Image reconstruction

Abstract

Some 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 including 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 datasets including a dataset created 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 the 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 present to select noise compensation to apply when processing the base image with the measurement dataset to create a new base image representing the measurement dataset. The approach described herein can be implemented in any standard iterative image reconstruction method, and provides a method that allows powerful state-of-the-art denoising algorithms to be directly embedded in relatively simple image reconstruction through the use of only one bootstrapped resampled dataset, for example. Some approaches provide mechanisms for automatically and accurately optimizing the strength of any denoising in a data-dependent manner at each update.

Description

[Technical field]

[0001] Certain aspects and embodiments relate to a method of creating an image representative of a measurement dataset, a computer program product and an apparatus operable to perform the method. [Background technology]

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

[0003] When dealing with inverse problems in the field of imaging, the objective 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 usually called image reconstruction, in which values ​​of interest are estimated in voxels of a 3D array, or pixels of a 2D array. These values ​​of interest can represent, in some examples, for example, concentrations, binding capacities and / or uptake rates of radioactive tracers inside the human body (e.g., positron emission tomography (PET) and single photon emission computed tomography (SPECT)), or proton densities and tissue relaxation parameters for anatomical imaging (MRI).

[0004] Such reconstructed images and density estimation have a wide range of applications. In the medical field, functional, molecular and anatomical images have applications including understanding, diagnosing and staging disease and understanding how the healthy human body functions. In the field of preclinical imaging, reconstructed images are valuable in researching disease and developing new drugs. In other fields, reconstructed images may be valuable in applications such as security, e.g. security checks, satellite surveillance or safety, e.g. non-destructive testing and seismic imaging.

[0005] A problem associated with all inverse problems is that there is often no unique noise compensation solution to the inverse problem, even if the collected data is noisy. In the absence of a unique solution, the burden of choice is placed on the person who makes and uses the imaging and sensing device to select one or more fixed noise compensation parameters for the image reconstruction process. The selection of such noise compensation parameters selects one of many solutions that may satisfy the inverse problem. It will be appreciated that noise in the collected data can impair image reconstruction in various ways, and noise compensation and correction approaches appear to compensate for these impairments. In conjunction with this, noise reduction methods can be deployed, the purpose of which may be to reduce and mitigate noise in the collected data set.

[0006] In the context of medical imaging, the image interpreted by the clinician will depend on the manufacturer, or user, according to a particular fixed choice of noise compensation procedures and noise compensation parameters, and if they use prior information, these fixed noise compensation parameters can control the strength of the prior information used. It will be appreciated that many possible images will be presented to the clinician, each of which may be interpreted in a different way, potentially leading to a different diagnosis, prognosis or medical evaluation.

[0007] The selection of noise compensation parameters, which determine the resulting image used for interpretation purposes, is a critical issue in the imaging field. This may be especially true in the context of multimodal or synergistic image reconstruction. In such approaches, where information from other modalities is used (e.g., magnetic resonance (MR) images to assist PET reconstruction), it is important not to misuse the information from the other modalities, which can happen if inappropriate parameters are chosen. Summary of the Invention [Means for solving the problem]

[0008] A first aspect provides a method of creating an image representative of a measurement dataset by iteratively updating a base image, the method comprising: generating a primary data set from the measurement data set, the primary data set comprising a data set having substantially the same level of noise as the measurement data set; generating at least one additional data set from the measurement data set, the additional data sets comprising a data set generated from the measurement data set such that each additional data set has substantially the same level of noise as the measurement data set and such that each additional data set is not identical to the primary data set; processing the base image without noise compensation using the primary data set and each additional data set 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 the noise present to select noise compensation to apply when processing the base image with the measurement data set to create a new base image representative of the measurement data set. Includes.

[0009] The first aspect recognizes that noise can be a significant problem in imaging. Noise can be particularly problematic in applications such as image reconstruction for emission tomography, where noise is significant. 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 when dealing with noise problems. Cross-validation provides data-driven selection of noise compensation parameters for image reconstruction.

[0010] The first aspect addresses some of the problems with known image reconstruction approaches while utilizing cross-validation techniques. In particular, the first aspect recognizes that by processing a measurement dataset and processing one or more bootstrap datasets, each of which suffers from substantially the same noise as the measurement data, it is possible to provide an objective mechanism for obtaining an indication of the level of noise in the measurement dataset. From the one or more processed bootstrap datasets and the processed measurement dataset, it is possible to compare the processed bootstrap dataset and the processed measurement dataset and calculate appropriate noise compensation parameters to apply to the measurement dataset when creating the image.

[0011] Thus, the noise compensation procedure applied in accordance with the first aspect is a mapping required to map each processed bootstrap data set as closely as possible to the processed measurement data set, and the method according to the first aspect is operable to determine an appropriate set of noise compensation parameters to apply in relation to the particular noise compensation procedure.

[0012] A first aspect may provide a method of creating an image representative of a measurement dataset by iteratively updating a base image. The method may include creating a primary dataset from the measurement dataset, the primary dataset including a dataset having noise at the same, similar, or same level as the noise level of the measurement dataset. The method may include creating at least one additional dataset from the measurement dataset, the additional dataset including a bootstrap dataset sampled from the measurement dataset, the bootstrap dataset being selected from the measurement dataset such that each additional bootstrap dataset has noise at the same, similar, or same level 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 some 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 noise present to select a level of noise compensation to apply when processing the base image with the measurement dataset to create a new base image representative of the measurement dataset. In particular, the noise compensation parameters applied in the noise compensation procedure may be selected based on the noise indication generated by the comparison step.

[0013] In some embodiments, the primary dataset comprises a measurement dataset. In some embodiments, the primary dataset comprises a bootstrap dataset created from the measurement dataset. In some embodiments, the primary dataset comprises datasets generated from the measurement dataset, as well as other sampling or machine learning methods.

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

[0015] In some embodiments, generating at least one additional data set comprises creating one or more bootstrap data sets sampled from the measurement data set.

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

[0017] In some embodiments, comparing the main intermediate image and the at least one additional intermediate image to determine an indication of the noise present comprises taking into account a comparison between the main intermediate image and the at least one additional intermediate image to determine an indication of the noise present, such that it is possible to take a more holistic view of the likely level of noise in the measurement dataset.

[0018] In some embodiments, the considering step includes one or more of the steps of calculating one or more characteristics of the distribution of the additional intermediate images relative to the main intermediate image. Such characteristics can include, for example, calculating an average measure of noise, calculating a median measure of noise, or calculating a maximum measure of noise.

[0019] In some embodiments, the considering step includes implementing an artificial neural network to determine an appropriate noise compensation to apply to the measurement dataset based on one or more additional intermediate images generated from the one or more additional datasets compared to a primary intermediate image generated from the measurement dataset. Thus, the optimal noise compensation approach (both parameters and procedures) to apply to a given dataset can be efficiently discovered by appropriate application of a suitably configured neural network.

[0020] In some embodiments, the method includes using the selected noise reduction to process the iterative updates of the base image based on the measurement dataset to obtain further iterative updates of the base image, such that, with successive iterations, any base image can be moved towards the "true" image represented by the measurement dataset.

[0021] In some embodiments, the method includes processing the base image with a selected noise compensation procedure. In some embodiments, the method includes processing the base image with a different selected noise compensation procedure. In some embodiments, the method includes comparing the selected noise compensation procedure with a production image acquired with a different selected noise compensation procedure to select an appropriate noise compensation procedure to apply to the measurement data set. In some embodiments, selecting an appropriate noise compensation procedure includes selecting which noise compensation procedure provides the closest additional intermediate image to the main intermediate image. Thus, some embodiments can open up a range of noise compensation possibilities and optimize its use according to the collected data. The noise compensation approach can be as simple as a Gaussian smoothing kernel, with an optimal kernel width being determined at each iteration step, or as complex as advanced guided smoothing (again with parameterization specifically optimized according to the measurement data) for inclusion in the reconstruction.

[0022] In some embodiments, the step of comparing the main intermediate image and the additional intermediate images to determine a measure of the noise present comprises implementing an objective function whose goal is to determine one or more parameters for a noise compensation procedure, which parameters, when determined and applied to the one or more additional intermediate images, lead to an update of each additional intermediate image such that its collective difference with the main intermediate image is minimized. In other words, it is possible to use a denoising procedure that can be directly embedded at any or each step in the image reconstruction iterative algorithm. Some embodiments can operate 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.

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

[0024] In some embodiments, the processing involving noise compensation 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 of the 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 an image representative of the measurement dataset can be selected from a variety of available noise compensation procedures.

[0025] In some embodiments, the noise compensation parameters are modified to induce a greater level of noise compensation than that determined by the optimization procedure in order to slow down the iterative updating of the base image. In some embodiments, the noise compensation parameters are modified to induce a greater level of noise compensation than that determined by the optimization procedure in order to avoid the accumulation of residual noise. Thus, a conservative update process can be implemented to iteratively update the base image more gently.

[0026] In some embodiments, the successive iterative updates are such that the parameters of the implemented noise compensation are selected to be increasingly closer to the parameters determined by the optimization of the objective function. In some embodiments, the successive iterative updates are such that the parameters of the implemented noise compensation are selected to be increasingly closer to the parameters determined by the optimization of the objective function. In some embodiments, the successive iterative updates are such that the parameters of the implemented noise compensation are selected to be increasingly closer to the parameters determined by the optimization procedure and such that the parameters are selected to correspond to the maximum level of noise compensation determined from all previous uses of the optimization procedure in the successive iterative updates.

[0027] In some embodiments, generating at least one additional data set comprises generating one or more additional data sets from the measurement data set, wherein the generating comprises sampling or machine learning methods, and each of the additional data sets comprises a data set generated from the measurement data set such that each additional data set has substantially the same level of noise as the measurement data set and such that each additional data set is not identical to the measurement data set.

[0028] In embodiments where the method includes processing the base image with 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 a denoising procedure is directly embedded at any or each step in the iterative image reconstruction algorithm, it will be appreciated that the method operates to adaptively and precisely optimize the parameterization of any denoising procedure for each iterative update of the base image for a given measurement data set, where this adaptive and precise optimization of the denoising procedure is automatic and does not require user-provided parameters or guidance.

[0030] In embodiments where the method includes a step of processing with noise compensation, the processing with noise compensation may correspond to a regularized iterative update derived from any regularized iterative reconstruction algorithm. Such an approach may allow an automatic and accurate optimization of the level of regularization from more than one choice of priors, making it possible to automatically select the strength of different choices of prior information, for example how much guided smoothing information to use compared to unguided smoothing. In other words, rather than choosing among a set of possible noise compensation procedures, it is possible to choose how much of each noise compensation procedure to apply. Such an embodiment means that the method may operate such that it is not necessary to select a single candidate from a set of possible noise compensation candidates, but instead different proportions of more than one noise compensation candidate may be applied.

[0031] For clarity, it is noted that the method of the first aspect is considered in some embodiments to be fully automatic, i.e., the method may occur without the need for a user to select operational parameters, i.e., the method may be fully data-driven, for example, by pre-selecting overly conservative initial parameters to suit all data sets and all noise levels, resulting in a fully automatic and precise procedure of processing the measurement data sets.

[0032] In summary, a first aspect provides a method of creating an image representative of a measurement dataset by iteratively updating a base image, the method comprising the steps of generating a primary dataset from the measurement dataset, the primary dataset including 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 including a dataset 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; processing the 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 the noise present to automatically select noise compensation to apply when processing the base image with the measurement dataset to create a new base image representative of the measurement dataset.

[0033] The at least one additional data set may include a bootstrap data set generated from the measurement data set in a purely data-driven approach. Such an approach is truly data-driven and mitigates the chance that the method has learned from other data. Of course, some embodiments may allow for the at least one additional data set to include a data set generated from the measurement data set by an artificial neural network (ANN). In some embodiments, an ANN may be used in part or in whole for the noise compensation procedure.

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

[0035] A third aspect provides an imaging device configured to create an image representative of a measurement dataset from a base image, the device including: dataset generation logic configured to generate a primary dataset from the measurement dataset and at least one additional dataset from the measurement dataset having substantially the same level of noise as the measurement dataset, each additional dataset selected to include a dataset 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 indication of noise to select a level of noise compensation to apply when processing the base image with the measurement dataset to create a new base image representative of the measurement dataset.

[0036] Embodiments of the third aspect correspond to those described in relation to the first aspect.

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

[0038] Where device features are described as operable to provide a functionality, this will be understood to include device features that provide that functionality or that are adapted or configured to provide that functionality. [Brief description of the drawings]

[0039] Next, embodiments of the present invention will be further described with reference to the accompanying drawings. [Figure 1]It contains a set of PET images acquired using three different count levels with different reconstruction methods. [Diagram 2] 2 is an MR image of the subject in FIG. 1. [Diagram 3] It includes a set of PET images acquired using three different count levels with different reconstruction methods that utilize structural prior information from the subject's MRI. [Figure 4] 1 illustrates a schematic of a general approach to data processing. [Diagram 5] 5 shows a schematic conceptual overview of the general imaging approach followed by a data processing approach according to FIG. 4. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0040] As mentioned above, 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 usually called image reconstruction.

[0041] This is a problem for the medical imaging industry because manufacturers and / or users must specify noise compensation parameters for image reconstruction. For example, in the context of PET imaging, these noise compensation parameters may include the number of iterations and the level of smoothing. The selected parameters will have a significant impact on the reconstructed image. In medical imaging applications, the reconstructed image affects how the clinician interprets the "results" of the scan, which may affect the diagnosis and decisions regarding patient management. In the context of PET and SPECT imaging, the acquired emission data is very noisy due to the limited scan time and the limited amount of radioactivity injected into the patient or study subject, and therefore the reconstructed image also has noise issues.

[0042] Typical solutions in noise-compensating image reconstruction fall into seven categories, each of which requires the manufacturer and / or user to make pre-set selections of noise compensation parameters.

[0043] 1) Post-smoothing These post-processing and / or smoothing after the image / parametric map is reconstructed can successfully reduce noise. However, this post-processing comes at the cost of reduced spatial resolution, resulting in the loss of important details in the medical image. This is also true for traditional filtered back projection (FBP) methods, as well as iterative image reconstruction methods such as ordered subsets expectation maximisation (OSEM). All of these methods will result in noisy images unless smoothing is applied. More advanced post-processing methods can be applied, but in any case the post-processing still requires the selection of a level of noise compensation, facing the same problems as described below in relation to category 3.

[0044] 2) Early stop Methods such as maximum likelihood expectation maximisation (MLEM), or its accelerated version, OSEM, are usually stopped early in the iteration process, so that the aforementioned smoothing is not necessary. However, this comes at the cost of potentially spatially varying noise and resolution characteristics, with some regions having lower noise than others and some details of the image being poorly resolved while others are. Finally, there is a requirement to select the number of iterations (the noise compensation parameter in this case is the number of iterations), so that the level of noise is directly selected by the user. Cross-validation and other stopping rules eliminate the choice of the number of iterations, but the problem of incomplete convergence of iterative reconstruction algorithms remains.

[0045] 3) Regularization method Bayesian and maximum a posteriori (MAP) methods are used in iterative algorithms that impose priors on the image, such as smoothness, or smoothness within a defined region (e.g., anatomical information or edge-preserving priors can be used to guide the regularization of PET reconstructions using MRI). A problem with these methods is the need to carefully select parameters (called hyperparameters in the Bayesian context) that affect the level of noise and resolution, and indeed this selection of parameters must be carefully tuned from scan to scan. In practice, it is extremely difficult to be sure that the best parameters have been selected for any given reconstruction of a given dataset. Overestimating the regularization parameters can result in important image details being lost, while underestimating the regularization can leave too much noise in the image. This is particularly problematic in multimodal imaging, where if (e.g.) MRI is to be used to guide the regularization of PET or SPECT image reconstructions, how much of the prior information should be used and how "strong" should the prior be?

[0046] 4) Basis transformation These methods use spatial basis functions other than traditional pixels or voxels, such as kernel spatial basis functions derived from larger regions of interest (ROIs), or from temporal similarity in detail, or from similarity measures from other imaging modalities (e.g., MRI). These methods successfully reduce noise, but impose a specific structure on the image, once again leaving the burden of parameter selection for generating the kernel to the user, which again places the level of detail and noise compensation, as well as the number of iterations used, in the hands of the user.

[0047] 5) Inter-update filtering This is similar to the post-smoothing method described above, but is performed between iterations. The same problem arises of needing to decide how much smoothing to apply, as well as the problem of parameter selection for noise compensation.

[0048] 6) Cross-validation based stopping Such approaches terminate the reconstruction prematurely, and thus may use a poorly converged reconstruction, with problems similar to those in category 2 above. As a result, the cross-validation stopping rule has not received noteworthy understanding, for example, in the emission tomography community.

[0049] 7) Parameter selection based on limited grid search In this approach, the user is required to preselect a limited number of fixed sets of candidate parameters for noise compensation. A full reconstruction is then performed for each set of candidate parameters, and either the L-curve method or the cross-validation method is used to select which of these sets of reconstruction parameters to use. These methods are limited in two main ways: the need for the user to preselect a limited number of fixed candidate parameters, and the need to perform a full (often computationally intensive) image reconstruction for each candidate set of parameters. Furthermore, in the case of cross-validation, it is also necessary to define a subset of data for cross-validation purposes, for which there are many possible choices.

[0050] Specific embodiments of these approaches in industrial use for clinical PET imaging include OSEM and / or HD-PET from Siemens, which typically rely on either early termination (category 2) or post-processing (category 1) to compensate for noise, and QClear from GE, which requires the user to determine key regularization parameters (category 3).

[0051] The main drawbacks with approaches to compensating image noise in emission tomography data that rely on approaches along the seven categories outlined above include the absence of a precisely optimal, practically robust or computationally efficient method of selecting the level of noise compensation. It is clear that different levels of noise compensation are required for different data sets depending on the noise level and the object being imaged. Furthermore, the user or manufacturer is required to specify how much noise compensation, e.g., smoothing or regularization, should be present in the image, which is subjective or at best not precisely optimal for the data actually acquired, with a user-defined trade-off between noise and image detail. With multimodal information to aid in reconstruction, it is unclear how much prior information should or should not be used.

[0052] Compendium Before describing in detail the details of specific embodiments of the arrangement, a general overview of the approach is provided.

[0053] It is known that noise can be a significant problem in imaging. It can be particularly problematic in applications such as image reconstruction for emission tomography, where noise is significant. As mentioned above, image reconstruction approaches using pure maximum likelihood or least squares estimation are not useful for clinical or research tasks.

[0054] Current methods for countering noise include post-reconstruction smoothing, with its attendant problems of how much to smooth; when to stop and what such images correspond to, with its concerns about spatially varying convergence; early termination of iterative algorithms; and maximum a posteriori reconstruction, with its attendant problems of how much to regularize (i.e., what is the choice of hyper-parameter, which is assumed to be β).

[0055] It has been recognized that cross validation (CV) can provide some assistance in dealing with the noise problem. CV provides a data-driven selection of noise compensation parameters for image reconstruction.

[0056] Known CV approaches are problematic, for example, because CV requires splitting the data, and early use of CV, for example in PET reconstruction, simply splits the acquired data in two, so that the "optimality" of the noise compensation parameters is ultimately based on a subset of the data. CV in known approaches is not used to provide reliable images (e.g., early stopping approaches with their associated early termination problems), or instead involves a relatively rough selection from a limited number of fixed choices of candidate noise compensation parameters, with each choice requiring reconstruction of the entire image.

[0057] Several approaches have recognised that a bootstrap adjustment approach may be a useful method: bootstrapping to obtain a new dataset means that data of the same size can be used as an "additional" dataset, thus solving the first problem with CV outlined above.

[0058] Similarly, several approaches recognise that new datasets can be obtained using data generation approaches (such as from artificial neural networks), meaning that data of the same size can be used as an "additional" dataset, again solving the first problem with CV outlined above.

[0059] FIG. 4 illustrates generally the general approach used in various embodiments described in detail below.

[0060] Processing the measured data and processing one or more generated (e.g., bootstrapped) data sets, each of which is subject to substantially the same noise as the measured data, provides an indication of the noise in the measured data. From the processed generated (e.g., bootstrapped) data sets and the processed measured data, it is possible to compare the processed generated (e.g., bootstrapped) data and the processed measured data and calculate appropriate noise compensation parameters to apply in processing the measured data.

[0061] The noise compensation procedure is the mapping required to match the processed, generated (eg, bootstrapped) data set as closely as possible to the processed measured data.

[0062] The noise compensation parameters for a given noise compensation procedure are given by the following equation:

[0063]

number

[0064] Several approaches work to determine an appropriate set of noise compensation parameters to apply in conjunction with a particular noise compensation procedure.

[0065] It will be appreciated that this approach can be applied to one or more noise compensation procedures for a given measurement data set, with each application of this approach providing an associated set of one or more noise compensation parameters for the given noise compensation procedure.

[0066] An approach can then be implemented to objectively "select" an appropriate noise compensation procedure to apply to a given measurement data set, in other words, in such a way as to identify the noise compensation procedure (for a given choice of noise compensation procedures) that is most suitable for the given measurement data set.

[0067] FIG. 5 shows a schematic conceptual overview of the general imaging approach following the data processing approach according to FIG.

[0068] 4 and 5 can provide an objective, user-independent solution to inverse problems. Such inverse problems can include, for example, image reconstruction and kinetic / functional parameter estimation in PET or SPECT.

[0069] Some approaches may allow image reconstruction without requiring the manufacturer or user to specify hyperparameters related to the level of noise compensation used. Some approaches may provide useful methods for embodiments related to multimodal imaging (such as simultaneous PET-MR), where it is desirable to leverage information from each modality, but it is unclear how much, if any, prior information can be safely used in the reconstruction.

[0070] Some approaches recognize that it is possible to use one or more easy-to-generate bootstrap data sets to estimate appropriate noise compensation parameters at every iterative update.

[0071] Several approaches recognize that almost any iterative image reconstruction method can be viewed, at any given step, as an update function U, which is the iteration of the current image (at iteration k) with parameters θ (k) Using the measured data m, we create a new image θ (k+1) Deliver.

[0072]

number

[0073] Iterative image reconstruction algorithms effectively progress at each iteration, adding a new "modified image" to the current image, moving towards an image that satisfies the requirements of an objective function (e.g., maximum likelihood (ML), least squares (LS), or maximum a posteriori probability (MAP)). For example, in the MLEM algorithm, it is the ML objective that needs to be met. In MAP, it is a user-specified regularization objective (with user-specified regularization hyper-parameters) that needs to be met, which can leverage prior information from other imaging modalities (e.g., MRI for PET). However, MLEM and other non-regularized objectives / algorithms (e.g., LS / conjugate gradient) lead to excessive noise amplification, while MAP and other regularization methods lead to a user-selected trade-off between image detail and image noise.

[0074] Several approaches have found it appropriate to provide a bootstrap update image at iteration k using a bootstrap replicate data set b obtained by resampling the measurement data m.

[0075]

number

[0076] The updated image will also suffer from the noise present in b, but obviously this will be a different noise than that in m (because the actual measurement data m is taken by bootstrapping to be a model of the average of a large collection of noisy data sets like b).

[0077] Some approaches optimize noise compensation parameters applied to the bootstrap update and fit the bootstrap update image to the conventional measured data update image by using these optimized noise compensation parameters to obtain the next iterative update of the image and then to process the standard iterative update from the measured data.

[0078] The optimization step is image space fitting, which can be achieved by implementing a cross objective function, an "ensemble average objective function," or cost function, as follows:

[0079]

number

[0080] The goal here is to

[0081]

number

[0082] When applied in some way (described in detail below) to the bootstrap iterative update of , the traditional update image , according to the crossover objective function,

[0083]

number

[0084] A noise reduction operator F that leads to a bootstrap update that best fits β The goal of the present invention is to find optimal noise compensation parameters for {}.

[0085] The intersection objective function is a measure related to the distance D between two images, which can be measured in many ways, but for Gaussian data it corresponds to a least-squares fit (to maximize the Gaussian intersection likelihood), and for Poisson distributed data it corresponds to the Kullback-Leibler (KL) distance measure (to maximize the Poisson intersection likelihood).

[0086] This crossover objective function can also be thought of as the "ensemble average objective function". The ensemble average objective function is the average (

[0087]

number

[0088] (modeled by) and noisy updates

[0089]

number

[0090] is a measure relating to the distance D between any one or more of

[0091] Optimal Noise Reduction Parameters

[0092]

number

[0093] Once we have found (which minimizes the intersection objective), the next update of the image can be given by

[0094]

number

[0095] This process can be repeated for the next iterative update, and so on.

[0096] To slow down the iterative updates and avoid the accumulation of residual noise due to the inability to perfectly fit the noise-compensated bootstrap update image to the conventional measured data update image, some approaches recognize that it may be necessary to modify the noise compensation parameters in early iterative updates to induce a greater level of noise compensation than that sought by the optimization procedure.

[0097] Some approaches recognize that in successive iterative updates, the noise compensation parameters are selected to be increasingly closer to the noise compensation parameters determined by the optimization procedure, and that the noise compensation parameters are selected to correspond to the maximum level of noise compensation determined from all previous uses of the optimization procedure in the successive iterative updates.

[0098] FIG. 5 shows a schematic conceptual overview of the general image reconstruction approach following the data processing approach according to FIG. 4. As conceptually shown in FIG. 5, a base image is processed through iterative updates U using a measurement data set to give a "standard" update. Also conceptually shown is processing of a base image using the same iterative update function U but using a bootstrap data set to give a "bootstrap" update. These updates can be considered as "intermediate" images or updates. As shown diagrammatically in FIG. 5, noise compensation parameters can be determined that operate on the bootstrap image updates to minimize the difference between the standard and bootstrap image updates. Once noise compensation parameters that satisfy the minimized difference criterion have been determined, noise compensation can also be applied while processing the base image through iterative updates U using these noise compensation parameters to give a new updated base image.

[0099] Having given a general overview, some specific embodiments of the approach are detailed below.

[0100] a) Filtering of additively modified images This is a simple and intuitive approach that is likely to appeal to many people given its simplicity, flexibility and robustness. The update function is modeled as follows:

[0101]

number

[0102] Here, Δ (k)(b) is the "modified image" at iteration k that is effectively added to the current image to get the next update. Several approaches choose a denoising procedure for the modified image, which can be anything from simple Gaussian smoothing, to a multimodal guided filtering process, or even machine learning based denoising such as artificial neural networks. The denoising procedure is defined by the operator F β It can be represented by {}.

[0103]

number

[0104] An objective is then set to seek the "optimal" choice of noise compensation parameter β through the use of a 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 measure arises directly from seeking the maximum Poisson log-likelihood estimate). It will be appreciated that objectives other than minimizing the KL distance can be chosen.

[0105] In formula (6), F β {}The noise compensation procedure (e.g., simple smoothing, or multimodal guided edge-preserving smoothing in the case of MR guidance for 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 parameter β. Cross-objective fitting according to some approaches works automatically to adapt to the noise level in the measurement data and select the appropriate noise compensation parameters.

[0106] Although the above example relates to the case of noise compensation applied to an additive update (the "modified image"), it will be appreciated that the approach can be applied equally well to a multiplicative update, or even to the entire updated image.

[0107] Once the "optimal" noise compensation parameters β have been found through the use of a cross-objective function, it is possible to update the image acquired from the original measurement data with the optimized noise compensation parameters according to the following equation:

[0108]

number

[0109] b) A simple inter-update filter In a variation of the method described in (a), (6) is replaced by the following equation:

[0110]

number

[0111] Such a method differs from the one described in (a) because the entire updated image is subject to noise compensation, rather than an isolated noisy updated "modified image".

[0112] c) MAP-EM update Another embodiment of the general approach is applied to a Bayesian method, which uses the MAP objective: Any MAP update algorithm can be used to generate the processed bootstrap update, depending on the choice of prior distribution and regularization hyperparameters.

[0113] For example, using the method of DePierro [1] on a weighted quadratic Gibbs prior for the images, it is possible to obtain an iterative EM update based on a MAP objective, which is of the general form:

[0114]

number

[0115] where terms B and C are the time series of the current image θ (k)This relies on a weighted combination of neighboring voxels from, for example, allowing for multimodal guided regularization via a spatially varying weighted quadratic prior (e.g., the method of Bowsher [2]). According to one such embodiment, the noise compensation parameter β is known as a hyperparameter of the Bayesian prior, and choosing β is a crucial task, since it is clear that β=0 corresponds to no noise compensation.

[0116] Based on equation (9), it is possible to use cross-objective optimization of β on the bootstrap data, allowing an appropriate amount of prior information to be included in the iterative MAP-EM update. This embodiment of the general approach addresses significant challenges associated with regularized methods, especially in the context of multimodal guided image reconstruction.

[0117] Such an approach allows for an automatic and accurate optimization of β, without the user having to specify the level of regularization to achieve a convergent MAP-EM image reconstruction algorithm that delivers a final converged estimate of the reconstructed image that satisfies the desired regularized objective function.

[0118] It will be appreciated that more than one regularization component can be used in the objective function, e.g., β1 for a first part, β2 for a second part, etc. This can be particularly valuable in the context of guided image reconstruction, whereby the level of guided regularization can be determined automatically and accurately along with the level of traditional unguided regularization (e.g., a quadratic penalty function).

[0119] It will be appreciated that since noise tends to zero in the measured data (i.e., infinite counts), the bootstrap data will tend toward the measured data. As a result, no noise compensation is required for noiseless data (the optimal β from the cross-objective function, the “ensemble average objective function”, will approach zero). In contrast, as noise increases (i.e., low counts), the updates from the bootstrap data will require increasing levels of noise compensation to fit the updates derived from the measured data. In other words, the optimal β from the cross-objective fitting will increase with increasing noise in the measured data, since more noise compensation will be required to map the noisy updates toward a model of the average of the ensemble of noisy updates.

[0120] Demonstration of the approach To illustrate the effectiveness of an embodiment of the general approach outlined above, the case of MAP EM 3D reconstruction is presented on real data.

[0121] The figures described below show how effective this general strategy is for automatic noise reduction of PET data at various noise levels without the user having to select the noise compensation level.

[0122] FIG. 1 includes low, medium and high count data comparisons (for 1%, 10% and 100% of the actual data measured). The first column includes conventional MLEM reconstructions for these three cases, and the second column shows these images with a typical post-smoothing with a 4 mm Gaussian kernel (as is often done as standard for clinical images). The three columns on the right (columns 4, 5 and 6) show standard MAPEM reconstructions for different choices of the hyper-parameter β, and it can be seen that visually better results are obtained for different choices of hyper-parameters for different count levels. The third column, outlined in the figure, shows that the bootstrap optimized MAPEM method automatically delivers good quality images for all count levels, which cannot be obtained using other methods unless the hyper-parameters are tuned and explored by the user.

[0123] FIG. 2 shows MR images for the subject data from FIG.

[0124] FIG. 3 includes a similar comparison to that of FIG. 1, where the general structure of the columns and images is the same as described in connection with FIG. 1, but now utilizing the MR images from FIG. 2 to provide a priori structural information to the MAP EM that aids in noise compensation using the Bowsher method [2]. Again, the bootstrap optimized MAPEM method automatically selects appropriate hyperparameters for all noise levels. It will be appreciated that the level of noise compensation applied by the above embodiment will be appropriate to the level of noise in the data. It is believed that clinicians will prefer images such as those shown in the third outlined column compared to the current standard methods shown in the other columns.

[0125] 1 and 3 show possible results using embodiments of the described approach on high count data and extremely low count data, with the same algorithm being used in both cases. It can be seen that consistent, good quality images are obtained by applying the described approach. The third outlined column shows good results where the strength of smoothing and amount of prior used are visually appropriate.

[0126] It will be understood that there is scope for applying the described approach in connection with various other priors and filters, and for all of the various hyper-parameters associated with such priors and filters. An infinite number of priors and image processing filters can be considered, and the described approach means that there is considerable potential for leveraging state-of-the-art image denoising methods (e.g., those based on guided smoothing, local patch-based methods, or various artificial neural network architectures) by embedding them into a rigorous framework that provides an automatically selected level of noise compensation for image reconstruction, such that the user or manufacturer only needs to select which noise compensation method to use, without the need to specify noise compensation parameters (i.e., how much noise compensation to apply).

[0127] Some approach embodiments allow for objective and accurate selection of the tradeoff between image detail and image noise throughout iterative updates by cross-objective fitting. Some approaches remove any noise compensation parameter selection from the user and / or manufacturer and provide robustness of the reconstruction image quality. Such robustness to highly varying count levels has not been previously available in emission tomography. Some approaches may be particularly useful in the context of multimodal imaging, where other images can be used to assist in noise reduction and where determining up to what intensity such additional information sources should be used is highly subjective.

[0128] Advantages of embodiments using the described approach may include, for example:

[0129] 1) Confidence in the objectivity of the resulting image quality. Automatic selection of the level of noise compensation to apply means that the reconstructed image via bootstrap cross-objective denoising parameter estimation is a low-noise image with only as much detail as is supported by the data. Results show that the described approach converges to a good quality image according to the statistical quality of the data. Existing methods typically rely on different levels of noise reduction specified by the user or manufacturer, and are usually traded off against image features that may not necessarily be supported by the data and may misrepresent the scan.

[0130] 2) Room for implementation with any denoising or noise compensation method. Several approaches allow for the implementation within a framework that allows for the "optimal" exploitation of any denoising procedure, for example from simple Gaussian kernel smoothing methods, simple regularisation (as shown in Fig. 1) to multimodal guided regularisation methods (as shown in Fig. 3) and the use of methods from machine learning, such as artificial neural networks. This can be particularly important in the context of multimodal guidance, which often overuses any prior structural information, giving misleading and / or artificial looking images. Results obtained by using approaches such as the one presented above show how prior image guidance can be used with intensity and edge sensitivity that automatically adapts to the quality of the data, avoiding major problems with existing guided regularisation methods.

[0131] 3) Simplicity, scope and practicality. The manufacturer or user no longer has the task of specifying the noise compensation parameters to reconstruct a given data set, so the level of information in the image (spatial resolution and amount of detail vs. noise) does not depend on subjective parameter selection. The method is very simple to implement and any iterative image reconstruction method can be adjusted with the embedding of any preferred noise compensation procedure, the strength of the noise compensation becomes data-dependent and is automatically determined by the method. There is considerable scope for the exploration of different state-of-the-art noise compensation methods, making it possible to implement multi-modality based noise compensation with the strength supported by the measurement data.

[0132] 4) Theoretical attractiveness: The reconstruction image uses noise compensation parameters determined from a statistically motivated objective function, which optimizes the cross-objective for a given update step in the iterative reconstruction, which can be a cross-likelihood (Poisson or Gaussian).

[0133] As can be seen from the diagrams in Figures 1 and 3, an embodiment of the described approach has been successfully implemented on 3D real PET data for three different count levels, from low to high noise levels. In the illustrated example, the approach is implemented with noise compensation via MAP regularization and for the case of MRI-guided MAP regularization (whereby a structural image is used in the prior distribution, with the level of regularization controlled by a bootstrap crossover objective).

[0134] It will be appreciated that several approaches can also be implemented in 2D and 4D imaging methods.

[0135] It will be further understood that the described approach is applicable to any inverse problem where parameter estimation occurs and noise in the data is a performance limiting factor. Prime example commercial applications include medical imaging, especially PET or SPECT scanners for reconstruction in clinical and preclinical imaging for cancer, heart and brain, where scan time and injection work are limited leading to count-limited (noisy) data, low-dose computed tomography (CT) for reconstructing anatomical images, angiographic images whenever data quality is low (to reduce radiation exposure or for fast dynamic imaging), low SNR magnetic resonance imaging (MRI) sequences where some MR images suffer from SNR limitations and therefore have noisy k-space data.

[0136] Outside of medical imaging, some of the approaches can be used for any parameter estimation problem that suffers from noisy data. Other areas where the approaches can 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 and seismic imaging), astrophysics (e.g., multispectral imaging), and security imaging (e.g., CT).

[0137] Cross-validation [3] and bootstrap filtering [4] are known. The known methods rely on cross-validation as a stopping criterion, which means that the results are sensitive to spatially varying convergence (spatially varying resolution and noise). More recent advanced cross-validation methods [5] require pre-selecting the noise compensation parameters for a limited number of examples, specifying a subset of the data to cross-validate, and then performing a global reconstruction for each set of examples of the noise compensation parameters. This results in a less accurate selection of the noise compensation parameters, which also depends on the selection of the subset of the data for the purposes of cross-validation. Other more advanced generalized cross-validation methods [6] rely on a fixed instance of regularization, such as total variation, and do not provide flexibility, scope, and general applicability. Bootstrap filtering uses forward projection of the cross-validation stopping images. The forward projection is used as a means to generate the bootstrap samples. This known method involves finding the reconstruction and expectation values ​​from a large number of bootstrap samples.

[0138] The approach and embodiments described herein are distinct from known approaches in the following ways:

[0139] Some approaches may involve methods that do not involve stopping criteria and can only be run once for convergence.

[0140] Some approaches are such that the bootstrap dataset is derived directly from a resampling of the raw measurement data, rather than from a forward projection of cross-validated stationary images.

[0141] Some approaches are such that a single bootstrap dataset can be used rather than selecting multiple datasets or data subsets for cross-validation.

[0142] Some approaches are such that any denoising procedure can be directly embedded into any iterative reconstruction algorithm at any or each step. Some approaches are such that any denoising parameterisation can be adaptively and accurately optimised at every update. Some approaches are such that any denoising parameterisation can be automatically and accurately optimised at every update.

[0143] Some approaches involve only one iterative reconstruction procedure to deliver precisely optimized noise reduction parameters, without the need to perform multiple reconstructions and then retrospectively compare them by cross-validation for low-precision selection from among a limited number of preselected noise reduction parameters.

[0144] It will be appreciated that several approaches open up a range of possibilities for noise compensation and their use can be optimized depending on the collected data. Noise compensation approaches can be as simple as a Gaussian smoothing kernel, with an optimal kernel width being determined at each iteration step, or as complex as advanced guided smoothing (again with parameterization specifically optimized according to the measured data) for inclusion in the reconstruction. In contrast, known methods such as those in [3] and [4] concern a stopping or single "nonlinear" filtering method, defined by the average of multiple approximated bootstrap MLEM results. This provides a one-time averaging process, which is further constrained by the central use of a stopping image estimate, with unknown spatial variation convergence.

[0145] The approaches described herein can be implemented for any standard iterative image reconstruction method, providing methods that allow for embedding powerful state-of-the-art denoising algorithms directly into relatively simple image reconstruction, for example, by using only one (or more) bootstrapped resampled datasets. Some approaches provide mechanisms for automatic, data-dependent and accurate optimization of the strength of any denoising at each update.

[0146] Although exemplary embodiments of the present invention have been disclosed in detail herein with reference to the accompanying drawings, it is understood that the present invention is not limited to the precise embodiments, and various changes and modifications can be made therein by those skilled in the art without departing from the scope of the present invention as defined by the appended claims and their equivalents.

[0147] References [1]AR De Pierro (1995) A Modified Expectation Maximization Algorithm for Penalized Likelihood Estimation in Emission Tomography, IEEE Trans. Med. Imaging, vol. 14, no. 1, pp. 132-137

[0148] [2]JE Bowsher 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.

[0149] [3]Coakley, K. J. (1991), A cross-validation procedure for stopping the EM algorithm and deconvolution of neutron depth profiling spectra IEEE Transactions on Nuclear Science Volume: 38, Issue: 1

[0150] [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

[0151] [5]Zhang et al (2017) Regularization parameter selection for penalized-likelihood list-mode image reconstruction in PET Phys. Med. Biol. 62 5114

[0152] [6]Xiongjun Zhang, Bahram Javidi, and Michael K. Ng (2017), Automatic regularization parameter selection by generalized cross-validation for total variational Poisson noise removal Applied Optics Vol. 56, Issue 9, pp. D47-D51

Claims

1. 1. A method for creating an image representative of a measurement dataset by iteratively updating a base image, comprising: generating a primary data set from the measurement data set, the primary data set comprising a data set having substantially the same level of noise as the measurement data set; generating at least one additional data set from the measurement data set, the at least one additional data set including a data set generated from the measurement data set such that each additional data set has substantially the same level of noise as the measurement data set and such that each additional data set is not identical to the primary data set; processing the base image without noise compensation using the main data set and each additional data set to obtain a main intermediate image and at least one additional intermediate image, respectively; comparing said primary intermediate image and said at least one additional intermediate image to determine an indication of the level of noise present; and using the determined indicator of noise present to select a noise compensation to apply when processing the base image with the measurement dataset to create a new base image representative of the measurement dataset.

2. The method of producing an image according to claim 1 , wherein the primary data set is the measurement data set.

3. The method of claim 1 , wherein the primary data set comprises a bootstrap data set generated from the measurement data set.

4. 4. A method for generating an image according to any one of claims 1 to 3, wherein the step of generating at least one additional dataset comprises creating one or more bootstrap datasets sampled from the measurement dataset.

5. 5. A method for producing an image according to any one of claims 1 to 4, wherein the step of generating at least one additional data set comprises the step of generating one or more additional data sets from the measurement data set, each of the additional data sets comprising a data set generated from the measurement data set such that each additional data set has substantially the same level of noise as the measurement data set and such that each additional data set is not identical to the measurement data set.

6. 6. A method for creating an image as claimed in any preceding claim, wherein the step of comparing the main intermediate image and the at least one additional intermediate image to determine an indication of noise present comprises taking into account a comparison between the main intermediate image and at least one additional intermediate image to determine an indication of noise present.

7. The method of claim 6 , wherein the step of considering includes one or more of the steps of: calculating one or more characteristics of a distribution of the additional intermediate images relative to the main intermediate image.

8. A method for creating an image according to any one of claims 1 to 7, comprising using the selected noise compensation for iteratively updating the base image based on the measurement dataset to obtain the new base image representative of the measurement dataset.

9. A method for producing an image according to claim 8, comprising the step of processing said base images with different selected noise compensation procedures.

10. 10. A method for creating an image as described in claim 9, comprising a step of comparing created images obtained using the selected noise compensation procedure with the different selected noise compensation procedure to select which noise compensation procedure to apply when processing the base image with the measurement data set to create a new base image representative of the measurement data set.

11. The method of producing an image according to claim 10 , wherein selecting an appropriate noise compensation procedure comprises comparing an intermediate image acquired using said noise compensation procedure to said primary intermediate image.

12. A method for creating an image as claimed in any one of claims 1 to 11, wherein the step of comparing the main intermediate image and at least one or more additional intermediate images to determine an indication of the noise present comprises the step of implementing an objective function whose goal is to determine one or more parameters for a noise compensation procedure, which parameters, when determined and applied to the one or more additional intermediate images, lead to an update of each additional intermediate image such that its collective difference with the main intermediate image is minimised.

13. The method of claim 12 , wherein the objective function includes a measure related to a distance between the one or more additional intermediate images and the main intermediate image.

14. 14. The method of claim 13, wherein the measure related to distance comprises one of a sum of squared distances, a Kullback-Leibler distance measure, any norm as a distance measure, or any other suitable cross-likelihood measure that correlates to distance.

15. The method of claim 8 , wherein the iterative updates include additive updates or multiplicative updates.

16. A method for creating an image as described in any of claims 1 to 15, wherein the processing with selected noise compensation corresponds to a regularized iterative update derived from any regularized iterative image reconstruction algorithm using the measurement data set.

17. A method for creating an image according to any one of claims 9 to 14, wherein the noise compensation procedure corresponds to an artificial neural network trained to map any of the additional intermediate images to match the primary intermediate image, such that the trained artificial neural network is applied to the primary intermediate image to obtain an update to the base image.

18. A method for producing an image according to any of claims 9 to 14 or 17, wherein the parameters of the noise compensation are modified to induce a greater level of noise compensation than that determined by an optimization procedure in order to slow down the iterative updating of the base image and avoid accumulation of residual noise.

19. 20. A method for producing an image as described in claim 18, wherein successive iterative updates are such that the parameters of the implemented noise compensation are selected to become increasingly closer to the parameters determined by the optimization procedure, and such that the parameters are selected to correspond to the maximum level of noise compensation determined from all previous uses of the optimization procedure in the successive iterative updates.

20. A computer program product operable to perform the method according to any of claims 1 to 19 when executed on a computer.

21. 1. An imaging device configured to generate an image representative of a measurement dataset from a base image, the imaging device comprising: a dataset generation logic configured to generate a main dataset from the measurement dataset having substantially the same level of noise as the measurement dataset and at least one additional dataset from the measurement dataset, each additional dataset being selected to include a dataset having substantially the same level of noise as the measurement dataset; processing logic configured to process the base image using the primary data set and the at least one additional data set to obtain a primary intermediate image and at least one additional intermediate image, respectively; 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; image creation logic configured to use the determined measure of noise to select a level of noise compensation to apply when processing the base image with the measurement dataset to create a new base image representative of the measurement dataset; The apparatus comprising:

Images