into Image-Space.
  • successive steps (b) and (c) may be initiated using the Fourier-Space data.
  • the method preferably employs the procedure whereby the image data items are data items previously generated in steps (b) and (c) and represent the second image in Fourier-Space, the method may then comprise the steps of: (III) performing step (b) by transforming the image data items from Fourier-Space to Image Space; and, in respect of image data items so generated, (IV) performing step (c) by modifying (e.g. replacing) the phase or amplitude component of the image data items in image space according to low spatial resolution image data items generated in step (a) .
  • the modifying step may involve replacing the phase component or the amplitude component of step (b) image data items with a replacement phase/amplitude component derived from low resolution step (a) image data items .
  • the Fourier-Space results of previous steps (b) and (c) such as resulting from steps (I) and (II) discussed above may be employed in a subsequent repetition of steps (b) and (c) in Image Space.
  • This procedure of amplitude or phase modification (e.g. replacement) alternately in Fourier-Space and Image Space may be applied repetitively and iteratively in order to cause the phase component (or amplitude component) of the resulting image data items to be forced or aligned towards the phase component (or to more closely approximate the amplitude component) of image data items generated in step (a) to any desired degree of convergence .
  • the present invention in its first aspect, may provide a method of iteratively processing image data items comprising the steps of: (d) processing data items according to the procedure above involving steps (I) and (II); (e) processing data items generated in step (d) according to the procedure above involving steps (III) and (IV) ; and, iteratively repeating a given/suitable number of times the sequence of steps (d) to (e) wherein each of the two steps is performed in respect of data items generated according to the other of the two steps .
  • the resulting data items may be employed in a second stage of iterative image construction of the low spatial resolution image generated in step (a) to a higher resolution as follows.
  • the number of iterations performed may be predetermined or may be governed by a predetermined "stop" criterion whereby iteration stops once an acceptable degree of convergence is reached.
  • image reconstruction may proceed by subsequently incorporating low resolution amplitude data into the phase-aligned high resolution image data produced as discussed above or by incorporating low resolution phase data into the amplitude-converged high resolution image data produce as discussed above.
  • this incorporation procedure takes place via a selective data modification (e.g. replacement) process discussed above but merely involving the modification (e.g. replacement) of the amplitude component of the phase-aligned high resolution data according to (e.g. with) the amplitude component of the low spatial resolution image data acquired in step (a), or vice versa.
  • This amplitude modifying procedure may occur in Fourier-Space while phase-modification (e.g. replacement) continues to occur but now in Image Space, or vice versa. These two modification steps preferably occur in a repeating or iterative fashion.
  • the present invention in its first aspect, may provide that the method step (II) performs step (c) by modifying the phase component of image data items, and the method step (IV) performs step (c) by modifying the amplitude component of image data items.
  • the method step (II) may perform step (c) by modifying the amplitude component of image data items
  • the method step (IV) may perform step (c) by modifying the phase component of image data items.
  • the method step (II) and the method step (IV) may each perform (c) by modifying the amplitude component of image data items. In this way, method steps (II) and (IV) may perform the same or different component modifications to image data items.
  • the method step (c) may be applied to the modification of all image data items generated in method step (b) , or may be applied to the modification of only some of those data items. In the latter case, those image data items generated in step (b) which are not modified according to step (c) are preferably still employed in reconstructing the first image at high spatial resolution. It is also to be noted that in either or both of the method steps (II) and (IV) , the method step (c) may perform modification of the phase component and of the amplitude component of image data items. For example, both phase and amplitude components in selected regions of image space may be replaced with values taken from the first image (i.e. image data generated in step (a)); or phase and amplitude components may be set to zero everywhere outside a certain region in image space. In such an example the regions for replacement or zeroing are defined from features in the high- or low- resolution images .
  • the present invention may provide a two-stage method of processing image data comprising the steps of: (h) iteratively processing said image data according to the methods discussed above including steps (I), (II), (III) and (IV) in which step (II) and step (IV) perform the same data modification (e.g. both perform phase modification or both perform amplitude modification) (i) iteratively processing either: said image data according to the method discussed above including steps (I), (II), (III) and (IV) in which step (II) and step
  • step (IV) perform different data modification, and according to image data generated in step (h) ; or, image data generated in step (h) according to the method discussed above including steps (I), (II), (III) and (IV) in which step (II) and step (IV) perform different data modification (e.g. one performs phase modification while the other performs amplitude modification) .
  • the aligned phase component or amplitude components generated in step (h) may be used as a constraint when processing the original image data (i.e. the original input data to step (h) ) according to the method discussed above including steps (I) to (IV) .
  • the number of times iteration is repeated may be predetermined or may be governed by a predetermined "stop" criterion.
  • the present invention may provide a two- stage iterative .image reconstruction scheme whereby in the first stage of the scheme only amplitude or phase- modification (e.g. replacement) is performed as discussed above in order to generate high spatial resolution image data items having amplitude or phase components converged/aligned with the amplitude or phase components of low spatial resolution data items generated in step (a) , and a subsequent second stage in which phase- modification (e.g. replacement) may no longer occur in Fourier-Space but, instead, may occur in Image-Space and in which only amplitude modification/replacement may take place in Fourier-Space rather than in Image-Space.
  • Each one of the two stages may be conducted for any suitable period of time (i.e.
  • the modification/replacement- phase of the phase component employed in that step may use a modification/replacement phase component estimated or derived from the low spatial resolution image data items generated in step (a) according to any phase estimation equations, procedures or algorithms such as would be readily apparent to the skilled person.
  • step (c) When undertaking phase-modification/replacement according to step (c) in Fourier-Space it is preferable to employ the actual phase components of low spatial resolution image data items generated in step (a) as the modification/replacement phase components employed in step (c) .
  • This procedure is particularly simple when the present invention is applied to the reconstruction of NMR images since, as has been discussed above, the raw data generated by an NMR imaging device automatically resides in Fourier-Space since that raw data is merely the
  • This raw data may be the data generated in step (a) , or alternatively, the data generated in step (a) may be the aforementioned raw data having been subject to any necessary preliminary pre-processing procedures.
  • the modification/replacement amplitude employed is preferably simply the amplitude component of image data items generated in step (a) .
  • this modification/replacement amplitude component may simply be the raw NMR signal amplitudes subject to preprocessing or otherwise.
  • the image data items generated in step (a) may represent said second image in Fourier-Space (k) , and the modification/replacement amplitude component
  • employed in the alternative step according to which step (II) is modified as discussed above is preferably an amplitude component in Fourier-Space (k) derived from Fourier-Space low spatial resolution image data items S(k) generated in step (a) according to the formula:
  • the invention may be applied to provide a method of reconstructing Nuclear Magnetic Resonance (NMR) images according to the invention in its first aspect, and including none, some or all of the preferably features, alternative features and modified steps discussed above.
  • NMR Nuclear Magnetic Re
  • the present invention may provide a Nuclear Magnetic Resonance (NMR) imaging system comprising: image acquisition means for acquiring NMR image data; and, image reconstruction means arranged to perform image reconstruction upon acquired NMR image data according to the method of the first aspect of the present invention, and including none, some or all of the preferable/alternative/modified features or steps discussed above.
  • NMR Nuclear Magnetic Resonance
  • the present invention may provide a computer system for use in image reconstruction according to the method of the present invention in its first aspect including none, some or all variants/ modifications discussed above.
  • the present invention may also provide for the use of a computer system for image reconstruction according to the method of the present invention in its first aspect
  • the present invention may provide a program for a computer comprising computer code which when executed on a computer system implements a method of image reconstruction according to the invention in its first aspect including none, some or all of the variants or modifications thereto discussed above using acquired image data.
  • the invention may provide a computer program product storing a program for a computer according the fourth aspect of the invention.
  • the present invention may provide an image data processing apparatus for the reconstruction of an image e . g. representing an object or otherwise) , the image data comprising complex-valued data items possessing an amplitude component and a phase component, the apparatus comprising: image data generator means for generating first image data items for a first image of the object including only low spatial resolution image data items which represent the object at low image resolution; image data generator means for generating second image data items for a second image of the object including low spatial resolution image data items which represent the object at low image resolution and high spatial resolution image data items which represent the object at high image resolution; image data modifying means for modifying (e.g.
  • phase component or said amplitude component may occur by a replacement of phase or amplitude components, or by addition, subtraction or multiplication of existing phase/amplitude components by a modifying phase/amplitude component.
  • the image data modifying means may be arranged to modify the said component by replacing (or otherwise modifying) the phase component or amplitude component thereof with a replacement (or modification) phase or amplitude component derived from low spatial resolution first image data items .
  • the image data generating means is arranged to generate said first and second images such that the spatial frequency (k) of each of said second image data items resides within a first range of values, and the spatial frequency (k) of each of said first image data items resides within a second range of values which is smaller than and is included within said first range of values.
  • the image data generating means is preferably arranged to generate said second image data items such that said first range of values and said second range of values are each substantially centred upon a common spatial frequency (k) value.
  • the image data generator means is preferably arranged to generate said second image data items such that said second image data items represent said second image in: Image Space wherein said phase or amplitude component is modified in Image Space; or, Fourier-Space wherein said phase or amplitude component is modified in Fourier-Space.
  • the image data generator means is preferably arranged to generate said first image data items such that said first image data items represent said first image in Fourier- Space.
  • the image data generating means is arranged to transform said image data items generated by said image data modifying means from Image Space to Fourier- Space; and, in respect of image data items so generated, (II) the image data modifying means is arranged to modify (e.g. replace) the phase or amplitude component of said image data items in Fourier-Space from low spatial resolution first image data items.
  • the image data modifying means is arranged to derive said modifying/replacement phase component in Fourier-Space from said first image data items.
  • the image data generating means is arranged to transform said image data items generated by said image data modifying means from Fourier-Space to Image-Space; and, in respect of image data items so generated, (IV) the image data modifying means is arranged to modify (e.g. replace) the phase or amplitude component of said image data items in Image-Space according to low spatial resolution first image data items.
  • the image data modifying means is preferably arranged to derive said modifying/replacement phase component in image space.
  • the apparatus for processing image data items may comprise : (d) apparatus for processing data items using means (I) and (II) ; and, (e) apparatus for processing data items generated by apparatus (d) using means (III) and (IV) ; and, iterating means for iteratively repeating a given or suitable number of times a sequence of data processing wherein the output of any one of apparatus (d) and (e) is subsequently processed by the other of apparatus (d) and (e) .
  • the number of times iteration may be repeated could be predetermined or could be governed by a "step" criterion defining a convergence threshold which, when reached stops iteration.
  • the image data modifying means (II) of apparatus (d) and the image data modifying means (IV) of apparatus (e) may each be arranged to modify the phase component of image data items according to low spatial resolution first image data items. That is to say, each of these means may be dedicated to phase modification.
  • the image data modifying means (II) of apparatus (d) and the image data modifying means (IV) of apparatus (e) may each be arranged to modify the amplitude component of image data items according to low spatial resolution first image data items.
  • each modifying means may be dedicated to amplitude modification/replacement.
  • the image data modifying means (II) of apparatus (d) may be arranged to modify the phase component of image data items according to low spatial resolution first image data items, and the image data modifying means (IV) of apparatus (e) may be arranged to modify the amplitude component of image data items according to low spatial resolution first image data items.
  • the two image data modifying means may be dedicated to modifying different components of image data items.
  • the image data modifying means (II) of apparatus (d) may be arranged to modify the amplitude component of image data items according to low spatial resolution first image data items, while the image data modifying means (IV) of apparatus (e) may be arranged to modify the phase component of image date items according to low spatial resolution first image data items.
  • the Invention in its fifth aspect may employ image modifying means arranged to modify all second image data items generated by the image data generator means thereof. Alternatively, only some of the second image data items may be so modified. Furthermore, the invention in its fifth aspect may comprise image modifying means which are arranged to modify both the phase component and the amplitude component of image data items .
  • the apparatus comprises: (h) means for iteratively processing image data using apparatus (d) and (e) arranged to perform the same data modification (e.g. both perform phase modification or both perform amplitude modification) and associated iterating means as described above; (i) means for iteratively processing using data modifying means (I), (II), (III) and (IV) as described above in which modifying means (II) and (IV) perform different data modification (e.g. one modifies phase, the other modifies amplitude) either: said image data according to image data generated by iteration means (h) ; or, image data generated by iteration means (h) .
  • data modification e.g. both perform phase modification or both perform amplitude modification
  • the apparatus comprises: (h) means for iteratively processing image data using apparatus (d) and (e) arranged to perform the same data modification (e.g. both perform phase modification or both perform amplitude modification) and associated iterating means as described above; (i) means for iteratively processing
  • the apparatus may comprise means for generating said modifying (e.g. replacement) amplitude component
  • u(k) I
  • s(k) I, where k ⁇ k.n, n is an integer satisfying nl ⁇ n ⁇ n2 , nl and n2 are integers defining the second range of values, and ⁇ k is the discrete data sampling interval in Fourier- Space of first image data items.
  • the present invention may provide an image generated according to, or using, and of the methods or apparatus of the present invention in any of its aspects.
  • Figure 1 illustrates dynamic image sequence acquisition adding to Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) ;
  • Figure 2 schematically illustrates an example of data replacement employed in image reconstruction;
  • Figure 3 schematically illustrates a two-step iterative image reconstruction procedure;
  • Figure 4 schematically represents the application of constraints in the iterative image reconstruction procedure schematically illustrated in part (a) of Figure 3;
  • Figure 5 schematically illustrates the application of constraints according to the second part (b) of the iterative image reconstruction process schematically illustrated in Figure 3;
  • Figure 6 lists the individual steps employed in a first subiteration (a) and a second subiteration (b) as illustrated in Figure 3, Figure 4 and Figure 5;
  • Figure 7 illustrates RMSE ("Root Mean Squared Error") error as a function of POCS image processing iterations for a variety of pre-processing iterations and post-processing iterations within a total number of 6 POCS iterations ("Pro
  • NMR imaging has proved a valuable technique for imaging human body tissues and fluids and, because of its high contrast sensitivity, is well suited to imaging the properties of the many different tissues and fluids in the human body.
  • Contrast enhanced NMR imaging employs a paramagnetic contrast media, such as gadolinium diethylene triamine penta-acetate acid (Gd-DTPA) , which when introduced intravenously to a patient appears in high contrast in an NMR image.
  • Gd-DTPA gadolinium diethylene triamine penta-acetate acid
  • Gd-DTPA gadolinium diethylene triamine penta-acetate acid
  • the ability to differentiate between benign and malignant lesions can depend upon the rate of change of contrast enhancement and the magnitude of that enhancement change resulting from uptake of Gd-DTPA by suspected lesions in the patient.
  • time-dependent image contrast changes may be measured and analysed using a variety of physiological phar acokinetic models describing contrast agent uptake. This is achieved by taking a series of NMR images during the process of contrast agent administration and uptake which record the contrast agent uptake dynamically over a period of time. This is known as Dynamic Contrast- Enhanced Magnetic Resonance Imaging (DCE-MRI) , and its success depends sensitively upon the time interval between successive NMR images in the sequence in relation to the speed of contrast agent uptake and, therefore, the speed of dynamic change in the NMR images themselves. The lower the time interval between successive NMR images the better - or put another way - high "temporal resolution" of a dynamic image sequence is desirable. As discussed above, high temporal resolution in a dynamic image sequence is typically achieved at the expense of lower spatial resolution within some or all images within that sequence.
  • DCE-MRI Dynamic Contrast- Enhanced Magnetic Resonance Imaging
  • raw data is acquired in Fourier- Space, and a real-space or Image-Space image is calculated from the raw image data by performing an inverse Fourier transform (FT -1 ) on the raw data. This being the inverse of a Fourier transform (FT) .
  • FT -1 inverse Fourier transform
  • Both Fourier-Space and Image-Space image data are complex- valued having an amplitude component and a phase component .
  • the high image signal amplitudes are typically distributed symmetrically in the centre of Fourier-Space and thus have low spatial frequency, whereas image signals conveying information regarding detail, shape and structure of the imaged object typically reside in the outer regions of Fourier-Space and have high spatial frequency.
  • spatial image resolution of images within a dynamic image sequence acquired for the purposes of DCE- MRI is proposed to be improved by an image reconstruction method requiring a full Fourier-Space (i.e. both low spatial resolution and high spatial resolution image data items) acquisition of a pre-contrast reference image of an object prior to the administration of a contrast agent to the object and prior to the subsequent DCE-MRI dynamic image sequence acquisition.
  • Image 1 is a reference image fully sampled over a first predetermined range of Fourier-Space and includes data items representing the imaged pre-contrast object at both low and high spatial image resolution.
  • each of the subsequent post-contrast images (Image 2, Image 3 etc.) are sampled only over a small second range of Fourier-Space central to the first range of Fourier-Space over which the reference image (Image 1) is sampled and so each post-contrast image lacks image data items having the ability to represent post-contrast images at a resolution as high as that provided by the spatial resolution image data items obtained for the reference image .
  • Figure 2 schematically represents the relationship between the image data sampling ranges implied as between the pre-contrast reference Image 1, and post-contrast images 2, 3 etc.
  • .kj . is the sampling interval in Fourier-Space
  • n and N are integers
  • i x, y or z such that k x , k y or k z is the spatial frequency in the x-direction, y-direction or z-direction of the corresponding Image-Space respectively.
  • the first range of spatial frequency values includes both low spatial-resolution image data items having low spatial frequency (k) such that n ⁇ n 2 , and high spatial-resolution image data items having high spatial frequency (k) such that n > n 2 .
  • the second range of spatial frequency values includes only low spatial frequency (k) image data items such that n ⁇ n 2 , and is further limited in range (i.e. n ⁇ n ) such that significantly fewer image data items are sampled in the post-contrast images than are sampled in the pre-contrast reference image.
  • This limitation reduces image acquisition time and enables high temporal resolution as between successive images 2, 3 etc.
  • the data replacement operation 25 employed herein employs a constrained reconstruction method for incorporating the a priori high resolution information from the reference image 1 using deterministic constraints.
  • Ci be a convex set.
  • a deterministic constraint is incorporated by a non- expansive proj ection opera tor and is defined by the map Pi mapping any u not contained in Ci to an element inside Ci in the sense that
  • u 0 is a vector representing the fully sampled data set 30 of the reference Image 1
  • the idea is to construct a concatenation of constraints, P ⁇ P 2 ...P m , to force the initial vector u Q to converge onto a desired reconstructed image vector ⁇ n which satisfies all of the constraints simultaneously.
  • the constraint in question whether it be ⁇ est i mate ( x ) ' & ⁇ S[S k)] r or I S(k)
  • phase constraint in Image-Space is an estimate of the Image-Space phases of data items representing a post-contrast image and is given by:
  • ⁇ eslimate (x) arg £ 2
  • k ⁇ k.n
  • x ⁇ x.n, with n being an integer satisfying nl ⁇ n ⁇ n2 , nl and n2 being integers
  • ⁇ k and ⁇ x being the discrete image data sampling- interval in Fourier- Space and Image Space respectively of the image data generated in step (a) .
  • the constraint is expressed in the x-dimension of Image-Space for illustration. It is to be understood that the constraint may be applied also in the y-dimension and z-dimension (in the case of 3D images) .
  • the phase constraint in Fourier-Space is the phase component, arg[S(k)], in Fourier-Space of post-contrast image data items.
  • the amplitude constraint in Fourier-Space is the amplitude component,
  • ni (N/2 - N 0 )
  • n 2 (N/2 4- N 0 ) and N 0 « ⁇ x or n 2 so that the post-contrast low resolution images 2, 3 etc. are sampled over only a small central region of the Fourier-Space of the image data samples representing the pre-contrast reference Image 1.
  • the invention according to the present embodiment applies constraints Ci and C 2 iteratively in a first subiteration in order to align the phases of image data items of the reference Image 1 to the phases of a given one of the subsequent low resolution post-contrast images 2, 3 etc.
  • the resulting pre-processed output u(x) of the first subiteration is then subject to the second subiteration as follows .
  • phase constraint Ci and the amplitude constraints C 3 are successively and iteratively applied to the result u(x) of the first subiteration.
  • Image data items S(k) of low resolution only have been generated in respect of a given post-contrast image 2 (or image 3 etc.) in Fourier-Space, and as a first step in the second subiteration, the phase of the Image-Space data items u(x) of the first subiteration is modified by replacing it with the replacement phase derived according to projection operator Pi and Eq. (9) and Eq. (6) in Image- Space.
  • Equation (11) and (13) wherein the amplitude components
  • the result of the application of the amplitude constraint C 3 is then transformed back into Image-Space via an inverse Fourier transform (FT -1 ) whereupon the cycle of successively applying constraints C x and C 3 is repeated/iterated a suitable number of times (e.g. k 2 times) in order to produce in the processed image data u(k) or u(x) an acceptable level of high spatial resolution reconstruction of the low resolution post- contrast image 2 (or image 3 etc.) to high resolution as illustrated in Figure 5 and Figure 6 and in Figure 3, part (b) .
  • FT -1 inverse Fourier transform
  • Figure 3 schematically illustrates the two-step iterative image reconstruction procedure employing a pre-processing subiteration (part (a) of Fig.3) and a post-processing subiteration (part (b) of Fig.3).
  • Figure 4 schematically represents the application of phase constraints (only) in the iterative image reconstruction procedure schematically illustrated in part (a) of Figure 3
  • Figure 5 schematically illustrates the application of both a phase constraint and an amplitude constraint according to the second part (b) of the iterative image reconstruction process schematically illustrated in Figure 3.
  • first subiteration in order to provide a phase-aligned high resolution image data set for use in the second subiteration, it is not essential to do so.
  • the invention may be applied in the absence of the first subiteration by using only the second subiteration.
  • Figure 7 illustrates the performance of the present method as a function of varying amounts of pre-processing (i.e. use of the first subiteration) and post-processing (i.e. use of the second subiteration) iterations.
  • Three examples are shown which illustrate the development of the Root Mean Square Error (RMSE) of a given reconstructed image data set ⁇ (x) subject to up to six image processing iterations (i.e. cycles of constraint application) in total and comprising either one, three or five pre-processing iterations.
  • the RMSE is a measure of convergence of the image reconstruction method and provides a means for measuring the difference between an original reference image having image data items u(x) and a reconstructed image ⁇ (x) as follows:
  • Figure 8 illustrates the difference in the calculated RMSE for three different Fourier-Space data sampling ranges employed in the central sampling of a given post- contrast low resolution image data set.
  • the three low resolution data sets in question correspond to 16, 32 and 48 lines sampled along the direction of dynamic encoding in Fourier-Space of a post-contrast image, that is to say, in the direction of the k-space axis along which image data is acquired one bit at a time with phase encoding.
  • the sampled data corresponds to 25%, 50% and 75% respectively of the Fourier-Space sampling range employed in sampling the pre-contrast reference Image 1.
  • convergence increases more rapidly (i.e. RMSE falls more rapidly) when the post-contrast central sampling range increases.
  • an increase in the post-contrast sampling range in Fourier-Space necessarily results in an increase in data acquisition and processing times and therefore results in a reduction in temporal image resolution.
  • constraints may preferably also be applied to each of the other dimensions of an image data set (e.g., the y-dimension for 2-D images, and also the z-dimension for 3-D images) .
  • constraints could be selectively applied to fewer than all of the dimensions of a given image data set. For example, constraints may be applied only in one, image data dimension in a given space (e.g. the x-dimension in Image-Space, and the k x -dimension in Fourier-Space) .

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Abstract

L'invention concerne un procédé de traitement de données d'image utilisées dans la reconstruction d'une image, lesdites données d'image comprenant des éléments de données à valeur complexe possédant une composante d'amplitude et une composante de phase. Ledit procédé consiste (a) à générer des éléments de données d'image pour une première image de l'objet, comprenant seulement des éléments de données d'image à faible résolution spatiale représentant l'objet selon une faible résolution d'image; (b) à générer des éléments de données d'image pour une seconde image de l'objet, comprenant des éléments de données d'image à faible résolution spatiale représentant l'objet selon une faible résolution d'image, et des éléments de données d'image à résolution spatiale élevée représentant l'objet selon une résolution d'image élevée; (c) à modifier ladite composante de phase ou ladite composante d'amplitude des éléments de données d'image générés dans l'étape (b) en fonction des éléments de données d'image à faible résolution spatiale générés dans l'étape (a), afin d'évaluer les données d'image à résolution spatiale élevée utilisées dans la reconstruction de ladite première image selon une résolution spatiale élevée, ladite modification étant associée à une projection sur des ensembles convexes (POCS).
PCT/GB2004/003998 2003-09-18 2004-09-17 Imagerie par rm dynamique a reconstruction contrainte a l'aide d'un algorithme pocs WO2005026765A1 (fr)

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US7917189B2 (en) 2005-07-08 2011-03-29 Wisconsin Alumni Research Foundation Backprojection reconstruction method for undersampled MR imaging
US7519412B2 (en) 2005-07-08 2009-04-14 Wisconsin Alumni Research Foundation Highly constrained image reconstruction method
US7545901B2 (en) 2005-07-08 2009-06-09 Wisconsin Alumni Research Foundation Backprojection reconstruction method for CT imaging
US7865227B2 (en) 2005-09-22 2011-01-04 Wisconsin Alumni Research Foundation Image reconstruction method for cardiac gated magnetic resonance imaging
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US7408347B2 (en) 2005-09-22 2008-08-05 Wisconsin Alumni Research Foundation Highly constrained magnetic resonance spectroscopy image reconstruction method
US7917190B2 (en) 2005-09-22 2011-03-29 Wisconsin Alumni Research Foundation Image acquisition and reconstruction method for functional magnetic resonance imaging
US7358730B2 (en) 2005-09-22 2008-04-15 Wisconsin Alumni Research Foundation Diffusion tensor imaging using highly constrained image reconstruction method
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CN113506212A (zh) * 2021-05-21 2021-10-15 大连海事大学 一种改进的基于pocs的高光谱图像超分辨率重建方法
CN113506212B (zh) * 2021-05-21 2023-05-23 大连海事大学 一种改进的基于pocs的高光谱图像超分辨率重建方法

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