CN108537755B - PET image enhancement method and system based on geometric structure constraint - Google Patents
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Abstract
The application discloses a method for PET image enhancement based on geometric structure constraint, which comprises the following steps: establishing a PET image enhancement model based on geometric structure constraint; acquiring an observed PET image; performing domain transformation on the PET image by using a B-spline small wave tight frame to obtain a PET image structure under a corresponding transformation domain; and enhancing the PET image structure on the conversion domain by using the PET image enhancement model to obtain an optimal PET enhanced image. According to the method, when the PET image enhancement model is used for enhancing the PET image, the non-smooth region can be accurately positioned and the boundary of the PET image can be determined by using the communication characteristics of the geometric structure in the image, so that the task of repairing and enhancing the degraded PET image is completed, and the quality of the PET image is improved. The application also provides a system, a device and a computer readable storage medium for PET image enhancement based on geometric structure constraint, which have the beneficial effects and are not repeated herein.
Description
Technical Field
The present application relates to the field of PET image processing, and in particular, to a method, system, device, and computer-readable storage medium for PET image enhancement based on geometric constraint.
Background
PET Positron Emission Tomography (PET) provides specific image information of metabolic functions of tissues in the human body, reflects physiological or pathological changes of tissues in the human body, and is also called "in vivo biochemical imaging". The method comprises the steps of collecting projection data in a human body by using a radioactive tracer labeled by positive electron nuclide, and carrying out model solving by using a related mathematical method, thereby constructing and obtaining a spatial concentration distribution map of radioactive substances in the human body.
Clinical PET imaging usually adopts a dynamic scanning mode, that is, tracer activity images at continuous time points are acquired within a fixed time period, however, dynamic scanning easily results in short scanning time of a single frame image and few detectable photon counts, which causes severe degradation of PET image quality. The constructed objective function typically contains a data fitting term for describing the statistical properties of the image data and a constraint term for modifying the properties of the solution. However, the conventional bounded variation function is easy to cause the loss of the edge information of the restored image and even generate false edges when the image restoration is carried out as a constraint item.
Therefore, how to effectively enhance the PET image is a technical problem that needs to be solved by those skilled in the art.
Disclosure of Invention
It is an object of the present application to provide a method, system, device and computer readable storage medium for geometry constraint based PET image enhancement for efficiently enhancing PET images.
In order to solve the above technical problem, the present application provides a method for PET image enhancement based on geometric constraint, the method comprising:
establishing a PET image enhancement model based on geometric constraint according to an input geometric constraint condition; wherein the geometric constraint condition is used for determining the boundary and smooth area of the image;
acquiring an observed PET image;
performing domain transformation on the PET image by using a B-spline small wave tight frame to obtain a PET image structure under a corresponding transform domain;
and enhancing the PET image structure on the conversion domain by using the PET image enhancement model to obtain an optimal PET enhanced image.
Optionally, the establishing a PET image enhancement model based on geometric constraints according to the input geometric constraint conditions includes:
receiving input geometry constraint condition O ═ { Ω: C (Ω, H) ═ Ω } and scarcity parameter t0；
According to the geometric constraint condition O ═ { Ω: C (Ω, H) ═ Ω } and the deficiency parameter t0Establishing a PET image enhancement model based on geometric structure constraint
Wherein omega is the uneven area of the image,
is a complementary set of omega and represents a smooth region of the image, O is a feasible region of omega, Λ is a smooth region of the modified image, C is a 'closed' operation operator, H is a structural element template used in the 'closed' operation, giFor the i frame PET image observed in the transform domain, fiFor the ith frame of PET enhanced image, A is a linear operator, lambda is a regularization parameter, W is an analysis operator of a B spline wavelet tight frame, and t0Are sparse parameters.
Optionally, the enhancing the PET image structure on the transform domain by using the PET image enhancement model to obtain an optimal PET enhanced image includes:
initializing the ith frame PET enhanced image fi；
By optimizing the model
Updating an unsmooth region omega of the image;
according to the formula
Updating the smooth region Lambda of the corrected image;
enhancing the model of the PET image according to the unsmooth region omega of the image and the smooth region Lambda of the corrected image
Solving to update the i frame PET enhanced image fi；
Judging whether the smooth area Lambda of the corrected image is converged;
if not, repeatedly executing the steps of updating the unsmooth area omega of the image and updating the smooth area of the corrected imageDomain Λ and updating the i frame PET enhanced image fiA step (2);
if yes, converging the corresponding f when the smooth area Lambda of the corrected image is convergediAnd the optimal PET enhanced image is used as the ith frame.
Optionally, the enhancing the PET image structure on the transform domain by using the PET image enhancement model to obtain an optimal PET enhanced image includes:
querying the initial model
Corresponding to the minimum value of [ omega, f ]i,Λ]min；
Will f isiAnd the optimal PET enhanced image is used as the ith frame.
The present application further provides a system for PET image enhancement based on geometric constraints, the system comprising:
the model establishing module is used for establishing a PET image enhancement model based on geometric structure constraint according to the input geometric structure constraint condition; wherein the geometric constraint condition is used for determining the boundary and smooth area of the image;
an acquisition module for acquiring an observed PET image;
the domain transformation module is used for performing domain transformation on the PET image by using a B-spline small compact frame to obtain a PET image structure under a corresponding transformation domain;
and the image enhancement module is used for enhancing the PET image structure on the conversion domain by using the PET image enhancement model to obtain an optimal PET enhanced image.
Optionally, the model building module includes:
a receiving submodule for receiving an input geometry constraint condition O ═ omega: (omega, H) ═ omega ═ and a deficiency parameter t0；
A model establishing submodule for establishing the constraint condition O ═ omega: C (omega, H) ═ omega } and the scarce parameter t according to the geometric structure constraint condition O ═ omega0Establishing a PET image enhancement model based on geometric structure constraint
Wherein omega is the uneven area of the image,
is a complementary set of omega and represents a smooth region of the image, O is a feasible region of omega, Λ is a smooth region of the modified image, C is a 'closed' operation operator, H is a structural element template used in the 'closed' operation, giFor the i frame PET image observed in the transform domain, fiFor the ith frame of PET enhanced image, A is a linear operator, lambda is a regularization parameter, W is an analysis operator of a B spline wavelet tight frame, and t0Are sparse parameters.
Optionally, the image enhancement module includes:
an initialization sub-module for initializing the i frame of PET enhanced image fi；
A first update submodule for passing through the optimization model
Updating an unsmooth region omega of the image;
a second update submodule for updating according to a formula
Updating the smooth region Lambda of the corrected image;
a third updating submodule for enhancing the model of the PET image according to the unsmooth region omega of the image and the smooth region Lambda of the corrected image
Solving to update the i frame PETEnhanced image fi；
The judgment submodule is used for judging whether the smooth region lambada of the corrected image is converged;
a decision submodule, configured to, when the smoothed region Λ of the modified image is not converged, cause the first update submodule, the second update submodule, and the third update submodule to repeatedly perform updating of the unsmooth region Ω of the image, updating of the smoothed region Λ of the modified image, and updating of the i-th frame PET enhanced image fiA step (2); when the smooth area Lambda of the corrected image converges, converging the corresponding f when the smooth area Lambda of the corrected image convergesiAnd the optimal PET enhanced image is used as the ith frame.
Optionally, the image enhancement module includes:
a query submodule for querying the initial model
Corresponding to the minimum value of [ omega, f ]i,Λ]min；
Establishing a submodule for converting fiAnd the optimal PET enhanced image is used as the ith frame.
The present application further provides a PET image enhancement device based on geometric constraint, comprising:
a memory for storing a computer program;
a processor for implementing the steps of the method for geometry constraint based PET image enhancement as defined in any of the above when said computer program is executed.
The present application further provides a computer-readable storage medium having stored thereon a computer program which, when being executed by a processor, carries out the steps of the method for geometry constraint based PET image enhancement as defined in any of the previous claims.
The PET image enhancement method based on the geometric constraint provided by the application establishes a PET image enhancement model based on the geometric constraint according to the input geometric constraint condition; the geometric structure constraint condition is used for determining the boundary and the smooth area of the image; acquiring an observed PET image; performing domain transformation on the PET image by using a B-spline small wave tight frame to obtain a PET image structure under a corresponding transformation domain; and enhancing the PET image structure on the conversion domain by using the PET image enhancement model to obtain an optimal PET enhanced image.
According to the technical scheme, the PET image enhancement model based on the geometric structure constraint is established, so that when the PET image enhancement model is used for enhancing the PET image, the non-smooth region can be accurately positioned by using the communication characteristic of the geometric structure in the image, the sparse structure of the image is reconstructed by using the geometric constraint and the association to determine the boundary of the PET image, the problems that the boundary variation function in the prior art easily causes the loss of the recovered image edge information and even generates false edges are avoided, the repair enhancement task of the degraded PET image is completed, and the quality of the PET image is improved. The application also provides a system, a device and a computer readable storage medium for PET image enhancement based on geometric structure constraint, which have the beneficial effects and are not repeated herein.
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In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings needed to be used in the description of the embodiments or the prior art will be briefly introduced below, it is obvious that the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
FIG. 1 is a flowchart of a method for PET image enhancement based on geometric constraints according to an embodiment of the present disclosure;
FIG. 2 is a flow chart of an actual representation of S104 in a method of geometry constraint-based PET image enhancement provided in FIG. 1;
FIG. 3 is a block diagram of a system for PET image enhancement based on geometric constraints according to an embodiment of the present disclosure;
FIG. 4 is a block diagram of another system for PET image enhancement based on geometric constraints as provided by embodiments of the present application;
fig. 5 is a block diagram of a PET image enhancement device based on geometric constraint according to an embodiment of the present application.
Detailed Description
At the heart of the present application is to provide a method, system, device and computer readable storage medium for PET image enhancement based on geometric constraint for effectively enhancing PET images.
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Referring to fig. 1, fig. 1 is a flowchart illustrating a method for enhancing a PET image based on geometric constraint according to an embodiment of the present disclosure.
The method specifically comprises the following steps:
s101: establishing a PET image enhancement model based on geometric constraint according to an input geometric constraint condition;
based on dynamic scanning, the scanning time of a single frame image is easy to be short, the number of detectable photons is extremely small, the quality of a PET image is seriously degraded, and when the conventional bounded variation function is used as a constraint item to restore the image, the edge information of the restored image is easy to lose, even false edges are generated;
wherein, the geometric structure constraint condition is used for determining the boundary and smooth area of the image;
optionally, the establishing of the PET image enhancement model based on the geometric constraint according to the input geometric constraint condition may specifically be:
receiving input geometry constraint condition O ═ { Ω: C (Ω, H) ═ Ω } and scarcity parameter t0；
According to the geometrical constraint condition O ═ { Ω: C (Ω, H) } and the scarce parameter t0Establishing a PET image enhancement model based on geometric structure constraint
Wherein omega is the uneven area of the image,
is a complementary set of omega and represents a smooth region of the image, O is a feasible region of omega, Λ is a smooth region of the modified image, C is a 'closed' operation operator, H is a structural element template used in the 'closed' operation, giFor the i frame PET image observed in the transform domain, fiFor the ith frame of PET enhanced image, A is a linear operator, lambda is a regularization parameter, W is an analysis operator of a B spline wavelet tight frame, and t0Is a sparse parameter;
c in the geometric constraint condition O ═ Ω ═ C (Ω, H) ═ Ω } is a morphological "closing" operator, and can repair the uneven region Ω of the image, and can connect the broken boundaries, and therefore can be used to repair the boundaries, and H is a structural element template used in the "closing" operation, and a 3 × 3 full 1 matrix can be used, that is:
according to the PET imaging process, the tracer activity x of an image pixel point K (K belongs to 1, 2.. multidot.K) in the ith (i belongs to 1, 2.. multidot.M) framek,iIs recorded as:
wherein c (k, t) represents tracer activity of pixel point k at time t, ti,eAnd ti,sRespectively representing the starting time and the ending time of the ith frame, wherein the longer the acquisition time corresponding to a single time frame is, the more projection data are acquired, and conversely, the shorter the acquisition time is, the less the projection data are, and the worse the quality of the reconstructed PET image is;
when the PET image is enhanced, each frame image x is recordedi＝[x1,i,x2,i,…,xK,i]Is giIts corresponding enhanced image is denoted as fiThis process of enhancement can be seen as the inverse of the image degradation, i.e. the process of enhancement
fi＝A-1gi+ε
Wherein f isi∈RNFor sharp images to be patched, gi∈RKFor the actually observed image, A-1∈RN×KIs an inverse linear operator related to the degradation process, and epsilon is equal to RKNoise present during observation;
to observe the image giTo obtain an enhanced image fiHere order gi≈AfiBased on the smooth characteristic of the image, a sparsity constraint can be added to the smooth region of the image, namely the energy of the enhanced smooth region of the image under a small tight frame is very small, and if the smooth region of the image is marked as Λ, the condition (Wf) should be satisfiedi)ΛIs approximately equal to 0, and finally, by means of the correlation characteristic of the boundary, the corresponding geometric constraint can be added in the smooth region of the image, so as to obtain the PET image enhancement model based on the geometric constraint
s.t.Λ＝O(ΩC),|ΩC|≥t0
The application assumes that the unsmooth region of the image satisfies a certain constraint, namely, the smooth region and the unsmooth region are in a complementary relationship, once the unsmooth region is determined, the smooth region is determined, and on the basis, the degraded image (namely, the observed image g) is obtained according to the PET image enhancement modeli) And taking the optimal inverse solution as the optimal PET enhanced image f of the degraded imagei。
S102: acquiring an observed PET image;
the acquisition of the observed PET image mentioned here can specifically acquire signal data by an isotope labeling method, and then process the signal to convert the photoelectron signal into the PET image.
S103: performing domain transformation on the PET image by using a B-spline small wave tight frame to obtain a PET image structure under a corresponding transformation domain;
based on the characteristic of a B-spline wavelet tight framework, the PET image is subjected to domain transformation to obtain a PET image structure under a domain to be converted, a non-smooth region can be accurately positioned by adding corresponding geometric structure constraint on the basis of the PET image structure, and the boundary of the PET image is determined.
S104: and enhancing the PET image structure on the conversion domain by using the PET image enhancement model to obtain an optimal PET enhanced image.
Optionally, the PET image structure on the conversion domain is enhanced by using a PET image enhancement model to obtain an optimal PET enhanced image, which specifically may be:
querying an initial model
Corresponding to the minimum value of [ omega, f ]i,Λ]min；
Will f isiAnd the optimal PET enhanced image is used as the ith frame.
Based on the technical scheme, the PET image enhancement method based on the geometric structure constraint enables the PET image enhancement model to accurately position a non-smooth region by using the connection characteristics of the geometric structure in the image when the PET image is enhanced, and reconstructs a sparse structure of the image by using the geometric constraint and association to determine the boundary of the PET image, thereby avoiding the problem that the boundary information of the recovered image is lost or even generates false edges due to the fact that a bounded variation function is easy to cause in the prior art, completing the task of repairing and enhancing the degraded PET image, and improving the quality of the PET image.
Based on the foregoing embodiment, as mentioned in step S104, the PET image structure on the transform domain is enhanced by using a PET image enhancement model to obtain an optimal PET enhanced image, and an actual representation manner thereof can also be shown in fig. 2, please refer to fig. 2, and fig. 2 is a flowchart of an actual representation manner of S104 in the method for enhancing PET image based on geometric constraint provided in fig. 1.
The method specifically comprises the following steps:
s201: initializing the ith frame PET enhanced image fi；
Since the PET enhances the image fiBased on the observed I frame PET image g in the transform domainiCalculated so that when g is receivediThen, by making fi＝giTo initialize the ith frame of PET enhanced image fi。
S202: by optimizing the model
Updating an unsmooth area omega of the image;
s203: according to the formula
Updating the smooth area Lambda of the corrected image;
s204: enhancing the model for the PET image according to the unsmooth region omega of the image and the smooth region Lambda of the corrected image
Solving to update the ith frame PET enhanced image fi；
Alternatively, a conjugate gradient algorithm pair may be used
Go on to solve, at this moment
S205: judging whether the smooth region lambada of the corrected image is converged;
if not, repeating the steps S202 to S205;
if yes, the process proceeds to step S206.
S206: f corresponding to the corrected smooth region Lambda convergenceiAnd the optimal PET enhanced image is used as the ith frame.
Referring to fig. 3, fig. 3 is a block diagram of a system for PET image enhancement based on geometric constraint according to an embodiment of the present application.
The system may include:
the model establishing module 100 is used for establishing a PET image enhancement model based on geometric constraint according to the input geometric constraint condition; the geometric structure constraint condition is used for determining the boundary and the smooth area of the image;
an acquisition module 200 for acquiring an observed PET image;
the domain transformation module 300 is used for performing domain transformation on the PET image by using a B-spline small compact frame to obtain a PET image structure under a corresponding transformation domain;
and the image enhancement module 400 is configured to enhance the PET image structure on the conversion domain by using a PET image enhancement model, so as to obtain an optimal PET enhanced image.
Referring to fig. 4, fig. 4 is a block diagram of another system for PET image enhancement based on geometric constraint according to an embodiment of the present application.
The model building module 100 may include:
a receiving submodule for receiving an input geometry constraint O ═ omega: C (omega)H) omega and the deficiency parameter t0；
A model establishing submodule for establishing a geometric constraint condition O-omega-C (omega, H-omega) and a scarce parameter t0Establishing a PET image enhancement model based on geometric structure constraint
Wherein omega is the uneven area of the image,
is a complementary set of omega and represents a smooth region of the image, O is a feasible region of omega, Λ is a smooth region of the modified image, C is a 'closed' operation operator, H is a structural element template used in the 'closed' operation, giFor the i frame PET image observed in the transform domain, fiFor the ith frame of PET enhanced image, A is a linear operator, lambda is a regularization parameter, W is an analysis operator of a B spline wavelet tight frame, and t0Are sparse parameters.
The image enhancement module 400 may include:
an initialization sub-module for initializing the i frame of the PET enhanced image fi；
A first update submodule for passing through the optimization model
Updating an unsmooth area omega of the image;
a second update submodule for updating according to a formula
Updating the smooth area Lambda of the corrected image;
a third updating submodule for updating the image according to the non-smooth region omega of the image and the smooth region of the corrected imageDomain lambda pair PET image enhancement model
Solving to update the ith frame PET enhanced image fi；
The judgment submodule is used for judging whether the smooth region lambada of the corrected image is converged;
a decision submodule for making the first update submodule, the second update submodule and the third update submodule repeatedly execute the non-smooth region omega of the updated image, the smooth region Lambda of the updated image and the i frame PET enhanced image f when the smooth region Lambda of the corrected image is not convergediA step (2); when the smooth area Lambda of the corrected image converges, the corresponding f when the smooth area Lambda of the corrected image convergesiAnd the optimal PET enhanced image is used as the ith frame.
The image enhancement module 400 may also include:
a query submodule for querying the initial model
Corresponding to the minimum value of [ omega, f ]i,Λ]min；
Establishing a submodule for dividing fiAnd the optimal PET enhanced image is used as the ith frame.
Since the embodiment of the system part corresponds to the embodiment of the method part, the embodiment of the system part is described with reference to the embodiment of the method part, and is not repeated here.
Referring to fig. 5, fig. 5 is a block diagram of a PET image enhancement apparatus based on geometric constraint according to an embodiment of the present application.
PET image enhancement devices based on geometric constraints may vary significantly due to differences in configuration or performance, and may include one or more processors (CPUs) 522 (e.g., one or more processors) and memory 532, one or more storage media 530 (e.g., one or more mass storage devices) storing applications 542 or data 544. Memory 532 and storage media 530 may be, among other things, transient storage or persistent storage. The program stored on the storage medium 530 may include one or more modules (not shown), each of which may include a sequence of instruction operations for the device. Still further, the central processor 522 may be configured to communicate with the storage medium 530 to execute a series of instruction operations in the storage medium 530 on the PET image enhancing device 500 based on the geometric constraint.
The geometry constraint based PET image enhancement apparatus 500 may also include one or more power supplies 526, one or more wired or wireless network interfaces 550, one or more input-output interfaces 558, and/or one or more operating systems 541, such as Windows ServerTM, Mac OS XTM, UnixTM, LinuxTM, FreeBSDTM, etc.
The steps in the method of geometry-constraint-based PET image enhancement described above with reference to fig. 1 to 2 are implemented by a geometry-constraint-based PET image enhancement device based on the structure shown in fig. 5.
It can be clearly understood by those skilled in the art that, for convenience and brevity of description, the specific working processes of the system, the apparatus and the module described above may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided in the present application, it should be understood that the disclosed apparatus, device and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, a division of modules is merely a division of logical functions, and an actual implementation may have another division, for example, a plurality of modules or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or modules, and may be in an electrical, mechanical or other form.
Modules described as separate parts may or may not be physically separate, and parts displayed as modules may or may not be physical modules, may be located in one place, or may be distributed on a plurality of network modules. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment.
In addition, functional modules in the embodiments of the present application may be integrated into one processing module, or each of the modules may exist alone physically, or two or more modules are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode.
The integrated module, if implemented in the form of a software functional module and sold or used as a separate product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present application may be substantially implemented or contributed to by the prior art, or all or part of the technical solution may be embodied in a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a function calling device, or a network device) to execute all or part of the steps of the method of the embodiments of the present application. And the aforementioned storage medium includes: various media capable of storing program codes, such as a usb disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disk.
A detailed description of a method, system, device and computer-readable storage medium for geometry constraint-based PET image enhancement provided herein is provided above. The principles and embodiments of the present application are explained herein using specific examples, which are provided only to help understand the method and the core idea of the present application. It should be noted that, for those skilled in the art, it is possible to make several improvements and modifications to the present application without departing from the principle of the present application, and such improvements and modifications also fall within the scope of the claims of the present application.
It is further noted that, in the present specification, relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
Claims (6)
1. A method of PET image enhancement based on geometric constraints, comprising:
establishing a PET image enhancement model based on geometric constraint according to an input geometric constraint condition; wherein the geometric constraint condition is used for determining the boundary and smooth area of the image;
acquiring an observed PET image;
performing domain transformation on the PET image by using a B-spline small wave tight frame to obtain a PET image structure under a corresponding transform domain;
enhancing the PET image structure on the conversion domain by using the PET image enhancement model to obtain an optimal PET enhanced image;
the method for establishing the PET image enhancement model based on the geometric constraint according to the input geometric constraint condition comprises the following steps:
receiving input geometry constraint condition O ═ { Ω: C (Ω, H) ═ Ω } and sparse parameter t0；
According to the geometric constraint condition O ═ { Ω: C (Ω, H) ═ Ω } and the sparse parameter t0Building a PET map based on geometric constraintsImage enhancement model
s.t.
Wherein omega is the uneven area of the image,
is a complementary set of omega and represents a smooth region of the image, O is a feasible region of omega, Λ is a smooth region of the modified image, C is a 'closed' operation operator, H is a structural element template used in the 'closed' operation, giFor the i frame PET image observed in the transform domain, fiFor the ith frame of PET enhanced image, A is a linear operator, lambda is a regularization parameter, W is an analysis operator of a B spline wavelet tight frame, and t0Is a sparse parameter;
and enhancing the PET image structure on the conversion domain by using the PET image enhancement model to obtain an optimal PET enhanced image, wherein the method comprises the following steps:
initializing the ith frame PET enhanced image fi；
By optimizing the model
s.t.|Ωc|≥t0Updating an unsmooth region omega of the image;
according to the formula
Updating the smooth region Lambda of the corrected image;
enhancing the model of the PET image according to the unsmooth region omega of the image and the smooth region Lambda of the corrected image
Solving to update the i frame PET enhanced image fi；
Judging whether the smooth area Lambda of the corrected image is converged;
if not, repeatedly executing the steps of updating the unsmooth region omega of the image, updating the smooth region Lambda of the corrected image and updating the ith frame PET enhanced image fiA step (2);
if yes, converging the corresponding f when the smooth area Lambda of the corrected image is convergediAnd the optimal PET enhanced image is used as the ith frame.
2. The method of claim 1, wherein the enhancing the PET image structure in the transform domain by the PET image enhancement model to obtain an optimal PET enhanced image comprises:
querying the initial model
s.t.
Corresponding to the minimum value of [ omega, f ]i,Λ]min；
Will f isiAnd the optimal PET enhanced image is used as the ith frame.
3. A system for PET image enhancement based on geometric constraints, comprising:
the model establishing module is used for establishing a PET image enhancement model based on geometric structure constraint according to the input geometric structure constraint condition; wherein the geometric constraint condition is used for determining the boundary and smooth area of the image;
an acquisition module for acquiring an observed PET image;
the domain transformation module is used for performing domain transformation on the PET image by using a B-spline small compact frame to obtain a PET image structure under a corresponding transformation domain;
the image enhancement module is used for enhancing the PET image structure on the conversion domain by utilizing the PET image enhancement model to obtain an optimal PET enhanced image;
the model building module comprises:
a receiving submodule for receiving an input geometry constraint condition O ═ { Ω: C (Ω, H) ═ Ω } and a sparse parameter t0；
A model establishing submodule for establishing a model according to the geometric constraint condition O ═ Ω ═ C (Ω, H) ═ Ω } and the sparse parameter t0Establishing a PET image enhancement model based on geometric structure constraint
s.t.
Wherein omega is the uneven area of the image,
is a complementary set of omega and represents a smooth region of the image, O is a feasible region of omega, Λ is a smooth region of the modified image, C is a 'closed' operation operator, H is a structural element template used in the 'closed' operation, giFor the i frame PET image observed in the transform domain, fiFor the ith frame of PET enhanced image, A is a linear operator, lambda is a regularization parameter, W is an analysis operator of a B spline wavelet tight frame, and t0Is a sparse parameter;
the image enhancement module includes:
an initialization sub-module for initializing the i frame of PET enhanced image fi；
A first update submodule for passing through the optimization model
s.t.|Ωc|≥t0Updating an unsmooth region omega of the image;
a second update submodule for updating according to a formula
Updating the smooth region Lambda of the corrected image;
a third updating submodule for enhancing the model of the PET image according to the unsmooth region omega of the image and the smooth region Lambda of the corrected image
Solving to update the i frame PET enhanced image fi；
The judgment submodule is used for judging whether the smooth region lambada of the corrected image is converged;
a decision submodule, configured to, when the smoothed region Λ of the modified image is not converged, cause the first update submodule, the second update submodule, and the third update submodule to repeatedly perform updating of the unsmooth region Ω of the image, updating of the smoothed region Λ of the modified image, and updating of the i-th frame PET enhanced image fiA step (2); when the smooth area Lambda of the corrected image converges, converging the corresponding f when the smooth area Lambda of the corrected image convergesiAnd the optimal PET enhanced image is used as the ith frame.
4. The system of claim 3, wherein the image enhancement module comprises:
a query submodule for querying the initial model
s.t.
Corresponding to the minimum value of [ omega, f ]i,Λ]min；
Establishing a submodule for converting fiAnd the optimal PET enhanced image is used as the ith frame.
5. A PET image enhancement device based on geometric constraints, comprising:
a memory for storing a computer program;
a processor for implementing the steps of the method of geometry constraint based PET image enhancement as claimed in any one of claims 1 to 2 when executing the computer program.
6. A computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, which computer program, when being executed by a processor, carries out the steps of the method for geometry constraint based PET image enhancement as claimed in any one of the claims 1 to 2.
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