Systematic Review on Learning-based Spectral CT.

Spectral computed tomography (CT) has recently emerged as an advanced version of medical CT and significantly improves conventional (single-energy) CT. Spectral CT has two main forms: dual-energy computed tomography (DECT) and photon-counting computed tomography (PCCT), which offer image improvement, material decomposition, and feature quantification relative to conventional CT. However, the inherent challenges of spectral CT, evidenced by data and image artifacts, remain a bottleneck for clinical applications. To address these problems, machine learning techniques have been widely applied to spectral CT. In this review, we present the state-of-the-art data-driven techniques for spectral CT.

A Review on Low-Dose Emission Tomography Post-Reconstruction Denoising with Neural Network Approaches.

Low-dose emission tomography (ET) plays a crucial role in medical imaging, enabling the acquisition of functional information for various biological processes while minimizing the patient dose. However, the inherent randomness in the photon counting process is a source of noise which is amplified in low-dose ET. This review article provides an overview of existing post-processing techniques, with an emphasis on deep neural network (NN) approaches. Furthermore, we explore future directions in the field of NN-based low-dose ET. This comprehensive examination sheds light on the potential of deep learning in enhancing the quality and resolution of low-dose ET images, ultimately advancing the field of medical imaging.

Systematic Review on Learning-based Spectral CT.

Spectral computed tomography (CT) has recently emerged as an advanced version of medical CT and significantly improves conventional (single-energy) CT. Spectral CT has two main forms: dual-energy computed tomography (DECT) and photon-counting computed tomography (PCCT), which offer image improvement, material decomposition, and feature quantification relative to conventional CT. However, the inherent challenges of spectral CT, evidenced by data and image artifacts, remain a bottleneck for clinical applications. To address these problems, machine learning techniques have been widely applied to spectral CT. In this review, we present the state-of-the-art data-driven techniques for spectral CT.

PET scatter estimation using deep learning U-Net architecture.

Objective.Positron emission tomography (PET) image reconstruction needs to be corrected for scatter in order to produce quantitatively accurate images. Scatter correction is traditionally achieved by incorporating an estimated scatter sinogram into the forward model during image reconstruction. Existing scatter estimated methods compromise between accuracy and computing time. Nowadays scatter estimation is routinely performed using single scatter simulation (SSS), which does not accurately model multiple scatter and scatter from outside the field-of-view, leading to reduced qualitative and quantitative PET reconstructed image accuracy. On the other side, Monte-Carlo (MC) methods provide a high precision, but are computationally expensive and time-consuming, even with recent progress in MC acceleration.Approach.In this work we explore the potential of deep learning (DL) for accurate scatter correction in PET imaging, accounting for all scatter coincidences. We propose a network based on a U-Net convolutional neural network architecture with 5 convolutional layers. The network takes as input the emission and computed tomography (CT)-derived attenuation factor (AF) sinograms and returns the estimated scatter sinogram. The network training was performed using MC simulated PET datasets. Multiple anthropomorphic extended cardiac-torso phantoms of two different regions (lung and pelvis) were created, considering three different body sizes and different levels of statistics. In addition, two patient datasets were used to assess the performance of the method in clinical practice.Main results.Our experiments showed that the accuracy of our method, namely DL-based scatter estimation (DLSE), was independent of the anatomical region (lungs or pelvis). They also showed that the DLSE-corrected images were similar to that reconstructed from scatter-free data and more accurate than SSS-corrected images.Significance.The proposed method is able to estimate scatter sinograms from emission and attenuation data. It has shown a better accuracy than the SSS, while being faster than MC scatter estimation methods.

LRR-CED: low-resolution reconstruction-aware convolutional encoder-decoder network for direct sparse-view CT image reconstruction.

Objective. Sparse-view computed tomography (CT) reconstruction has been at the forefront of research in medical imaging. Reducing the total x-ray radiation dose to the patient while preserving the reconstruction accuracy is a big challenge. The sparse-view approach is based on reducing the number of rotation angles, which leads to poor quality reconstructed images as it introduces several artifacts. These artifacts are more clearly visible in traditional reconstruction methods like the filtered-backprojection (FBP) algorithm.Approach. Over the years, several model-based iterative and more recently deep learning-based methods have been proposed to improve sparse-view CT reconstruction. Many deep learning-based methods improve FBP-reconstructed images as a post-processing step. In this work, we propose a direct deep learning-based reconstruction that exploits the information from low-dimensional scout images, to learn the projection-to-image mapping. This is done by concatenating FBP scout images at multiple resolutions in the decoder part of a convolutional encoder-decoder (CED).Main results. This approach is investigated on two different networks, based on Dense Blocks and U-Net to show that a direct mapping can be learned from a sinogram to an image. The results are compared to two post-processing deep learning methods (FBP-ConvNet and DD-Net) and an iterative method that uses a total variation (TV) regularization.Significance. This work presents a novel method that uses information from both sinogram and low-resolution scout images for sparse-view CT image reconstruction. We also generalize this idea by demonstrating results with two different neural networks. This work is in the direction of exploring deep learning across the various stages of the image reconstruction pipeline involving data correction, domain transfer and image improvement.

Multi-channel convolutional analysis operator learning for dual-energy CT reconstruction.

Objective.Dual-energy computed tomography (DECT) has the potential to improve contrast and reduce artifacts and the ability to perform material decomposition in advanced imaging applications. The increased number of measurements results in a higher radiation dose, and it is therefore essential to reduce either the number of projections for each energy or the source x-ray intensity, but this makes tomographic reconstruction more ill-posed.Approach.We developed the multi-channel convolutional analysis operator learning (MCAOL) method to exploit common spatial features within attenuation images at different energies and we propose an optimization method which jointly reconstructs the attenuation images at low and high energies with mixed norm regularization on the sparse features obtained by pre-trained convolutional filters through the convolutional analysis operator learning (CAOL) algorithm.Main results.Extensive experiments with simulated and real computed tomography data were performed to validate the effectiveness of the proposed methods, and we report increased reconstruction accuracy compared with CAOL and iterative methods with single and joint total variation regularization.Significance.Qualitative and quantitative results on sparse views and low-dose DECT demonstrate that the proposed MCAOL method outperforms both CAOL applied on each energy independently and several existing state-of-the-art model-based iterative reconstruction techniques, thus paving the way for dose reduction.

Effect of attenuation mismatches in time of flight PET reconstruction.

While the pursuit of better time resolution in positron emission tomography (PET) is rapidly evolving, little work has been performed on time of flight (TOF) image quality at high time resolution in the presence of modelling inconsistencies. This works focuses on the effect of using the wrong attenuation map in the system model, causing perturbations in the reconstructed radioactivity image. Previous work has usually considered the effects to be local to the area where there is attenuation mismatch, and has shown that the quantification errors in this area tend to reduce with improved time resolution. This publication shows however that errors in the PET image at a distance from the mismatch increase with time resolution. The errors depend on the reconstruction algorithm used. We quantify the errors in the hypothetical case of perfect time resolution for maximum likelihood reconstructions. In addition, we perform reconstructions on simulated and patient data. In particular, for respiratory-gated reconstructions from a wrong attenuation map, increased errors are observed with improved time resolutions in areas close to the lungs (e.g. from 13.3% in non-TOF to up to 20.9% at 200 ps in the left ventricle).

Benefits of Using a Spatially-Variant Penalty Strength With Anatomical Priors in PET Reconstruction.

In this study, we explore the use of a spatially-variant penalty strength in penalized image reconstruction using anatomical priors to reduce the dependence of lesion contrast on surrounding activity and lesion location. This work builds on a previous method to make the local perturbation response (LPR) approximately spatially invariant. While the dependence of lesion contrast on the local properties introduced by the anatomical penalty is intentional, the method aims to reduce the influence from surroundings lying along the lines of response (LORs) but not in the penalty neighborhood structure. The method is evaluated using simulated data, assuming that the anatomical information is absent or well-aligned with the corresponding activity images. Since the parallel level sets (PLS) penalty is convex and has shown promising results in the literature, it is chosen as the representative anatomical penalty and incorporated into the previously proposed preconditioned algorithm (L-BFGS-B-PC) for achieving good image quality and fast convergence rate. A 2D disc phantom with a feature at the center and a 3D XCAT thorax phantom with lesions inserted in different slices are used to study how surrounding activity and lesion location affect the visual appearance and quantitative consistency. A bias and noise analysis is also performed with the 2D disc phantom. The consistency of the algorithm convergence rate with respect to different data noise and background levels is also investigated using the XCAT phantom. Finally, an example of reconstruction for a patient dataset with inserted pseudo lesions is used as a demonstration in a clinical context. We show that applying the spatially-variant penalization with PLS can reduce the dependence of the lesion contrast on the surrounding activity and lesion location. It does not affect the bias and noise trade-off curves for matched local resolution. Moreover, when using the proposed penalization, significant improvement in algorithm convergence rate and convergence consistency is observed.

PET Reconstruction With Non-Negativity Constraint in Projection Space: Optimization Through Hypo-Convergence.

Standard positron emission tomography (PET) reconstruction techniques are based on maximum-likelihood (ML) optimization methods, such as the maximum-likelihood expectation-maximization (MLEM) algorithm and its variations. Most methodologies rely on a positivity constraint on the activity distribution image. Although this constraint is meaningful from a physical point of view, it can be a source of bias for low-count/high-background PET, which can compromise accurate quantification. Existing methods that allow for negative values in the estimated image usually utilize a modified log-likelihood, and therefore break the data statistics. In this paper, we propose to incorporate the positivity constraint on the projections only, by approximating the (penalized) log-likelihood function by an adequate sequence of objective functions that are easily maximized without constraint. This sequence is constructed such that there is hypo-convergence (a type of convergence that allows the convergence of the maximizers under some conditions) to the original log-likelihood, hence allowing us to achieve maximization with positivity constraint on the projections using simple settings. A complete proof of convergence under weak assumptions is given. We provide results of experiments on simulated data where we compare our methodology with the alternative direction method of multipliers (ADMM) method, showing that our algorithm converges to a maximizer, which stays in the desired feasibility set, with faster convergence than ADMM. We also show that this approach reduces the bias, as compared with MLEM images, in necrotic tumors-which are characterized by cold regions surrounded by hot structures-while reconstructing similar activity values in hot regions.

Fast Quasi-Newton Algorithms for Penalized Reconstruction in Emission Tomography and Further Improvements via Preconditioning.

This paper reports on the feasibility of using a quasi-Newton optimization algorithm, limited-memory Broyden-Fletcher-Goldfarb-Shanno with boundary constraints (L-BFGS-B), for penalized image reconstruction problems in emission tomography (ET). For further acceleration, an additional preconditioning technique based on a diagonal approximation of the Hessian was introduced. The convergence rate of L-BFGS-B and the proposed preconditioned algorithm (L-BFGS-B-PC) was evaluated with simulated data with various factors, such as the noise level, penalty type, penalty strength and background level. Data of three 18F-FDG patient acquisitions were also reconstructed. Results showed that the proposed L-BFGS-B-PC outperforms L-BFGS-B in convergence rate for all simulated conditions and the patient data. Based on these results, L-BFGS-B-PC shows promise for clinical application.

Evaluation of a direct motion estimation/correction method in respiratory-gated PET/MRI with motion-adjusted attenuation.

PURPOSE: Respiratory motion compensation in PET/CT and PET/MRI is essential as motion is a source of image degradation (motion blur, attenuation artifacts). In previous work, we developed a direct method for joint image reconstruction/motion estimation (JRM) for attenuation-corrected (AC) respiratory-gated PET, which uses a single attenuation-map (µ-map). This approach was successfully implemented for respiratory-gated PET/CT, but since it relied on an accurate µ-map for motion estimation, the question of its applicability in PET/MRI is open. The purpose of this work is to investigate the feasibility of JRM in PET/MRI and to assess the robustness of the motion estimation when a degraded µ-map is used. METHODS: We performed a series of JRM reconstructions from simulated PET data using a range of simulated Dixon MRI sequence derived µ-maps with wrong attenuation values in the lungs, from -100% (no attenuation) to +100% (double attenuation), as well as truncated arms. We compared the estimated motions with the one obtained from JRM in ideal conditions (no noise, true µ-map as an input). We also applied JRM on 4 patient datasets of the chest, 3 of them containing hot lesions. Patient list-mode data were gated using a principal component analysis method. We compared SUVmax values of the JRM reconstructed activity images and non motion-corrected images. We also assessed the estimated motion fields by comparing the deformed JRM-reconstructed activity with individually non-AC reconstructed gates. RESULTS: Experiments on simulated data showed that JRM-motion estimation is robust to µ-map degradation in the sense that it produces motion fields similar to the ones obtained when using the true µ-map, regardless of the attenuation errors in the lungs (< 0.5% mean absolute difference with the reference motion field). When using a µ-map with truncated arms, JRM estimates a motion field that stretches the µ-map in order to match the projection data. Results on patient datasets showed that using JRM improves the SUVmax values of hot lesions significantly and suppresses motion blur. When the estimated motion fields are applied to the reconstructed activity, the deformed images are geometrically similar to the non-AC individually reconstructed gates. CONCLUSION: Motion estimation by JRM is robust to variation of the attenuation values in the lungs. JRM successfully compensates for motion when applied to PET/MRI clinical datasets. It provides a potential alternative to existing methods where the motion fields are pre-estimated from separate MRI measurements.

Direct Parametric Reconstruction With Joint Motion Estimation/Correction for Dynamic Brain PET Data.

Direct reconstruction of parametric images from raw photon counts has been shown to improve the quantitative analysis of dynamic positron emission tomography (PET) data. However it suffers from subject motion which is inevitable during the typical acquisition time of 1-2 hours. In this work we propose a framework to jointly estimate subject head motion and reconstruct the motion-corrected parametric images directly from raw PET data, so that the effects of distorted tissue-to-voxel mapping due to subject motion can be reduced in reconstructing the parametric images with motion-compensated attenuation correction and spatially aligned temporal PET data. The proposed approach is formulated within the maximum likelihood framework, and efficient solutions are derived for estimating subject motion and kinetic parameters from raw PET photon count data. Results from evaluations on simulated [11C]raclopride data using the Zubal brain phantom and real clinical [18F]florbetapir data of a patient with Alzheimer's disease show that the proposed joint direct parametric reconstruction motion correction approach can improve the accuracy of quantifying dynamic PET data with large subject motion.

PETPVC: a toolbox for performing partial volume correction techniques in positron emission tomography.

Positron emission tomography (PET) images are degraded by a phenomenon known as the partial volume effect (PVE). Approaches have been developed to reduce PVEs, typically through the utilisation of structural information provided by other imaging modalities such as MRI or CT. These methods, known as partial volume correction (PVC) techniques, reduce PVEs by compensating for the effects of the scanner resolution, thereby improving the quantitative accuracy. The PETPVC toolbox described in this paper comprises a suite of methods, both classic and more recent approaches, for the purposes of applying PVC to PET data. Eight core PVC techniques are available. These core methods can be combined to create a total of 22 different PVC techniques. Simulated brain PET data are used to demonstrate the utility of toolbox in idealised conditions, the effects of applying PVC with mismatched point-spread function (PSF) estimates and the potential of novel hybrid PVC methods to improve the quantification of lesions. All anatomy-based PVC techniques achieve complete recovery of the PET signal in cortical grey matter (GM) when performed in idealised conditions. Applying deconvolution-based approaches results in incomplete recovery due to premature termination of the iterative process. PVC techniques are sensitive to PSF mismatch, causing a bias of up to 16.7% in GM recovery when over-estimating the PSF by 3 mm. The recovery of both GM and a simulated lesion was improved by combining two PVC techniques together. The PETPVC toolbox has been written in C++, supports Windows, Mac and Linux operating systems, is open-source and publicly available.

Maximum-likelihood joint image reconstruction and motion estimation with misaligned attenuation in TOF-PET/CT.

This work is an extension of our recent work on joint activity reconstruction/motion estimation (JRM) from positron emission tomography (PET) data. We performed JRM by maximization of the penalized log-likelihood in which the probabilistic model assumes that the same motion field affects both the activity distribution and the attenuation map. Our previous results showed that JRM can successfully reconstruct the activity distribution when the attenuation map is misaligned with the PET data, but converges slowly due to the significant cross-talk in the likelihood. In this paper, we utilize time-of-flight PET for JRM and demonstrate that the convergence speed is significantly improved compared to JRM with conventional PET data.

Maximum-Likelihood Joint Image Reconstruction/Motion Estimation in Attenuation-Corrected Respiratory Gated PET/CT Using a Single Attenuation Map.

This work provides an insight into positron emission tomography (PET) joint image reconstruction/motion estimation (JRM) by maximization of the likelihood, where the probabilistic model accounts for warped attenuation. Our analysis shows that maximum-likelihood (ML) JRM returns the same reconstructed gates for any attenuation map (µ-map) that is a deformation of a given µ-map, regardless of its alignment with the PET gates. We derived a joint optimization algorithm accordingly, and applied it to simulated and patient gated PET data. We first evaluated the proposed algorithm on simulations of respiratory gated PET/CT data based on the XCAT phantom. Our results show that independently of which µ-map is used as input to JRM: (i) the warped µ-maps correspond to the gated µ-maps, (ii) JRM outperforms the traditional post-registration reconstruction and consolidation (PRRC) for hot lesion quantification and (iii) reconstructed gated PET images are similar to those obtained with gated µ-maps. This suggests that a breath-held µ-map can be used. We then applied JRM on patient data with a µ-map derived from a breath-held high resolution CT (HRCT), and compared the results with PRRC, where each reconstructed PET image was obtained with a corresponding cine-CT gated µ-map. Results show that JRM with breath-held HRCT achieves similar reconstruction to that using PRRC with cine-CT. This suggests a practical low-dose solution for implementation of motion-corrected respiratory gated PET/CT.

Joint parametric reconstruction and motion correction framework for dynamic PET data.

In this paper we propose a novel algorithm for jointly performing data based motion correction and direct parametric reconstruction of dynamic PET data. We derive a closed form update for the penalised likelihood maximisation which greatly enhances the algorithm's computational efficiency for practical use. Our algorithm achieves sub-voxel motion correction residual with noisy data in the simulation-based validation and reduces the bias of the direct estimation of the kinetic parameter of interest. A preliminary evaluation on clinical brain data using [18F]Choline shows improved contrast for regions of high activity. The proposed method is based on a data-driven kinetic modelling method and is directly applicable to reversible and irreversible PET tracers, covering a range of clinical applications.

Markov random field and Gaussian mixture for segmented MRI-based partial volume correction in PET.

In this paper we propose a segmented magnetic resonance imaging (MRI) prior-based maximum penalized likelihood deconvolution technique for positron emission tomography (PET) images. The model assumes the existence of activity classes that behave like a hidden Markov random field (MRF) driven by the segmented MRI. We utilize a mean field approximation to compute the likelihood of the MRF. We tested our method on both simulated and clinical data (brain PET) and compared our results with PET images corrected with the re-blurred Van Cittert (VC) algorithm, the simplified Guven (SG) algorithm and the region-based voxel-wise (RBV) technique. We demonstrated our algorithm outperforms the VC algorithm and outperforms SG and RBV corrections when the segmented MRI is inconsistent (e.g. mis-segmentation, lesions, etc) with the PET image.