Image reconstruction

Abstract

Aspects and embodiments relate to a method for creating an image representing a measurement dataset by iteratively updating a base image. The method includes generating a primary dataset from the measurement dataset, the primary dataset comprising a dataset having substantially the same level of noise as the measurement dataset. The method includes generating at least one additional dataset from the measurement dataset, the additional dataset comprising datasets generated from the measurement dataset such that each additional dataset has substantially the same level of noise as the measurement dataset and such that each additional dataset is not identical to the primary dataset. The method includes processing a base image without noise compensation using the primary dataset and each additional dataset to obtain a primary intermediate image and at least one additional intermediate image, respectively; comparing the primary intermediate image and the at least one additional intermediate image to determine an indication of the level of noise present; and using the determined indication of noise presence to select noise compensation to apply when processing the base image using the measurement dataset to create a new base image representing the measurement dataset. The approach described herein can be implemented for any standard iterative image reconstruction method and provides a method where, for example, the use of only a single bootstrapped sampled dataset allows powerful state-of-the-art denoising algorithms to be directly embedded in image reconstruction with relative simplicity. The approach provides a mechanism for automatic and precise data-dependent optimization of any denoising strength at each update.

Description

Technical Field

[0001] Aspects and embodiments relate to a method of creating an image representing a measurement data set, a computer program product and an apparatus operable to perform the method. Background Art

[0002] Inverse problems arise in many fields, including medicine and preclinical imaging.

[0003] When dealing with inverse problems in the field of imaging, the goal is to estimate one or more parameters or multidimensional density functions that represent some object of interest, often called an image. For example, in medical imaging, the inverse problem of interest is often called image reconstruction, and estimates values of interest within a 3D voxel array or a 2D pixel array. In some examples, these values of interest can represent, for example, the concentration, binding potential, and / or uptake rate of a radioactive tracer in the human body (e.g., positron emission tomography (PET) and single-photon emission computed tomography (SPECT)), or proton density and tissue relaxation parameters for anatomical imaging (MRI).

[0004] Such reconstructed images and density estimates have far-reaching applications. In medicine, applications of functional, molecular, and anatomical images include understanding, diagnosing, and staging diseases, as well as understanding how the healthy human body functions. In preclinical imaging, reconstructed images are valuable for disease research and new drug development. In other fields, reconstructed images may be valuable in security applications such as security inspections, satellite surveillance, or nondestructive testing and seismic imaging.

[0005] A problem associated with all inverse problems is that if the collected data is noisy, a unique noise compensation solution to the inverse problem typically does not exist. If a unique solution does not exist, the burden of choice falls on those who manufacture and use imaging and sensing devices to select one or more fixed noise compensation parameters for the image reconstruction process. The choice of these noise compensation parameters can select one of many possible solutions to the inverse problem. It should be understood that noise in the collected data can impair image reconstruction in various ways, and noise compensation and correction methods are intended to counteract these impairments. In conjunction with this, noise reduction methods can be deployed, which can aim to reduce and mitigate noise in the collected dataset.

[0006] With respect to medical imaging, the image interpreted by the clinician will depend on the manufacturer or user, depending on a particular fixed choice of noise compensation procedure and noise compensation parameters, and if a priori information is used, these fixed noise compensation parameters can control the strength of the a priori information to be used. It should be understood that many possible images may have been presented to the clinician, each of which may have been interpreted differently, potentially leading to a different diagnosis, prognosis, or medical assessment.

[0007] The choice of noise compensation parameters that determine the resulting image for interpretation purposes is a significant issue in the field of imaging. This is particularly true for multimodal or collaborative image reconstruction. In these modalities, where information from another modality is used (e.g., magnetic resonance (MR) images to assist PET reconstruction), it is important not to misuse the information from the other modality, as can occur if inappropriate parameters are selected. Summary of the Invention

[0008] A first aspect provides a method for creating an image representing a measurement dataset by iteratively updating a base image, the method comprising: generating a main dataset from the measurement dataset, the main dataset comprising a dataset having substantially the same level of noise as the measurement dataset; generating at least one additional dataset from the measurement dataset, the additional dataset comprising: a dataset generated from the measurement dataset such that each additional dataset has substantially the same level of noise as the measurement dataset, and each additional dataset is not identical to the main dataset; processing the base image without noise compensation using the main dataset and each additional dataset to obtain a main intermediate image and at least one additional intermediate image, respectively; comparing the main intermediate image and the at least one additional intermediate image to determine an indication of the level of noise present; and using the determined indication of noise present to select noise compensation to apply when processing the base image using the measurement dataset to create a new base image representing the measurement dataset.

[0009] First, it is recognized that noise can be a key issue in imaging. Noise is particularly problematic in applications where noise is significant (e.g., emission tomography image reconstruction). As described in more detail below, image reconstruction approaches using pure maximum likelihood or least squares estimation are not useful for clinical or research tasks. It is recognized that cross-validation can provide some assistance in addressing the noise problem. Cross-validation provides a data-driven selection of noise compensation parameters for image reconstruction.

[0010] The first aspect addresses some of the issues with known image reconstruction approaches while utilizing cross-validation techniques. Specifically, the first aspect recognizes that processing a measurement dataset and processing one or more bootstrapped datasets (each subject to substantially the same noise as the measurement dataset) can provide an objective mechanism for obtaining an indication of the noise level in the measurement dataset. Based on the one or more processed bootstrapped datasets and the processed measurement dataset, the processed bootstrapped datasets can be compared with the processed measurement dataset and appropriate noise compensation parameters calculated for application to the measurement dataset when creating the image.

[0011] Therefore, the noise compensation procedure applied according to the first aspect is one that requires mapping each processed bootstrapped data set as closely as possible to a processed measurement data set, and the method according to the first aspect can be run to find a suitable set of noise compensation parameters to apply to a particular noise compensation procedure.

[0012] A first aspect may provide a method for creating an image representing a measurement dataset by iteratively updating a base image. The method may include creating a primary dataset from the measurement dataset, the primary dataset comprising a dataset having the same, similar, or identical level of noise as the measurement dataset. The method may include creating at least one additional dataset from the measurement dataset, the additional dataset comprising bootstrap datasets sampled from the measurement dataset, the bootstrap datasets being selected from the measurement dataset such that each additional bootstrap dataset has the same, similar, or identical level of noise as the measurement dataset. Each additional bootstrap dataset may be substantially the same size as the measurement dataset. The method may include processing the base image without noise compensation using the first dataset and each additional dataset to obtain a primary intermediate image and at least one additional intermediate image, respectively. The method may include performing a comparison between the primary intermediate image and the at least one additional intermediate image. The comparison may be used to determine an indication of the level of noise present in the measurement (and bootstrap) datasets. The method may include using the determined indication of the presence of noise to select a noise compensation level to apply when processing the base image using the measurement dataset to create a new base image representing the measurement dataset. In particular, noise compensation parameters applied in the noise compensation process may be selected based on the indication of noise generated by the comparison step.

[0013] In some embodiments, the primary dataset comprises a measured dataset. In some embodiments, the primary dataset comprises a bootstrapped dataset created from the measured dataset. In some embodiments, the primary dataset comprises a dataset generated from the measured dataset by other sampling or machine learning methods.

[0014] In some embodiments, the step of creating at least one additional data set includes creating two or more additional data sets from the measured data set, each of the additional data sets comprising: a bootstrapped data set sampled from a selected measured data set, such that each additional data set has substantially the same level of noise as the measured data set.

[0015] In some embodiments, the step of generating at least one additional data set comprises creating one or more bootstrapped data sets sampled from the measured data set.

[0016] In some embodiments, the step of generating at least one additional data set includes generating one or more additional data sets from the measured data set, each of the additional data sets comprising: a data set generated from the measured data set such that each additional data set has substantially the same level of noise as the measured data set, and such that each additional data set is not identical to the measured data set.

[0017] In some embodiments, comparing the primary intermediate image and the at least one additional intermediate image to determine the indication of the presence of noise includes considering the comparison between the primary intermediate image and the at least one additional intermediate image to determine the indication of the presence of noise. Thus, a more complete understanding of the potential noise level in the measurement dataset can be obtained.

[0018] In some embodiments, the step of considering comprises one or more times calculating one or more characteristics of the distribution of the additional intermediate images relative to the primary intermediate image. Such characteristics may comprise, for example, calculating an average noise indicator, calculating a median noise indicator, or calculating a maximum noise indicator.

[0019] In some embodiments, considerations include implementing an artificial neural network to seek appropriate noise compensation to apply to the measured dataset based on one or more additional intermediate images created from the one or more additional datasets, as compared to a primary intermediate image created from the measured dataset. Thus, the optimal noise compensation regime (parameters and procedures) to apply to a given dataset can be efficiently discovered through appropriate application of a suitably configured neural network.

[0020] In some embodiments, the method includes using the selected noise removal for processing iterative updates of the base image based on the measurement dataset to obtain further iterative updates of the base image. Thus, continued iteration can move any base image towards the "true" image represented by the measurement dataset.

[0021] In some embodiments, the method includes processing the base image using a selected noise compensation procedure. In some embodiments, the method includes processing the base image using a different selected noise compensation procedure. In some embodiments, the method includes comparing a created image obtained using the selected noise compensation procedure and a different selected noise compensation procedure to select an appropriate noise compensation procedure to apply to the measurement data set. In some embodiments, the selection of the appropriate noise compensation procedure includes selecting a noise compensation procedure that provides an additional intermediate image that is closest to the primary intermediate image. Thus, embodiments can expand the range of noise compensation possibilities and can optimize its use based on the collected data. Noise compensation methods can be as simple as a Gaussian smoothing kernel (where an optimal kernel width can be found at each iterative step) or as complex as advanced guided smoothing (again, with parameterization specifically optimized based on the measurement data) to be included in the reconstruction.

[0022] In some embodiments, comparing the primary intermediate image and the additional intermediate images to determine an indication of the presence of noise includes implementing an objective function, according to which the goal is to find one or more parameters for a noise compensation procedure that, when found and applied to one or more additional intermediate images, causes an update of each of the additional intermediate images such that their collective difference from the primary intermediate image is minimized. In other words, a denoising procedure can be used that can be directly embedded into any or every step of the image reconstruction iterative algorithm. Embodiments can operate such that they adaptively and precisely optimize the parameterization of any denoising procedure for each iterative update of the base image for a given measurement data set.

[0023] In some embodiments, the objective function includes a metric related to the distance between the additional intermediate image and the primary intermediate image. In some embodiments, the distance-related metric includes a sum of squared distances, a Kullback-Leibler metric of distances, a norm of any distance metric, or other suitable distance-related cross-likelihood metrics. In some embodiments, the iterative update includes an additive or multiplicative update. That is, the comparison between the primary intermediate image and the additional intermediate image can be performed in various ways to determine the noise level in the measurement dataset and, therefore, to determine appropriate noise compensation parameters for a given noise compensation procedure.

[0024] In some embodiments, the noise compensation process corresponds to a regularized iterative update derived from any regularized iterative image reconstruction algorithm. In some embodiments, the noise compensation procedure corresponds to an artificial neural network trained to map any additional intermediate images to match the primary intermediate image, such that the artificial neural network training can be applied to the primary intermediate image to obtain an update of the base image. That is, the noise compensation procedure applied when processing the base image to obtain the image representing the measurement dataset can be selected from a variety of available noise compensation procedures.

[0025] In some embodiments, the parameters of the noise compensation are modified to induce a higher level of noise compensation than found by the optimization process to slow down the iterative update of the base image. In some embodiments, the parameters of the noise compensation are modified to induce a higher level of noise compensation than found by the optimization process to avoid the accumulation of residual noise. Thus, a cautious update process can be implemented to more gently iteratively update the base image.

[0026] In some embodiments, continued iterative updating causes the implemented noise compensation parameter selection to become closer and closer to the parameters found by the optimization of the objective function. In some embodiments, continued iterative updating causes the implemented noise compensation parameter selection to become closer and closer to the parameters found by the optimization of the objective function. In some embodiments, continued iterative updating causes the implemented noise compensation parameter selection to become closer and closer to the parameters found by the optimization procedure, and the parameter selection corresponds to the highest level of noise compensation found from all optimization procedures previously used in the continued iterative updating.

[0027] In some embodiments, the step of generating at least one additional data set includes generating one or more additional data sets from the measured data set, the generating including a sampling or machine learning method, and each of the additional data sets includes: a data set generated from the measured data set, such that each additional data set has substantially the same level of noise as the measured data set, and such that each additional data set is not exactly the same as the measured data set.

[0028] In embodiments where the method comprises processing the base image using a selected noise compensation procedure, the noise compensation approach may be as advanced as the use of an artificial neural network.

[0029] In embodiments where the denoising process is directly embedded in any or each step of the image reconstruction iterative algorithm, it will be appreciated that the method operates to adaptively and accurately optimize the parameterization of any denoising procedure for each iterative update of the base image for a given measurement data set. The adaptive and accurate optimization of the denoising process is automatic and does not require any user-provided parameters or guidance.

[0030] In embodiments where the method includes a step of applying noise compensation, the noise compensation process can correspond to a regularized iterative update derived from any regularized iterative reconstruction algorithm. This approach can allow for automatic and precise optimization of the regularization level from more than one a priori choice, allowing for automatic selection of the strength of different choices of a priori information. For example, how much guided smoothing information to use compared to unguided smoothing. In other words, rather than selecting from a set of possible noise compensation procedures, how much of each noise compensation procedure to apply can be selected. This implementation means that the method can be run such that, rather than selecting a single candidate from a set of possible noise compensation candidates, different portions of more than one noise compensation candidate can be applied.

[0031] As a matter of clarification, it should be noted that, in some embodiments, the method of the first aspect is contemplated to be fully automatic. That is, the method can occur without requiring any user selection of operating parameters. In other words, the method can be fully data-driven, as, for example, overly cautious preselection of initial parameters to accommodate all data sets and all noise levels results in a fully automatic and precise process for processing any measurement data set.

[0032] In summary, a first aspect provides a method for creating an image representing a measurement dataset by iteratively updating a base image, the method comprising: generating a main dataset from the measurement dataset, the main dataset comprising a dataset having substantially the same level of noise as the measurement dataset; generating at least one additional dataset from the measurement dataset, the additional dataset comprising: a dataset generated from the measurement dataset such that each additional dataset has substantially the same level of noise as the measurement dataset, and each additional dataset is not identical to the main dataset; processing the base image without noise compensation using the main dataset and each additional dataset to obtain a main intermediate image and at least one additional intermediate image, respectively; comparing the main intermediate image and the at least one additional intermediate image to determine an indication of the level of noise present; and using the determined indication of noise present to automatically select noise compensation to apply when processing the base image using the measurement dataset to create a new base image representing the measurement dataset.

[0033] The at least one additional data set may comprise a bootstrapped data set generated from the measured data set in a purely data-driven manner. This approach is truly data-driven and reduces any chance that the method will learn from other data. Of course, some embodiments may allow the at least one additional data set to comprise a data set generated from the measured data set by an artificial neural network (ANN). In some embodiments, the ANN may be used in part or in whole for the noise compensation procedure.

[0034] A second aspect provides a computer program product which, when executed on a computer, is operable to perform the method of the first aspect.

[0035] A third aspect provides an imaging device configured to create an image representing a measurement dataset from a base image, the device comprising: dataset generation logic configured to generate a primary dataset (which has substantially the same level of noise as the measurement dataset) from the measurement dataset and at least one additional dataset from the measurement dataset, each additional dataset being selected so that they include datasets having substantially the same level of noise as the measurement dataset; processing logic configured to process the base image using the primary dataset and the at least one additional dataset to obtain a primary intermediate image and at least one additional intermediate image, respectively; comparison logic configured to compare the primary intermediate image and the at least one additional intermediate image to determine an indication of a level of noise present; and image creation logic configured to use the determined noise indication to select a level of noise compensation to apply when processing the base image using the measurement dataset to create a new base image representing the measurement dataset.

[0036] The embodiments of the third aspect correspond to the embodiments described with respect to the first aspect.

[0037] Further particular and preferred aspects are set out in the accompanying independent and dependent claims. Features of the dependent claims may be combined with features of the independent claims as appropriate, and in combinations other than those explicitly set out in the claims.

[0038] Where an apparatus feature is described as being operable to provide a function, it will be understood that this includes apparatus features that provide that function or that are adapted or configured to provide that function. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The embodiments of the present invention will now be further described with reference to the accompanying drawings, in which:

[0040] Figure 1 A set of PET images obtained with different reconstruction methods using three different count levels was included;

[0041] Figure 2 yes Figure 1 MR images of subjects in

[0042] Figure 3 Included are a set of PET images acquired using three different count levels with different reconstruction methods that exploit structural prior information from the subject's MRI;

[0043] Figure 4 The general way of data processing is shown schematically;

[0044] Figure 5 Schematically shows the Figure 4 A conceptual overview of general imaging methods for data processing. DETAILED DESCRIPTION

[0045] As mentioned earlier, when dealing with inverse problems in the field of imaging, the goal is to estimate a set of object representation parameters or a multidimensional density function that represents some object of interest, often called an image. For example, in medical imaging, the inverse problem of interest is often called image reconstruction.

[0046] This is a problem in the medical imaging industry, as manufacturers and / or users are required to specify noise compensation parameters for image reconstruction. For example, in PET imaging, these noise compensation parameters can include the number of iterations and the level of smoothing. The selected parameters can have a significant impact on the reconstructed image. In medical imaging applications, the reconstructed image influences how clinicians interpret the scan "results," which in turn impacts diagnostic and patient management decisions. For PET and SPECT imaging, the emission data obtained is very noisy due to the limited scan time and the limited amount of radioactivity injected into the patient or subject, resulting in the reconstructed image also being subject to noise.

[0047] Typical solutions for compensating noise in image reconstruction fall into seven categories, each of which requires the manufacturer and / or the user to preselect noise compensation parameters:

[0048] 1) Post-smoothing

[0049] Post-reconstruction post-processing and / or smoothing of images / parameter maps can successfully mitigate noise. However, this post-processing comes at the expense of reduced spatial resolution: important details in medical images are lost. This applies to traditional filtered back-projection (FBP) methods as well as iterative image reconstruction methods such as ordered subset expectation maximization (OSEM). Unless smoothing is applied, these methods all produce noisy images. More advanced post-processing methods can be applied, but in each case, post-processing still requires selecting a noise compensation level, facing the same issues described below for Category 3.

[0050] 2) Early stopping

[0051] Methods such as Maximum Likelihood Expectation Maximization (MLEM) or its accelerated version, OSEM, are often stopped early during the iteration process, eliminating the need for the aforementioned smoothing. However, this comes at the expense of potentially spatially varying noise and resolution properties, with some regions having lower noise than others and some details in the image being incompletely resolved while others are. Finally, the number of iterations needs to be chosen (the noise compensation parameter in this case is the number of iterations), so the noise level is directly selected by the user. Cross-validation and other stopping rules eliminate the need for choosing the number of iterations, but leave the problem of incomplete convergence of iterative reconstruction algorithms.

[0052] 3) Regularization method

[0053] Bayesian and maximum a posteriori (MAP) methods are used with iterative algorithms that impose a prior expectation on the image, such as smoothness or smoothness within a defined region (e.g., by using anatomical information and edge-preserving priors, such as the regularization used to guide PET reconstruction using MRI). The problem with these methods is that the parameters (called hyperparameters in the Bayesian context) need to be carefully selected, which affects the level of noise and resolution, and in practice the parameter selection needs to be carefully tuned for each scan. In fact, it is extremely difficult to ensure that the best parameters are selected for any given reconstruction of a given data set. Underestimating the regularization will leave too much noise in the image, while overestimating the regularization parameter will damage important image details. This is particularly problematic for multimodal imaging, if MRI (for example) is to be used to guide the regularization of PET or SPECT image reconstruction: how much prior information should be used and how "strong" should the prior be?

[0054] 4) Benchmark changes

[0055] These methods use spatial basis functions other than traditional pixels or voxels, such as larger regions of interest (ROIs), or kernel spatial basis functions derived from temporal similarity of details or derived from similarity measures of other imaging modalities (e.g., MRI). These methods successfully reduce noise but impose a certain structure on the image, again placing the burden of parameter selection for kernel generation on the user, and thus the level of detail and noise compensation, as well as the number of iterations to use, is again in the hands of the user.

[0056] 5) Filtering between updates

[0057] This is similar to the post-smoothing method described above, but is performed between iterations. The need to decide how much smoothing to apply also raises the same issue: the problem of parameter selection for noise compensation.

[0058] 6) Stopping based on cross-validation

[0059] This approach terminates the reconstruction early and thus uses an incompletely converged reconstruction, potentially suffering from similar problems as in category 2 above. Consequently, cross-validation stopping rules have not gained any significant adoption in, for example, the emission tomography community.

[0060] 7) Parameter selection based on limited grid search

[0061] This approach requires the user to preselect a limited number of fixed candidate parameter sets for noise compensation. A complete reconstruction is then performed for each candidate parameter set, and either an L-curve approach or a cross-validation method is used to select which of these reconstruction parameter sets to use. These approaches are limited in two main ways: they require the user to preselect a limited number of fixed candidate parameters, and they require a complete (and often computationally intensive) image reconstruction for each candidate parameter set. Furthermore, in the case of cross-validation, it is also necessary to define the subset of data used for cross-validation purposes, for which there are many possible options.

[0062] Specific implementations of these modalities used in the industry for clinical PET imaging include: OSEM and / or HD-PET from Siemens, which typically rely on early termination (category 2) or post-processing (category 1) to compensate for noise; and QClear from GE, which requires the user to decide on key regularization parameters (category 3).

[0063] The main drawbacks of methods that rely on methods that fit into the seven categories above to compensate for image noise in emission tomography data include the following: there is no precisely optimized, practically robust, or computationally efficient method for selecting the level of noise compensation. Clearly, different datasets will require different levels of noise compensation, depending on the noise level and the object being imaged. Furthermore, the user or manufacturer needs to specify how much noise compensation (e.g., smoothing or regularization) should be present in the image, which is subjective or, at best, not optimal for the actual data acquired and involves a user-defined trade-off between noise and image detail. If multimodal information is used to assist in reconstruction, it is unknown a priori how much information should or should not be used.

[0064] Overview

[0065] Before describing in detail the details of a specific implementation of the arrangement, a general overview of the approach is provided.

[0066] It is well known that noise can be a critical issue in imaging. It is particularly problematic in applications where noise is significant, such as emission tomography image reconstruction. As mentioned above, image reconstruction approaches that purely use maximum likelihood or least squares estimation are not useful for clinical or research tasks.

[0067] Current methods for counteracting noise include: post-reconstruction smoothing, which carries with it the question of how much smoothing to do; early termination of iterative algorithms, which brings with it the question of when to terminate, what such an image corresponds to, and what to focus on for convergence of spatial variables; and maximizing a posteriori reconstruction, which carries with it the question of how much regularization should be done (i.e., what is the choice of a hyperparameter, usually labeled β).

[0068] It is well known that cross-validation (CV) can provide some help in solving noise problems. CV provides data-driven noise compensation parameter selection for image reconstruction.

[0069] Known CV methods have problems, for example, because CV requires data partitioning, and early use of CV in, for example, PET reconstruction simply divides the acquired data into two, so the "optimality" of the noise compensation parameters ultimately depends on a subset of the data. CV in known approaches either does not provide reliable images (e.g., early stopping methods suffer from early termination problems) or involves relatively coarse selection from a limited number of fixed candidate noise compensation parameter choices, where a complete image reconstruction is required for each choice.

[0070] The method recognizes that bootstrapping can be a useful approach. Bootstrapping a new dataset means that data of the same size can be used as an "additional" dataset, which solves the first problem of CV mentioned above.

[0071] Likewise, the approach recognizes that data generation methods (e.g. from artificial neural networks) can be used to obtain new datasets, which also means that data of the same size can be used as an “additional” dataset, again solving the first problem of CV mentioned above.

[0072] Figure 4 The general approach used in the various implementations described in detail below is schematically illustrated.

[0073] Processing the measurement data and processing one or more generated (e.g., bootstrapped) data sets (each subject to substantially the same noise as the measurement data) provides an indication of noise in the measurement data. From the processed generated (e.g., bootstrapped) data sets and the processed measurement data, the processed generated (e.g., bootstrapped) data and the processed measurement data can be compared and appropriate noise compensation parameters calculated for application to the processing of the measurement data.

[0074] The noise compensation procedure is the mapping required to make each processed generated (eg bootstrapped) data set match the processed measured data as closely as possible.

[0075] The noise compensation parameters for a given noise compensation procedure are given by:

[0076]

[0077] The method is used to find a suitable set of noise compensation parameters to be applied to a specific noise compensation procedure.

[0078] It will be appreciated that a regime may be applied to one or more noise compensation procedures for a given set of measurement data, each application of the regime giving an associated set of one or more noise compensation parameters for the given noise compensation procedure.

[0079] The method may then be implemented to objectively "select" an appropriate noise compensation procedure to apply to a given measurement data set. In other words, the method may be implemented in this way to identify the noise compensation procedure (of a given choice of noise compensation procedure) that is most suitable for a given measurement data set.

[0080] Figure 5 Schematically shows the Figure 4 A conceptual overview of general imaging methods for data processing. Figure 4 and Figure 5 The described approach can provide objective, user-independent solutions to inverse problems such as image reconstruction and dynamic / functional parameter estimation in PET or SPECT.

[0081] The approach can allow image reconstruction without requiring the manufacturer or user to specify hyperparameters related to the level of noise compensation to be used. The approach can provide a useful approach related to multimodality imaging (e.g., simultaneous PET-MR), where it is desirable to utilize information from each modality but how much prior information, if any, can be safely used for reconstruction is unknown.

[0082] The approach recognizes that one or more easily generated bootstrapped datasets can be used to estimate appropriate noise compensation parameters for each and every iterative update.

[0083] The method recognizes that almost all iterative image reconstruction methods can be viewed as updating a function U at any given step to provide a new image θ (k+1) , where the update function U uses the current image (parameters θ of iteration k) (k) Description) and measurement data m:

[0084] θ (k+1) =U(θ (k) ,m) (1)

[0085] Iterative image reconstruction algorithms actually proceed at each iteration to add a new "change image" to the current image, thereby moving towards an image that satisfies the requirements of an objective function (e.g., maximum likelihood (ML), least squares (LS), or maximum a posteriori (MAP)). For example, for the MLEM algorithm, it is the ML objective that needs to be satisfied. For MAP, it is a user-specified regularization objective (with user-specified regularization hyperparameters) that needs to be satisfied, which can utilize prior information from other imaging modalities (e.g., MRI for PET). However, MLEM and other non-regularized objectives / algorithms (e.g., LS / conjugate gradient) can lead to excessive noise amplification, while MAP and other regularization methods lead to the user choosing a trade-off between image detail and image noise.

[0086] The method recognizes that it is appropriate to use a bootstrapped replicate dataset b, obtained by resampling the measurement data m, to give a bootstrapped update image at iteration k:

[0087]

[0088] The updated image will also be affected by the noise present in b, but it is worth noting that this will be different from the noise in m (bootstrapping treats the actual measurement data m as a model of the mean of a large noisy dataset such as b).

[0089] The method optimizes noise compensation parameters applied to the bootstrapped update and then uses these optimized noise compensation parameters to process the standard iterative update from the measurement data, thereby fitting the bootstrapped update image to the regular measurement data update image to obtain the next iterative update of the image.

[0090] The optimization phase is the image space fitting, which can be achieved by implementing a cross objective function, an "ensemble average objective function," or a cost function as follows:

[0091]

[0092] The goal is to be the denoising operator F β {}Find one or more optimal noise compensation parameters, when the noise reduction operator F is set in some way (to be described in detail below) β {}Apply to image bootstrap iterative update When , the bootstrapped update that best fits the regular update image is obtained according to the cross-objective function

[0093] The cross-objective function is a metric related to the distance D between the two images (which can be measured in a variety of ways), but for Gaussian data it corresponds to a least squares fit (to maximize the Gaussian cross likelihood), and for Poisson distributed data it corresponds to the Kullback-Leibler (KL) distance metric (to maximize the Poisson cross likelihood).

[0094] This cross objective function can also be viewed as a “grand average objective function”. The grand average objective function is a function that updates images with a large group of noises (given by modeling) and any one or more noise updates The distance D between them is a measure of correlation.

[0095] Finding the optimal noise reduction parameters (which minimizes the cross-objective), the next image update can be given by:

[0096] θ (k+1) =F β {U(θ(k) ,m)} (4)

[0097] The process can be repeated for the next iterative update, and so on.

[0098] The approach recognizes that it is necessary to modify the noise compensation parameters in early iterative updates to produce a higher level of noise compensation than found by the optimization procedure, thereby slowing down the iterative updates and avoiding the accumulation of residual noise caused by the inability to perfectly fit the noise-compensated bootstrap update image to the regular measurement data update image.

[0099] The approach recognizes that with successive iterative updates, the noise compensation parameters are selected to get closer and closer to the noise compensation parameters found by the optimization routine, and that the noise compensation parameters are selected to correspond to the highest level of noise compensation found from all optimization routines previously used in successive iterative updates.

[0100] Figure 5 Schematically shows the Figure 4 A conceptual overview of the general image reconstruction method of the data processing method. Figure 5 Conceptually shown is the processing of a base image by iterative updates U using a measurement dataset to provide a "standard" update. Also conceptually shown is the processing of the base image using the same iterative update function U, but using a bootstrapped dataset to provide a "bootstrapped" update. These updates can be considered "intermediate" images or updates. Figure 5 As schematically shown in , noise compensation parameters can be found that operate on the bootstrapped image updates to minimize the difference between the standard image update and the bootstrapped image update. Once the noise compensation parameters that satisfy the minimum difference criterion are found, these noise compensation parameters can be used to process the basis image by iteratively updating U while also applying noise compensation to give a new, updated basis image.

[0101] After giving a general overview, the following details the specific implementations of some of the methods:

[0102] a) Additional filter for changing images

[0103] This is a simple and intuitive approach that may appeal to many people due to its simplicity, flexibility, and stability. The updated function is modeled as follows:

[0104]

[0105] where Δ (k) (b) is the "change image" of iteration k, which is effectively added to the current image to get the next update. The method selects a denoising procedure for the change image, which can be anything from a simple Gaussian smoothing to a multimodal guided filtering procedure, or even a machine learning based denoising (e.g. artificial neural network). The denoising procedure can be represented by the operator Fβ {}express,

[0106]

[0107] The objective is to find the "best" choice of one or more noise compensation parameters β by using the cross-objective function (3). In the case of PET or SPECT data, the objective would correspond to minimizing the KL distance between the two images (this distance metric comes directly from seeking the maximum Poisson log-likelihood estimate). It will be appreciated that an objective other than minimizing the KL distance could be chosen.

[0108] In equation (6), F β A noise compensation procedure (e.g., simple smoothing, or multimodality-guided edge-preserving smoothing in the case of MR-guided PET or SPECT) has one or more noise compensation parameters β. In one example, the user selects the noise compensation procedure rather than the noise compensation parameters β. A cross-target fit based on the modality is automatically run to adapt to the noise level in the measurement data and select appropriate noise compensation parameters.

[0109] It will be appreciated that although the examples above relate to the case where noise compensation is applied to additive updates ("change images"), the approach may be similarly applied to multiplicative updates, or even to the entire update image.

[0110] One or more “optimal” noise compensation parameters β are found by using the cross-objective function, and the optimized noise compensation parameters can be used to update the image obtained from the original measurement data according to the following equation.

[0111]

[0112] b) Simple update between filters

[0113] A variation of the method described in (a) wherein (6) is replaced by:

[0114]

[0115] This approach differs from the approach described in (a) in that the entire update image is noise compensated, not just a separate noisy update "change image".

[0116] c) MAP-EM Update

[0117] Another implementation of the general approach is to apply it to Bayesian methods using a MAP objective. Any MAP update algorithm that relies on a chosen prior and regularization hyperparameters can be used to generate processed bootstrapped updates.

[0118] For example, for the weighted quadratic Gibbs prior probability of an image, the method of DePierro [1] can be used to obtain an iterative EM update based on the MAP objective, which has the following general form:

[0119]

[0120] where terms B and C depend on the current image θ (k) The weighted combination of neighboring voxels allows, for example, multimodal guided regularization via spatially variable weighted quadratic priors (e.g., the method of Bowsher [2]). According to such an implementation, the noise compensation parameter β is called a hyperparameter of the Bayesian prior, where it is obvious that β = 0 corresponds to no noise compensation, so choosing β is a crucial challenge.

[0121] Based on Equation (9), cross-objective optimization of β can be used together with bootstrapped data to include an appropriate amount of prior information in the iterative MAP-EM update. This general implementation addresses significant challenges associated with regularization methods, especially in the context of multimodal guided image reconstruction.

[0122] This approach allows for automatic and accurate optimization of β, and the user does not need to specify any level of regularization to achieve a converged MAP-EM image reconstruction algorithm. The algorithm provides a final converged estimate of the reconstructed image that satisfies the desired regularization objective function.

[0123] It should be understood that more than one regularization component can be used in the objective function, e.g., β1 for the first part, β2 for the second part, etc. This may be of particular value in the context of guided image reconstruction, whereby the level of guided regularization can be automatically and accurately found, as well as the level of conventional unguided regularization (e.g., a quadratic penalty function).

[0124] It should be understood that as the noise in the measured data approaches zero (i.e., infinite counts), the bootstrapped data will tend toward the measured data. Therefore, no noise compensation is required for data without noise (the optimal β from the cross-objective function, the "grand average objective function," will approach zero). In contrast, as noise increases (i.e., low counts), the updates derived from the bootstrapped data will require an increased level of noise compensation to accommodate the updates derived from the measured data. In other words, the optimal β from the cross-objective fit will increase as the noise in the measured data increases, as more noise compensation is required to map the noisy updates to the mean model of the set of noisy updates.

[0125] Display method

[0126] In order to demonstrate the implementation effect of the above general method, real data is used to demonstrate the situation of MAP EM 3D reconstruction.

[0127] The figures described below illustrate the effectiveness of the general strategy for automatic noise removal of PET data at different noise levels without requiring the user to select a noise compensation level.

[0128] Figure 1 Comparisons of low, medium, and high count data are included (1%, 10%, and 100% of the actual data were measured). The first column includes conventional MLEM reconstructions for these three cases, and the second column shows these images with a typical post-smoothing using a 4mm Gaussian kernel (usually performed as a standard for clinical images). The three rightmost columns (columns 4, 5, and 6) show standard MAPEM reconstructions for different choices of the hyperparameter β, from which it can be seen that visually better results are obtained due to different hyperparameter choices for different count levels. The contoured third column in the figure shows that the bootstrapped optimized MAPEM method automatically provides high-quality images for all count levels, which cannot be found using other methods unless the user adjusts and explores their hyperparameters.

[0129] Figure 2 Shown Figure 1 MR image of the object data.

[0130] Figure 3 Including Figure 1 Similar comparisons, the general structure of columns and images are similar to Figure 1 Same as described in , but now use Figure 2 MR images in order to provide prior structural information to MAP EM using the Bowsher method [2] to assist in noise compensation. In this case, the bootstrapped MAPEM method automatically selects appropriate hyperparameters for all noise levels. It should be understood that the level of noise compensation applied by the above embodiment is appropriate to the noise level in the data. It is believed that clinicians prefer images such as those shown in the third column compared to the current standard methods shown in the other columns.

[0131] Figure 1 and Figure 3 Possible results using an implementation according to the described approach are shown for high count data and very low count data, using the same algorithm in both cases. It can be seen that consistently high-quality images can be obtained by applying the method according to the described approach. The third column shows very good results where the intensity of the smoothing and the amount of prior used are visually appropriate.

[0132] It should be understood that there is scope for applying the described approach to a variety of other priors and filters, as well as all the various hyperparameters involved in these priors and filters. The large number of priors and image processing filters that can be considered means that the described approach has considerable potential for the development of state-of-the-art image denoising methods (e.g., guided smoothing-based methods, local patch-based methods, or those based on various artificial neural network architectures) by embedding them into a rigorous framework that provides an automatically selected level of noise compensation for image reconstruction, so that the user or manufacturer only needs to select which noise compensation method to use without having to specify the noise compensation parameters (i.e., how much noise compensation to apply).

[0133] The proposed method allows for objective and precise selection of the trade-off between image detail and image noise throughout iterative updates via cross-objective fitting. This approach removes arbitrary noise compensation parameter selections from users and / or manufacturers, providing robustness to reconstructed image quality. This robustness to highly variable count levels has not previously been achieved in emission tomography. This approach is particularly useful in the context of multimodality imaging, where additional images may be used to assist in noise removal, and the decision on the intensity of this additional information source can be highly subjective.

[0134] Advantages of using the described implementation may include, for example:

[0135] 1) Confidence in the objectivity of the resulting image quality. Automatic selection of the level of noise compensation to apply means that the image reconstructed by bootstrapping cross-target denoising parameter estimates is a low-noise image with only as much detail as supported by the data. Results show that the method described converges to images of good quality, based on the statistical quality of the data. Existing methods typically rely on varying levels of noise reduction specified by the user or manufacturer, often resulting in trade-offs with image features that are not necessarily supported by the data and may be misrepresentations of the scan.

[0136] 2) A range of implementations for any denoising or noise compensation method. This approach allows implementation within a framework that allows for the "optimal" development of any denoising procedure, such as simple Gaussian kernel smoothing methods, simple regularization (e.g. Figure 1 ) to the multimodal guided regularization method (as Figure 3 (as shown) and the use of machine learning methods (e.g., artificial neural networks). This may be particularly important for multimodal guidance, where it is common to overuse any prior structural information, thereby providing misleading and / or artificial-looking images. The results obtained using, for example, the above approach illustrate how to use prior image guidance with intensity and edge sensitivity (which automatically adapts to the quality of the data), avoiding the main problems of existing guidance regularization methods.

[0137] 3) Simplicity, Applicability, and Practicality: Manufacturers or users are no longer tasked with specifying noise compensation parameters to reconstruct a given dataset, so the level of information in the image (spatial resolution and detail versus noise level) no longer depends on subjective parameter selection. The method is very simple to implement and allows any iterative image reconstruction method to be adapted by embedding any preferred noise compensation procedure, where the strength of the noise compensation will depend on the data and be automatically found by the method. The scope of exploring different state-of-the-art noise compensation methods is considerable, allowing for multimodality-based noise compensation to be implemented at a strength supported by the measured data.

[0138] 4) Theoretical appeal: The reconstructed image uses noise compensation parameters found from a statistically motivated objective function: it is the image that optimizes the cross-objective for a given update step in the iterative reconstruction, which can be a cross-likelihood (Poisson or Gaussian).

[0139] from Figure 1 and Figure 3 As can be seen in the diagrams in Figure 1, the described approach has been successfully implemented using 3D real PET data for three different count levels, from low to high noise levels. In the example shown, the approach has been implemented using noise compensation via MAP regularization, and for the MRI case, guided MAP regularization (where the structural image is used in the prior - the regularization level is controlled by a bootstrapped cross-target).

[0140] It should be understood that this approach can also be implemented in 2D and 4D imaging methods.

[0141] It will be further appreciated that the described approach can be applied to any inverse problem where parameter estimation is present and noise in the data is a performance limiting factor. Prime examples of commercial applications include medical imaging, in particular: PET or SPECT scanners: for clinical and preclinical imaging reconstruction of cancer, heart, and brain, where limited scan times and limited injection activity result in count-limited (noisy) data; low-volume computed tomography (CT): for reconstruction of anatomical images, angiographic images when data quality is low (to reduce radiation exposure or for fast dynamic imaging); and magnetic resonance imaging (MRI) sequences with low signal-to-noise ratio (SNR): some MR images have limited signal-to-noise ratio and therefore have noisy k-space data.

[0142] Beyond medical imaging, the method can be used for any parameter estimation problem subject to noisy data. Other areas where this method could be applied include image processing and denoising (e.g., photo and image denoising, video denoising); non-destructive testing (e.g., CT and impedance tomography); remote sensing (e.g., satellite imaging and seismic imaging); astrophysics (e.g., multispectral imaging); and security imaging (e.g., CT).

[0143] Cross-validation methods [3] and bootstrap filtering methods [4] are known. The known methods rely on cross-validation as a stopping criterion - this means that the results are susceptible to spatially varying convergence (spatially varying resolution and noise). Newer advanced cross-validation methods [5] require pre-selection of a limited number of example noise compensation parameters, specifying a subset of data for cross-validation, and then performing a full reconstruction of each example noise compensation parameter set. This results in low selection accuracy of the noise compensation parameters and also depends on the choice of data subset for cross-validation purposes. Other more advanced generalized cross-validation methods [6] rely on fixed regularization instances (such as total variation) and therefore do not provide flexibility, scope, and general applicability. Bootstrap filtering uses cross-validation to stop the forward projection of the image. Forward projection is used as a means to generate bootstrap samples. The known methods involve the reconstruction of a large number of bootstrap samples and find the expectation.

[0144] The methods and implementations described here differ from known methods and implementations in that:

[0145] The approach may involve methods that can be run only once to converge and do not include a stopping criterion.

[0146] The method is used so that the bootstrapped dataset comes directly from the resampling of the original measurement data, rather than from the forward projection of the cross-validation stop images.

[0147] This approach allows for the use of a single bootstrapped dataset rather than multiple datasets or the selection of subsets of data for cross-validation.

[0148] The approach allows any denoising procedure to be directly embedded into any iterative reconstruction algorithm at any or every step. The approach allows any denoising parameterization to be adaptively and accurately optimized for each update. The approach allows any denoising parameterization to be automatically and accurately optimized for each update.

[0149] The approach involves only one iterative reconstruction procedure to provide accurately optimized noise cancellation parameters, eliminating the need for multiple reconstructions and subsequent retrospective comparisons by cross-validating low-precision selections from a limited number of pre-selected noise cancellation parameters.

[0150] It will be appreciated that the approach expands the range of noise compensation possibilities and its use can be optimized based on the data collected. Noise compensation approaches can be as simple as a Gaussian smoothing kernel (where the optimal kernel width is found at each iteration step) or as complex as advanced guided smoothing (again, with parameterization optimized specifically based on the measured data) to be incorporated into the reconstruction. In contrast, known approaches such as those in [3] and [4] involve stopping or a single "non-linear" filtering method defined by the average of multiple bootstrapped MLEM results to approximate this. This provides a one-shot averaging process that is further limited by its central use in stopping image estimation, with unknown spatially varying convergence.

[0151] The approach described herein can be implemented for any standard iterative image reconstruction method and provides a method where, for example, only one (or more) bootstrapped resampled datasets allow powerful state-of-the-art denoising algorithms to be embedded directly into image reconstruction with relative simplicity. The method provides a mechanism for automatic, data-dependent and accurate optimization of the strength of any denoising at each update.

[0152] Although illustrative embodiments of the present invention have been disclosed in detail herein with reference to the accompanying drawings, it should be understood that the invention is not limited to the precise embodiments and that various changes and modifications may be made therein by those skilled in the art without departing from the scope of the invention as defined by the appended claims and their equivalents.

[0153] References

[0154] [1]ARDe Pierro (1995) A Modified Expectation Maximization Algorithm for Penalized Likelihood Estimation in Emission Tomography, IEEETrans.Med.Imaging, vol.14, no.1, pp.132-137.

[0155] [2]JEBowsher et al(2004)Utilizing MRI Information to Estimate F18-FDG Distributions in Rat Flank Tumors,IEEE Nucl.Sci.Symp.Conf.Rec.,vol.4,2004,pp.2488-2492.

[0156] [3]Coakley,K.J.(1991),A cross-validation procedure for stopping theEM algorithm and deconvolution of neutron depth profiling spectra IEEETransactions on Nuclear Science Volume:38,Issue:1.

[0157] [4]Coakley,K.J.(1996),Bootstrap method for nonlinear filtering of EM-ML reconstructions of PET images.Int.J.Imaging Syst.Technol.,7:54-61.doi:10.1002 / (SICI)1098-1098(199621)7:1<54::AID-IMA7>3.0.CO;2-T.

[0158] [5]Zhang et al(2017)Regularization parameter selection for penalized-likelihood list-mode image reconstruction in PETPhys.Med.Biol.62 5114.

[0159] [6]Xiongjun Zhang,Bahram Javidi,and Michael K.Ng(2017),Automaticregularization parameter selection by generalized cross-validation for totalvariational Poisson noise removal Applied Optics Vol.56,Issue 9,pp.D47-D51.

Claims

1. A method for creating an image by iteratively updating a base image, the image representing a measurement dataset, the method comprising: using the measurement dataset as a primary dataset, or generating a primary dataset from the measurement dataset by generating a bootstrapped dataset from the measurement dataset; generating at least one different additional dataset from the measured dataset, the different additional dataset comprising: a dataset generated from the measured dataset by creating one or more bootstrapped datasets sampled from the measured dataset, such that each different additional dataset has substantially the same level of noise as the measured dataset and such that each different additional dataset is not identical to the primary dataset; processing the base image without noise compensation using the primary data set to obtain a primary intermediate image, and processing the base image without noise compensation using each different additional data set to obtain at least one additional intermediate image; comparing the primary intermediate image and the at least one additional intermediate image to determine an indication of a level of noise present; and using the determined indication of the presence of noise to select noise compensation to apply when processing a base image using the measurement dataset to create a new base image representing the measurement dataset; Wherein, comparing the primary intermediate image and at least one or more additional intermediate images to determine an indication of the presence of noise comprises: implementing an objective function according to which the goal is to find one or more parameters for a noise compensation procedure which, when found and applied to the one or more additional intermediate images, causes an update of each of the additional intermediate images such that their total difference with the main intermediate image is minimized; and The parameters of the noise compensation are modified to result in a higher level of noise compensation than found by the optimization procedure in order to slow down the iterative updating of the base image and avoid accumulation of residual noise, and wherein continued iterative updating causes the parameter selections of the implemented noise compensation to become increasingly close to the parameters found by the optimization procedure, and wherein the parameter selections correspond to the highest level of noise compensation found from all optimization procedures previously used in continued iterative updating.

2. The method for creating an image according to claim 1, wherein: The method comprises using the selected noise compensation to generate an iterative update of the base image based on the measurement data set to obtain the new base image representing the measurement data set.

3. The method of creating an image according to claim 2, comprising: The base image is processed using different selected noise compensation procedures.

4. The method of creating an image according to claim 3, comprising: The created images obtained using the selected noise compensation procedure and the different selected noise compensation procedure are compared to select a noise compensation procedure to apply when processing the base image using the measurement dataset to create a new base image representing the measurement dataset.

5. The method of creating an image according to claim 4, wherein: The selection of a suitable noise compensation procedure comprises comparing an intermediate image obtained using the noise compensation procedure and the primary intermediate image.

6. The method for creating an image according to any one of claims 1 to 5, wherein: The objective function comprises a metric related to a distance between the one or more additional intermediate images and the main intermediate image.

7. The method of creating an image according to claim 6, wherein: Distance-related metrics include: the sum of squared distances, the Kullback-Leibler metric of distances, any norm of the distance metric, or one of other appropriate distance-related cross-likelihood metrics.

8. The method of creating an image according to claim 2, wherein: The iterative updating includes additive updating or multiplicative updating.

9. The method of creating an image according to claim 1, wherein: Said processing with noise compensation corresponds to a regularized iterative update derived from any regularized iterative image reconstruction algorithm using said measurement data set.

10. A computer program product, which, when executed on a computer, is operable to perform the method of any one of claims 1 to 9.

11. An imaging apparatus configured to create an image representing a measurement data set from a base image by iteratively updating the base image, the apparatus comprising: a dataset generation logic configured to generate a primary dataset from the measurement dataset using the measurement dataset as a primary dataset or by generating a bootstrapped dataset from the measurement dataset, and the dataset generation logic is further configured to generate at least one different additional dataset from the measurement dataset, the additional different datasets comprising: datasets generated from the measurement dataset by creating one or more bootstrapped datasets sampled from the measurement dataset, such that each different additional dataset has substantially the same level of noise as the measurement dataset and such that each different additional dataset is not identical to the primary dataset; processing logic configured to process the base image without noise compensation using the primary data set to obtain a primary intermediate image, and to process the base image without noise compensation using each different additional data set to obtain at least one additional intermediate image; comparison logic configured to compare the primary intermediate image and at least one additional intermediate image to determine an indication of a level of noise present, the comparison comprising: implementing an objective function according to which an objective is to find one or more parameters for a noise compensation routine that, when found and applied to the one or more additional intermediate images, causes an update of each additional intermediate image such that their total difference from the primary intermediate image is minimized; and image creation logic configured to use the determined indication of noise to select a level of noise compensation to apply when processing a base image using the measurement dataset to create a new base image representing the measurement dataset; wherein the parameters of the noise compensation are modified to result in a higher level of noise compensation than found by the optimization procedure of the objective function in order to slow down the iterative updating of the base image and avoid accumulation of residual noise, and wherein continued iterative updating causes the parameter selections of the implemented noise compensation to become increasingly close to the parameters found by the optimization procedure of the objective function, and wherein the parameter selections correspond to the highest level of noise compensation found from all optimization procedures previously used in continued iterative updating.

Images