Denoising data

Abstract

A method for denoising data including data of interest and target-related noise is provided. Data is input into two models trained on data of interest and target-related noise, respectively. Thus, the data of interest may be estimated from the data and the outputs of the two separate models.

Description

Technical Field

[0001] The present invention relates to the field of denoising data containing correlated noise. The present invention also relates to denoising medical images containing correlated noise. Background Art

[0002] In cardiac ultrasound, multiple reverberations between ribs and tissues generate strongly correlated clutter that degrades the final image quality. This type of clutter is known as haze, which significantly reduces contrast and limits visibility of finer details in the resulting ultrasound image. This is particularly problematic in cardiac ultrasound, where it is important to be able to clearly image the ventricles, endocardium, and apex of the heart. Dehazing is a specific technique used to suppress the haze found in ultrasound images and retrieve the underlying signal.

[0003] Clutter and fog usually do not follow a simple noise distribution, such as white noise or Gaussian noise, but are highly structured and correlated. Many algorithms operating in the image domain have difficulty separating fog from actual tissue and are unable to remove fog without introducing artifacts or suppressing images of weakly reflective tissue. In addition, many existing algorithms are largely unaware of the rich statistical structure in ultrasound signals and anatomical images.

[0004] Conventional methods for denoising or dehazing images can be divided into two categories. First, heuristic methods such as non-local means (NLM) or 3D block matching (BM3D) assume simple noise statistics and fail to accurately retrieve the underlying signal from the associated non-zero mean fog. Secondly, data-driven methods such as supervised deep learning networks (e.g., U-Net) can be trained to map blurry images to clean images in an end-to-end manner. Although this method tends to produce good results, it is not robust to changes in data or noise distribution. This means that if the network is applied to a domain different from the domain on which the network has been trained, the denoising performance will drop significantly. In addition, supervised deep learning methods require accurate data pairs (clean, noisy) for training, which is not always available.

[0005] “Generative Modeling by Estimating Gradients of the Data Distribution” by Song Yang et al. discloses using a score-based generative model to denoise data. Summary of the invention

[0006] The invention is defined by the claims.

[0007] According to an example according to aspects of the present invention, there is provided a method for denoising data comprising data of interest and target-related noise, the method comprising:

[0008] inputting the data into a first model trained on the data of interest;

[0009] inputting the data into a second score-based generative model trained on target-related noise expected to be present in the data; and

[0010] The data of interest is estimated based on the data and outputs of the first model and the second scoring-based generative model.

[0011] Estimating the data of interest includes solving an inverse denoising problem on the data. The inverse denoising problem may be formulated based on the data as a combination of the data of interest and the target-related noise. The inverse denoising problem may be solved using maximum a posteriori (MAP) estimation.

[0012] Often, noisy data is expected to contain correlated noise. This can occur due to physical limitations when acquiring the data. For example, in cardiac ultrasound imaging, the ultrasound waves reverberate from the ribs, resulting in highly correlated noise in the image. This type of noise, called fog, can be expected in cardiac ultrasound images.

[0013] Therefore, it is proposed to use two models for noisy data. A first model is trained on the data of interest (i.e., the values ​​expected for the data), while a second score-based generative model is trained specifically on target-related noise that is expected to be present in the data. Target-related noise is a type of correlated / structured noise and therefore does not follow a conventional Gaussian distribution (i.e., it is not assumed to be random). The specific form of the correlated noise will depend on the type of data obtained and the source of the correlated noise.

[0014] The second score-based generative model enables obtaining accurate predictions of the correlated noise and estimating the data of interest accordingly. This is because the second score-based generative model has been trained on the target correlated noise and does not assume that only Gaussian distributed noise exists in the data.

[0015] Essentially, a first model is used to learn what the data of interest looks like, and a second, scoring-based generative model is used to learn what the target-related noise looks like. This means that priors can be used for both the data of interest and the target-related noise, rather than just assuming the presence of random noise. It has been found that using both together significantly improves the denoising process in data containing target-related noise. It has been found that generative models are a powerful way to learn distributions in data using unsupervised learning. This enables the model(s) to be trained in an unsupervised manner, which significantly simplifies the learning process of the models while still ensuring that they are robust.

[0016] It has been recognized that score-based models are particularly robust when learning correlated / structured noise, without being relatively computationally expensive. Score-based models can be used in denoising diffusion models to solve the inverse denoising problem. Score-based generative models used in denoising diffusion models are sometimes referred to as score-based diffusion models.

[0017] The first model may also be a generative model based on scoring.

[0018] Estimating the data of interest includes using outputs of the first model and the second score-based generative model in a sampling algorithm configured to estimate the data of interest from the data by solving an inverse denoising problem and applying the solution to the data.

[0019] Examples of sampling algorithms used for stochastic differential equations may be based on the Euler-Maruyama method or Langevin dynamics.

[0020] The data may be undersampled relative to the data of interest by a sampling matrix, and the method may include transforming the data to a size of the data of interest.

[0021] Often, the received data may be a noisy and undersampled version of the data of interest (e.g., compressed data). Therefore, the data may be transformed to match the expected sample size of the data of interest. In particular, the data may be modeled as the sum of the data of interest multiplied by a measurement matrix with correlated noise and potentially conventional Gaussian noise.

[0022] The sampling matrix also includes one or more of a subsampling function, a point spread function, and a blur kernel.

[0023] The data may be image data. For example, the data may be ultrasound image data.

[0024] It has been found that ultrasound data includes correlated noise. For example, fog (reverberation) is a common presence in cardiac ultrasound images. Fog is a highly correlated noise that can be handled using a model trained on ultrasound images containing fog. Of course, other types of correlated noise in ultrasound data can also be handled using models trained on each type (e.g., speckle, etc.).

[0025] A plurality of first models may be applied to different depths of the ultrasound image data, wherein each first model is trained on data of interest for a target depth in the ultrasound image data.

[0026] Additionally or alternatively, multiple second score-based generative models may be applied to different depths of the ultrasound image data, wherein each second score-based generative model is trained on target-related noise expected to be present at the target depth in the ultrasound image data.

[0027] Ultrasound data contains information about the object (e.g., a person) being imaged relative to depth. Noise statistics (especially for correlated noise) may vary relative to depth. As such, it may be advantageous to use different models trained for different depths at different depths in the ultrasound data.

[0028] The invention also provides a computer program carrier comprising computer program code, which, when executed on a processing system, causes the processing system to execute all the steps of the above method.

[0029] The computer program carrier may be a long term storage medium (eg a hard drive) or a temporary carrier (eg a bit stream).

[0030] The present invention also provides a system for denoising data including data of interest and target-related noise, the system comprising a processor, wherein the processor is configured to:

[0031] inputting the data into a first model trained on the data of interest;

[0032] inputting the data into a second score-based generative model trained on target-related noise expected to be present in the data; and

[0033] The data of interest is estimated based on the data and outputs of the first model and the second model.

[0034] The first model may also be a generative model based on scoring.

[0035] Estimating the data of interest may include using outputs of the first model and the second scoring-based generative model in a sampling algorithm configured to estimate the data of interest from the data by solving an inverse denoising problem and applying the solution to the data.

[0036] The data may be image data. For example, the data may be ultrasound image data.

[0037] A plurality of first models may be applied to different depths of the ultrasound image data, wherein each first model is trained on data of interest for a target depth in the ultrasound image data.

[0038] Additionally or alternatively, multiple second score-based generative models may be applied to different depths of the ultrasound image data, wherein each second score-based generative model is trained on target-related noise expected to be present at the target depth in the ultrasound image data.

[0039] These and other aspects of the invention will be apparent from and elucidated with reference to the embodiment(s) described hereinafter. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] For a better understanding of the invention and to show more clearly how it may be put into practice, reference will now be made, by way of example only, to the accompanying drawings, in which:

[0041] Figure 1 A flow chart for estimating data of interest from noisy data is shown;

[0042] Figure 2 shows the results of the method described herein on cardiac ultrasound data; and

[0043] Figure 3 Results of the method described in this paper on natural images are shown. DETAILED DESCRIPTION

[0044] The present invention will be described with reference to the accompanying drawings.

[0045] It should be understood that the detailed description and specific examples are intended to be for illustration purposes only and are not intended to limit the scope of the invention when indicating exemplary embodiments of the device, system and method. These and other features, aspects and advantages of the device, system and method of the present invention will be better understood from the following description, claims and drawings. It should be understood that the drawings are merely schematic and are not drawn to scale. It should also be understood that the same reference numerals are used throughout the drawings to indicate the same or similar parts.

[0046] The present invention provides a method for denoising data including data of interest and target-related noise. The data is input into two models trained on the data of interest and the target-related noise, respectively, wherein at least the model trained on the target-related noise is a scoring-based generative model. Therefore, the data of interest can be estimated based on the data and the outputs of the two separate models.

[0047] The focus of the present invention relies on the combination of separate models for the data of interest and the associated noise. This combination means using a convolutional neural network to learn the statistics of the two distributions (i.e., the data of interest and the associated noise). More specifically, it is proposed to use generative modeling based on scoring to capture the prior distribution of the data of interest and the associated noise. As will be shown below, a Bayesian formula can then be used to extract samples from the posterior distribution, which is affected by both the prior distribution and the likelihood of the measurement results.

[0048] The scoring-based generative model learns the gradient of the log probability density function of the noise-perturbed prior distribution p(x) during training. This quantity is often called the (Stein) scoring function.

[0049] When both models use score-based networks, they can both be trained in an unsupervised manner using score matching on "clean" images (e.g., ultrasound images) and data containing target-related noise (e.g., blurred ultrasound images), respectively. However, the training data does not need to have matching underlying data. Although any network can be used for score-based modeling, U-Net type architectures have been shown to be effective networks for score-based training. The RefineNet architecture has been used for the results discussed below.

[0050] With respect to the processing of ultrasound data, an algorithm using these two models can be incorporated as a software addition into the post-processing pipeline of an existing ultrasound device. The algorithm can operate in the image domain immediately after envelope detection of beam-summed RF data. This means that the generative model priors are learned in the image domain, and the denoising task is performed in the same domain. However, it should be understood that the use of separate models is not limited to the image domain, as will be discussed below.

[0051] The proposed scoring-based model is part of the unsupervised deep learning branch named as generative model. These models are able to learn the underlying distribution of data and are therefore able to express uncertainty about a particular measurement. Examples of generative models are generative adversarial networks (GANs), variational autoencoders (VAEs), and normalized flows (NFs). However, it has been found that these methods require strong restrictions on the model architecture or involve unstable training processes. For example, NFs require a dedicated network architecture that is computationally and memory expensive. Relatively speaking, it has been found that scoring-based networks easily learn priors using score matching, and scoring-based networks have achieved state-of-the-art performance on many downstream tasks and applications. Therefore, scoring-based models can be viewed as improvements to the above-mentioned generative models. Therefore, it is proposed to use scoring-based models.

[0052] Most existing approaches to inverse problems using deep generative models assume the setting of additive Gaussian noise. As mentioned earlier, this assumption does not hold in the case of ultrasonic dehazing, or more generally, in the case of removing correlated noise from measured / observed data. Normalized flow (NF) has been used to perform maximum a posteriori inference for correlated noise using an explicit generative model for the noise distribution. For example, see Whang, Lei, & Dimakis, 2021 Proceedings of the 38th International Conference on Machine Learning, PMLR139, 2021, “Solving Inverse Problems with a Flow-based Noise Model”.

[0053] However, NFs require specialized network architectures that are computationally and memory expensive. In contrast, scoring-based networks have been found to easily learn priors using score matching, and scoring-based networks have achieved state-of-the-art performance on many downstream tasks and applications.

[0054] Furthermore, it is important to note that there are some key differences between generative approaches that make it impossible to just replace the model to solve the same problem.

[0055] Flow-based models are generally the more understandable solution, as they can be used to compute the likelihood of the data (and subsequently the MAP solution). However, in this case, the score-based model is used for the reasons stated above (i.e., faster, less complex, and more flexible neural network architecture). In particular, when solving the inverse denoising problem addressed in this paper, the flow-based model cannot be simply replaced with the score-based model. This is because, although possible, the likelihood computation using the score-based model has not been found to be efficient (i.e., it takes a very long time). By substituting the proximal gradient update step size [s s ] from the two separate score-based models, the proximal gradient update step size [s s s ] is reduced to s s s . θ ,s φ ] is added to the sampler to take into account the likelihood of the measurement results to avoid this problem. The proximal gradient update step size [s θ ,s φ ] is used for both the correlated noise and the data of interest. Therefore, the inverse denoising problem must be reformulated - see equation (1) below.

[0056] Therefore, the focus of this paper is on the inverse problem, such as ultrasonic dehazing, where one attempts to retrieve the underlying signal (ie, data of interest) from corrupted data containing target-related noise.

[0057] Figure 1A flow chart is shown for estimating data of interest 110 from noisy data 102. In this case, the observed noisy data 102 is an ultrasound image containing fog. Therefore, a first score-based model 104 has been trained using clean ultrasound images, and a second score-based model 106 has been trained using blurry ultrasound images. A sampler 108 is then used to solve the inverse denoising problem (i.e., remove the correlated noise from the observed data).

[0058] The first and second models and the sampler are implemented in software executed by the processor 120 .

[0059] The inverse denoising problem can be formulated as:

[0060] y=x+h+n (1)

[0061] Among them, y is the measured signal, x~p X (x) is the data of interest (i.e., the clean ultrasound image in this case), h~p H (h) is the target-related noise (i.e., fog in this case), and is the Gaussian distribution noise component. X (x) is the prior distribution of the data of interest modeled by the first score-based model 104 after training on the data of interest, and p H (h) is the prior distribution modeled by the second score-based model 106 after training on target-related noise. According to the Bayesian framework, the maximum a posteriori (MAP) solution is given by:

[0062]

[0063]

[0064] λ and μ are hyperparameters that should be carefully chosen to balance prior knowledge with observations. They are fixed during the entire sampling process. Usually, after training a scoring-based model, it should be possible to find relatively good settings for λ and μ. Afterwards, they should not have to be changed when the sampler is used.

[0065] The application of the sampler 108 uses two separate scoring-based networks 104 and 106 [s θ ,s φ]. The scoring function in the scoring-based models 104 and 106 is the gradient of the data distribution, and the sampler 108 can be used to extract samples from the scoring-based models 104 and 106 using an iterative method (such as Langevin dynamics or Euler-Maruyama sampling method). These methods solve the reverse diffusion process formulated by the stochastic differential equation. The forward diffusion process gradually diffuses the data points into random noise by gradually perturbing the data with more noise. The scoring function appears in the reverse of this diffusion process, which is used to smoothly convert the correlated noise into a sample of the data distribution. The scoring-based models 104 and 106 will be used as priors on the data density of the data of interest and the target-related noise, respectively. This is different from existing sampling methods because it requires learning priors on both the data of interest and the target-related noise. The latter is useful in inverse problems involving correlated noise (such as fog).

[0066] Denoising can be done by sampling from the posterior using the Euler–Maruyama sampling method described in the following algorithm:

[0067]

[0068] Where λ and μ and hyperparameters (discussed below), functions f(t) and g(t) refer to the standard Wiener process and represent the trajectories of random variables in the random process, and π(x) and π(h) are predefined noise distributions. More details about the Euler-Maruyama sampling method can be found in: Song, Shen, Xing, & Ermon, 2021 "Solving Inverse Problems in Medical Imaging with Score-Based Generative Models" (ICLRConference 2022).

[0069] Note that in this algorithm, Lines 14-17 are similar to Lines 9-12 and are used to solve the sampling process for the target-related noise h in the same way as the data of interest x.

[0070] It has been shown previously that the Euler-Maruyama sampling method can be extended to conditional samplers by adding a proximal optimization step. The data consistency step in lines 4 and 5 ensures that the generated samples is consistent with the observed data y. However, previous methods are restrictive because they assume a simple measurement model y=x+n, where the noise n is Gaussian. Methods that rely on this assumption are generally unable to handle highly structured and correlated noise. The fog commonly seen in cardiac imaging is a good example of a real-world scenario where these methods fail.

[0071] In contrast, the method shown above extends the sampling method with a separate noise model. Lines 1, 7, and 14-17 show the explicit correlation noise model p H (h) The additional steps required to be incorporated into the sampler. Intuitively, both x and h are sampled simultaneously using the Euler-Maruyama method, while the additional data consistency step (line 7) ensures that both x and h are consistent with the measurement model in equation (1).

[0072] Then, by Figure 1 Sampler 108 in generates The samples of may be used to generate data of interest 110. In essence, the output of sampler 108 is the final sample of the iterative loop.

[0073] In addition, the prior distribution p X (x) and p H The design of (h) is important for optimal dehazing performance. The goal is to capture relevant features of the data of interest while still being able to generalize to unseen patterns in the data. For example, in the case of ultrasound, it is important to capture relevant ultrasound features while still being able to generalize to unseen anatomical features in the ultrasound data. To achieve this, the prior distribution can be factorized into multiple segments or patches. Each of these patches is individually denoised to maintain spatial independence. By design, this approach is less likely to overfit anatomical structures.

[0074] The scale at which the segments are factorized can be chosen so that basic features (e.g., boundaries between tissues in an ultrasound image) are present in the patches. At the same time, the patches should be small enough so that, for example, larger anatomical structures are not identified. The exact size of the prior distribution depends on the specific data of interest and should be tuned according to the above criteria. It has been found that when extracting patches and overlaying them with a rectangular window after denoising to reconstruct the data of interest, it is appropriate to choose a 50% overlap.

[0075] The noise statistics can sometimes vary greatly over different parts of the observed data, especially in ultrasound imaging where the correlated noise varies as a function of depth in the ultrasound data. H These differences are implicitly captured in (h). However, a variety of improvements can be made to more explicitly capture the exact noise characteristics of each part in the image. For example, multiple models can be trained at different depths and applied to different depths. A simpler approach uses a single model for all segments in the image, but weights the (λ,μ) prior differently with measurements depending on the depth. In areas with lower SNR (higher depth), it may be preferable to rely less on the observed data and more on the prior.

[0076] The way in which the two priors are weighted (using hyperparameters λ and μ) in the MAP inference shown in equation (2) is not trivial and can have a large impact on the final performance of the denoising process. In the case of the simplest forward model y = x + n, there is only one prior that is balanced with the likelihood using parameter λ. Here, λ can be simply tuned to control the amount of denoising. In the case of more complex models with the dual priors shown in equation (1), an additional weighting parameter μ is introduced to balance the correlated noise prior p H (h). It will be appreciated that there is a complex interaction between how these parameters are set and the resulting estimate of the data of interest. A Bayesian search algorithm may be employed to automatically find the two hyperparameters to improve the quality of the data of interest. It will be appreciated that other methods for arriving at values ​​for the hyperparameters (e.g., a grid search method) may also be used.

[0077] A sampler 108 is used in the algorithm because it "samples" or draws points (i.e., image x) from a data distribution conditioned on an observation (i.e., measurement y). Typically, methods for solving inverse problems (including non-deep learning methods) do so in an iterative manner. However, an iterative algorithm does not necessarily have to be a sampler, as some algorithms are not formulated in a probabilistic manner. For example, a so-called solver can be used instead of a sampler. The subtle difference is that samplers have some randomness embedded in them, which allows them to draw samples from a distribution (rather than just deterministic points), while non-sampling solvers only find the optimal solution deterministically (e.g., by gradient descent). In fact, the random component (lines 11 and 16) can also be removed from the above algorithm, and then it will not be a sampler, but will find the most likely image.

[0078] The current signal model of equation (1) can be further extended with the measurement result matrix A, which is usually done in a compressed sensing setting:

[0079] y=Ax+h+n (3)

[0080] In this case, y is not only a corrupted version of x, but also an undersampled version of x. The proximal update step (line 5) of the algorithm shown above can be rewritten to take into account the measurement matrix in the conditional model as follows:

[0081]

[0082] Similarly, the data consistency step for h (line 7) can be changed to incorporate the measurement result matrix A:

[0083]

[0084] It will be appreciated that more complex inverse problems may be solved using extended versions of the signal model in equation (3), where the measurement matrix may include sub-sampling, point spread functions or blur kernels.

[0085] Of course, the signal model can be further extended to solve nonlinear functions In this case, the forward operator (previously A, or even the identity I in the algorithm) is the nonlinear function Instead of a linear operator. This new formulation of the inverse problem can be solved similarly as long as the nonlinear function is differentiable.

[0086] The first scoring-based model and the second scoring-based model can be learned from a mixture of simulated data, phantom data, and in vivo data for generalization. Two separate networks are trained for the data of interest and the associated noise. Thus, two separate datasets are used for training. The first dataset includes clean data that does not contain target-related noise. Second, the second dataset includes target-related noise (e.g., ultrasound data containing only fog without any tissue signal) and is used to learn the statistics of the target-related noise.

[0087] In ultrasound, it can be challenging to separate the noise components to learn a prior. Therefore, noise priors are often trained only on simulation and phantom data. However, it is possible to extract the fuzzy regions from in vivo data and use them to train the noise prior.

[0088] Figure 2 The results of the method described herein on cardiac ultrasound data are shown. Specifically, as described above, two scoring-based models are trained on clean ultrasound images and fog, respectively. The model is used to estimate the data of interest (i.e., the clean ultrasound image) based on the ultrasound image containing the artificially added fog shown in column 204. The goal is to estimate the corresponding data of interest shown in column 202 (i.e., the ultrasound image before the artificial addition of fog). The estimated ultrasound image is shown in column 206. Rows 208, 210, 212, 214, and 216 show various views of the cardiac ultrasound image. It can be seen that the estimated image of column 206 has significantly less fog than the ultrasound image containing the fog in column 204.

[0089] For the case of ultrasound, the priors can be learned in and applied to the image domain. However, the method is not limited to images and can be applied anywhere in the signal path. For example, the denoising task can be performed on the RF data (after beamforming) or even on the raw channel data itself. It is recommended to use methods such as compression and expansion to suppress the dynamic range of the RF data to prepare the data for neural networks, which generally perform better in this case. Finally, the application can be extended from 2D to 3D ultrasound data. The network can be applied to slices of 3D data, or may be more interested in the data cube as a whole, thereby capturing the relationship between the dimensions in the prior distribution. Finally, the time dimension can be exploited by learning priors about a sequence of consecutive frames or conditioning on previous frames.

[0090] It is generally known that medical images (e.g., from computed tomography (CT) and magnetic resonance imaging (MRI)) often contain correlated noise. In this way, the two models described above can also be trained for specific scenarios in medical imaging.

[0091] Although the method was originally designed for application in cardiac ultrasound, it can be applied to any problem involving denoising and retrieving the underlying signal (i.e., data of interest) from measurements with highly correlated noise. As an example, the output of the method is applied to natural images. Figure 3 302 shows clean images (i.e., data of interest) in the form of images of different people, and column 304 shows images with target-related noise. The target-related noise includes handwritten reference marks of different colors written on the image. For ease of illustration, the superimposed reference marks are shown in black to make them visible.

[0092] Column 306 shows the estimated data of interest after using the denoising method of the present invention, column 308 shows the estimated target-related noise, and column 310 shows the actual target-related noise (i.e., the superimposed handwritten digits). Of course, the estimated data of interest and the estimate of the target-related noise can be found when two separate models are used. The method is applied to five different images shown in rows 312, 314, 316, 318, and 320. In this case, the distribution is not factored into segments, but rather the image as a whole is inferred.

[0093] It should be noted that score-based models have been introduced in many styles and have been used under various names. Any known score-based model will work with the methods described in this article. A few examples include score-based generative models, also known as: diffusion models; denoised diffusion probabilistic modeling (DDPM) and score-based diffusion models.

[0094] Furthermore, the Euler-Maruyama sampler is given as an example of the above sampler. Any sampling method for diffusion processes can work. More complex samplers such as ALD, probability flow ODE, and predictor-corrector samplers can be used to further improve the sample quality.

[0095] A skilled person will be easily able to develop a processor for executing any of the methods described herein. Therefore, each step of the flowchart may represent a different action performed by the processor and may be performed by a corresponding module of the processor.

[0096] As described above, the system utilizes a processor to perform data processing. The processor can be implemented in many ways using software and / or hardware to perform the various functions required. The processor typically employs one or more microprocessors that can be programmed using software (e.g., microcode) to perform the required functions. The processor can be implemented as a combination of dedicated hardware that performs some functions and one or more programmed microprocessors and associated circuits that perform other functions.

[0097] Examples of circuits that may be employed in various embodiments of the present disclosure include, but are not limited to, conventional microprocessors, application specific integrated circuits (ASICs), and field programmable gate arrays (FPGAs).

[0098] In various embodiments, the processor may be associated with one or more storage media, such as volatile and non-volatile computer memory, such as RAM, PROM, EPROM, and EEPROM. The storage media may be encoded with one or more programs that perform the desired functions when run on one or more processors and / or controllers. The various storage media may be fixed within the processor or controller or may be transportable so that one or more programs stored thereon may be loaded into the processor.

[0099] By studying the drawings, the disclosure and the appended claims, those skilled in the art can understand and implement variations of the disclosed embodiments when practicing the claimed invention. In the claims, the word "comprising" does not exclude other elements or steps, and the word "one" or "an" does not exclude a plurality.

[0100] The functions implemented by a processor may be implemented by a single processor or by multiple individual processing units which may be considered together to constitute a “processor.” In some cases, such processing units may be remote from each other and communicate with each other in a wired or wireless manner.

[0101] The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.

[0102] The computer program may be stored / distributed on suitable media, such as optical storage media or solid-state media provided together with or as part of other hardware, but the computer program may also be distributed in other forms, such as via the Internet or other wired or wireless telecommunications systems.

[0103] If the term "suitable for" is used in the claims or the description, it should be noted that the term "suitable for" is intended to be equivalent to the term "configured to". If the term "arranged" is used in the claims or the description, it should be noted that the term "arranged" is intended to be equivalent to the term "system", and vice versa.

[0104] Any reference signs in the claims should not be construed as limiting the scope.

Claims

1. A method for denoising data (102) comprising data of interest and target-related noise, the method comprising: inputting the data into a first model (104), the first model being trained on the data of interest; inputting the data into a second score-based generative model (106) trained on target-related noise expected to be present in the data; and The data of interest is estimated based on the data and an output of the first model and an output of the second scoring-based generative model (110).

2. The method according to claim 1, wherein: The first model is also a scoring-based generative model.

3. The method according to claim 1 or 2, wherein: Estimating the data of interest includes using the outputs of the first model and the second scoring-based generative model in a sampling algorithm configured to estimate the data of interest from the data by solving an inverse denoising problem and applying the solution to the data.

4. The method according to any one of claims 1 to 3, wherein: The data is undersampled relative to the data of interest by a sampling matrix, and wherein the method comprises transforming the data to a size of the data of interest.

5. The method according to claim 4, wherein: The sampling matrix also includes one or more of the following: a subsampling function, a point spread function, and a blur kernel.

6. The method according to any one of claims 1 to 5, wherein: The data is image data.

7. The method according to any one of claims 1 to 6, wherein: The data is ultrasound image data.

8. The method according to claim 7, wherein: A plurality of first models are applied to different depths of the ultrasound image data, wherein each first model is trained on the data of interest for a target depth in the ultrasound image data; and / or A plurality of second score-based generative models are applied to different depths of the ultrasound image data, wherein each second score-based generative model is trained on target-related noise expected to be present at the target depth in the ultrasound image data.

9. A computer program carrier comprising computer program code which, when run on a processing system, causes the processing system to perform all the steps of the method according to any one of claims 1 to 8.

10. A system for denoising data (102) comprising data of interest and target-related noise, the system comprising a processor (120) configured to: inputting the data into a first model (104), the first model being trained on the data of interest; inputting the data into a second score-based generative model (106) trained on target-related noise expected to be present in the data; and The data of interest is estimated based on the data and the output of the first model and the output of the second model (110).

11. The system according to claim 10, wherein: The first model is also a scoring-based generative model.

12. The system according to claim 10 or 11, wherein: Estimating the data of interest includes using the output of the first model and the output of the second score-based generative model in a sampling algorithm, the sampling algorithm being configured to estimate the data of interest from the data by solving an inverse denoising problem and applying the solution to the data.

13. A system according to any one of claims 10 to 12, wherein: The data is image data.

14. A system according to any one of claims 10 to 13, wherein: The data is ultrasound image data.

15. The system of claim 14, wherein: A plurality of first models are applied to different depths of the ultrasound image data, wherein each first model is trained on the data of interest for a target depth in the ultrasound image data; and / or A plurality of second score-based generative models are applied to different depths of the ultrasound image data, wherein each second score-based generative model is trained on target-related noise expected to be present at the target depth in the ultrasound image data.

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