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تسجيل مستخدم جديدCompartment model-based nonlinear unmixing for kinetic analysis of dynamic PET images
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When no arterial input function is available, quantification of dynamic PET images requires a previous step devoted to the extraction of a reference time-activity curve (TAC). Factor analysis is often applied for this purpose. This paper introduces a novel approach that conducts a new kind of nonlinear factor analysis relying on a compartment model, and computes the kinetic parameters of specific binding tissues jointly. To this end, it capitalizes on data-driven parametric imaging methods to provide a physical description of the underlying PET data, directly relating the specific binding with the kinetics of the non-specific binding in the corresponding tissues. This characterization is introduced into the factor analysis formulation to yield a novel nonlinear unmixing model designed for PET image analysis. This model also explicitly introduces global kinetic parameters that allow for a direct estimation of the binding potential with respect to the free fractions in each non-specific binding tissue. The performance of the method is evaluated on synthetic and real data to demonstrate its potential interest.
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To analyze dynamic positron emission tomography (PET) images, various generic multivariate data analysis techniques have been considered in the literature, such as principal component analysis (PCA), independent component analysis (ICA), factor analy
sis and nonnegative matrix factorization (NMF). Nevertheless, these conventional approaches neglect any possible nonlinear variations in the time activity curves describing the kinetic behavior of tissues with specific binding, which limits their ability to recover a reliable, understandable and interpretable description of the data. This paper proposes an alternative analysis paradigm that accounts for spatial fluctuations in the exchange rate of the tracer between a free compartment and a specifically bound ligand compartment. The method relies on the concept of linear unmixing, usually applied on the hyperspectral domain, which combines NMF with a sum-to-one constraint that ensures an exhaustive description of the mixtures. The spatial variability of the signature corresponding to the specific binding tissue is explicitly modeled through a perturbed component. The performance of the method is assessed on both synthetic and real data and is shown to compete favorably when compared to other conventional analysis methods. The proposed method improved both factor estimation and proportions extraction for specific binding. Modeling the variability of the specific binding factor has a strong potential impact for dynamic PET image analysis.
Factor analysis has proven to be a relevant tool for extracting tissue time-activity curves (TACs) in dynamic PET images, since it allows for an unsupervised analysis of the data. Reliable and interpretable results are possible only if considered wit
h respect to suitable noise statistics. However, the noise in reconstructed dynamic PET images is very difficult to characterize, despite the Poissonian nature of the count-rates. Rather than explicitly modeling the noise distribution, this work proposes to study the relevance of several divergence measures to be used within a factor analysis framework. To this end, the $beta$-divergence, widely used in other applicative domains, is considered to design the data-fitting term involved in three different factor models. The performances of the resulting algorithms are evaluated for different values of $beta$, in a range covering Gaussian, Poissonian and Gamma-distributed noises. The results obtained on two different types of synthetic images and one real image show the interest of applying non-standard values of $beta$ to improve factor analysis.
Direct reconstruction methods have been developed to estimate parametric images directly from the measured PET sinograms by combining the PET imaging model and tracer kinetics in an integrated framework. Due to limited counts received, signal-to-nois
e-ratio (SNR) and resolution of parametric images produced by direct reconstruction frameworks are still limited. Recently supervised deep learning methods have been successfully applied to medical imaging denoising/reconstruction when large number of high-quality training labels are available. For static PET imaging, high-quality training labels can be acquired by extending the scanning time. However, this is not feasible for dynamic PET imaging, where the scanning time is already long enough. In this work, we proposed an unsupervised deep learning framework for direct parametric reconstruction from dynamic PET, which was tested on the Patlak model and the relative equilibrium Logan model. The patients anatomical prior image, which is readily available from PET/CT or PET/MR scans, was supplied as the network input to provide a manifold constraint, and also utilized to construct a kernel layer to perform non-local feature denoising. The linear kinetic model was embedded in the network structure as a 1x1 convolution layer. The training objective function was based on the PET statistical model. Evaluations based on dynamic datasets of 18F-FDG and 11C-PiB tracers show that the proposed framework can outperform the traditional and the kernel method-based direct reconstruction methods.
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l or region-of-interest level. The relatively new field of 4D PET direct reconstruction, by contrast, seeks to move beyond this scheme and incorporate information from multiple time frames within the reconstruction task. Existing 4D direct models are based on a deterministic description of voxels TACs, captured by the chosen kinetic model, considering the photon counting process the only source of uncertainty. In this work, we introduce a new probabilistic modeling strategy based on the key assumption that activity time course would be subject to uncertainty even if the parameters of the underlying dynamic process were known. This leads to a hierarchical Bayesian model, which we formulate using the formalism of Probabilistic Graphical Modeling (PGM). The inference of the joint probability density function arising from PGM is addressed using a new gradient-based iterative algorithm, which presents several advantages compared to existing direct methods: it is flexible to an arbitrary choice of linear and nonlinear kinetic model; it enables the inclusion of arbitrary (sub)differentiable priors for parametric maps; it is simpler to implement and suitable to integration in computing frameworks for machine learning. Computer simulations and an application to real patient scan showed how the proposed approach allows us to weight the importance of the kinetic model, providing a bridge between indirect and deterministic direct methods.
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ally vary due to intrinsic component fluctuations or external factors (illumination). These redundant multiple endmember spectra within each class adversely affect the performance of unmixing methods. This paper proposes a mixing model that explicitly incorporates a hierarchical structure of redundant multiple spectra representing each class. The proposed method is designed to promote sparsity on the selection of both spectra and classes within each pixel. The resulting unmixing algorithm is able to adaptively recover several bundles of endmember spectra associated with each class and robustly estimate abundances. In addition, its flexibility allows a variable number of classes to be present within each pixel of the hyperspectral image to be unmixed. The proposed method is compared with other state-of-the-art unmixing methods that incorporate sparsity using both simulated and real hyperspectral data. The results show that the proposed method can successfully determine the variable number of classes present within each class and estimate the corresponding class abundances.
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