Locally linear constraint based optimization model for material decomposition

Multi-limited-angle spectral CT image reconstruction based on average image induced relative total variation model

In recent years, spectral computed tomography (CT) has attracted extensive attention. The purpose of this study is to achieve a low-cost and fast energy spectral CT reconstruction algorithm by implementing multi-limited-angle scans. General spectral CT projection data are collected over a full-angular range of 360 degrees. We simulate multi-source spectral CT by using a pair of X-ray source/detector. To speed up scanning, multi-limited-angle scanning was used in each energy channel. On this basis, an average image induced relative total variation (Aii-RTV) with multi-limited-angle spectral CT image reconstruction model is proposed. The iterative algorithm is used to solve Aii-RTV. Before iteration, the weighted average projection data of the multi-limited-angle energy spectral is carried out. In each step of the iterative algorithm flow is as follows: First, the relative total variation (RTV) reconstruction model is used to reconstruct the average image using average projection data. Then, the partial derivative of the average image is used to calculate the inherent variation in RTV model due to the integrity of the average image, and take its reciprocal as the weight coefficient of the windowing total variation of each energy channel reconstruction image. Finally, the average energy image is used to guide the multi-limited-angle projection data to reconstruct the image of each energy channel so as to suppress the limited-angle artifact of each energy channel image. In addition, we also discuss the influence of parameter selection on reconstructed image quality, which is important for regularization model. Through the reconstruction of multi-limited-angle spectral CT projection data, quantitative results and reconstructed images show that our algorithm has better performance than prior image constrained compressed sensing (PICCS) and RTV. The average PSNR of our reconstruction results in different channels was 35.6273, 4.533 and 2.301 higher than RTV (31.0943) and PICCS (33.3263), respectively.

A model-based direct inversion network (MDIN) for dual spectral computed tomography

Objective. Dual spectral computed tomography (DSCT) is a very challenging problem in the field of imaging. Due to the nonlinearity of its mathematical model, the images reconstructed by the conventional CT usually suffer from the beam hardening artifacts. Additionally, several existing DSCT methods rely heavily on the information of the spectra, which is often not readily available in applications. To address this problem, in this study, we aim to develop a novel approach to improve the DSCT reconstruction performance.Approach. A model-based direct inversion network (MDIN) is proposed for DSCT, which can directly predict the basis material images from the collected polychromatic projections. The all operations are performed in the network, requiring neither the conventional algorithms nor the information of the spectra. It can be viewed as an approximation to the inverse procedure of DSCT imaging model. The MDIN is composed of projection pre-decomposition module (PD-module), domain transformation layer (DT-layer), and image post-decomposition module (ID-module). The PD-module first performs the pre-decomposition on the polychromatic projections that consists of a series of stacked one-dimensional convolution layers. The DT-layer is designed to obtain the preliminary decomposed results, which has the characteristics of sparsely connected and learnable parameters. And the ID-module uses a deep neural network to further decompose the reconstructed results of the DT-layer so as to achieve higher-quality basis material images.Main results. Numerical experiments demonstrate that the proposed MDIN has significant advantages in substance decomposition, artifact reduction and noise suppression compared to other methods in the DSCT reconstruction.Significance. The proposed method has a flexible applicability, which can be extended to other CT problems, such as multi-spectral CT and low dose CT.

Feasibility study of YSO/SiPM based detectors for virtual monochromatic image synthesis

BACKGROUND

The development of photon-counting CT systems has focused on semiconductor detectors like cadmium zinc telluride (CZT) and cadmium telluride (CdTe). However, these detectors face high costs and charge-sharing issues, distorting the energy spectrum. Indirect detection using Yttrium Orthosilicate (YSO) scintillators with silicon photomultiplier (SiPM) offers a cost-effective alternative with high detection efficiency, low dark count rate, and high sensor gain.

OBJECTIVE

This work aims to demonstrate the feasibility of the YSO/SiPM detector (DexScanner L103) based on the Multi-Voltage Threshold (MVT) sampling method as a photon-counting CT detector by evaluating the synthesis error of virtual monochromatic images.

METHODS

In this study, we developed a proof-of-concept benchtop photon-counting CT system, and employed a direct method for empirical virtual monochromatic image synthesis (EVMIS) by polynomial fitting under the principle of least square deviation without X-ray spectral information. The accuracy of the empirical energy calibration techniques was evaluated by comparing the reconstructed and actual attenuation coefficients of calibration and test materials using mean relative error (MRE) and mean square error (MSE).

RESULTS

In dual-material imaging experiments, the overall average synthesis error for three monoenergetic images of distinct materials is 2.53% ±2.43%. Similarly, in K-edge imaging experiments encompassing four materials, the overall average synthesis error for three monoenergetic images is 4.04% ±2.63%. In rat biological soft-tissue imaging experiments, we further predicted the densities of various rat tissues as follows: bone density is 1.41±0.07 g/cm3, adipose tissue density is 0.91±0.06 g/cm3, heart tissue density is 1.09±0.04 g/cm3, and lung tissue density is 0.32±0.07 g/cm3. Those results showed that the reconstructed virtual monochromatic images had good conformance for each material.

CONCLUSION

This study indicates the SiPM-based photon-counting detector could be used for monochromatic image synthesis and is a promising method for developing spectral computed tomography systems.

Deep learning-based virtual noncalcium imaging in multiple myeloma using dual-energy CT

BACKGROUND

Dual-energy CT with virtual noncalcium (VNCa) images allows the evaluation of focal intramedullary bone marrow involvement in patients with multiple myeloma. However, current commercial VNCa techniques suffer from excessive image noise and artifacts due to material decomposition used in synthesizing VNCa images.

OBJECTIVES

In this work, we aim to improve VNCa image quality for the assessment of focal multiple myeloma, using an Artificial intelligence based Generalizable Algorithm for mulTi-Energy CT (AGATE) method.

MATERIALS AND METHODS

AGATE method used a custom dual-task convolutional neural network (CNN) that concurrently carries out material classification and quantification. The material classification task provided an auxiliary regularization to the material quantification task. CNN parameters were optimized using custom loss functions that involved cross-entropy, physics-informed constraints, structural redundancy in spectral and material images, and texture information in spectral images. For training data, CT phantoms (diameters 30 to 45 cm) with tissue-mimicking inserts were scanned on a third generation dual-source CT system. Scans were performed at routine dose and half of the routine dose. Small image patches (i.e., 40 × 40 pixels) of tissue-mimicking inserts with known basis material densities were extracted for training samples. Numerically simulated insert materials with various shapes increased diversity of training samples. Generalizability of AGATE was evaluated using CT images from phantoms and patients. In phantoms, material decomposition accuracy was estimated using mean-absolute-percent-error (MAPE), using physical inserts that were not used during the training. Noise power spectrum (NPS) and modulation transfer function (MTF) were compared across phantom sizes and radiation dose levels. Five patients with multiple myeloma underwent dual-energy CT, with VNCa images generated using a commercial method and AGATE. Two fellowship-trained musculoskeletal radiologists reviewed the VNCa images (commercial and AGATE) side-by-side using a dual-monitor display, blinded to VNCa type, rating the image quality for focal multiple myeloma lesion visualization using a 5-level Likert comparison scale (-2 = worse visualization and diagnostic confidence, -1 = worse visualization but equivalent diagnostic confidence, 0 = equivalent visualization and diagnostic confidence, 1 = improved visualization but equivalent diagnostic confidence, 2 = improved visualization and diagnostic confidence). A post hoc assignment of comparison ratings was performed to rank AGATE images in comparison to commercial ones.

RESULTS

AGATE demonstrated consistent material quantification accuracy across phantom sizes and radiation dose levels, with MAPE ranging from 0.7% to 4.4% across all testing materials. Compared to commercial VNCa images, the AGATE-synthesized VNCa images yielded considerably lower image noise (50-77% noise reduction) without compromising noise texture or spatial resolution across different phantom sizes and two radiation doses. AGATE VNCa images had markedly reduced area under NPS curves and maintained NPS peak frequency (0.7 lp/cm to 1.0 lp/cm), with similar MTF curves (50% MTF at 3.0 lp/cm). In patients, AGATE demonstrated reduced image noise and artifacts with improved delineation of focal multiple myeloma lesions (all readers comparison scores indicating improved overall diagnostic image quality [scores 1 or 2]).

CONCLUSIONS

AGATE demonstrated reduced noise and artifacts in VNCa images and ability to improve visualization of bone marrow lesions for assessing multiple myeloma.

Framelet tensor sparsity with block matching for spectral CT reconstruction

PURPOSE

Spectral computed tomography (CT) based on the photon-counting detection system has the capability to produce energy-discriminative attenuation maps of objects with a single scan. However, the insufficiency of photons collected into the narrow energy bins results in high quantum noise levels causing low image quality. This work aims to improve spectral CT image quality by developing a novel regularization based on framelet tensor prior.

METHODS

First, similar patches are extracted from highly correlated inter-channel images in spectral and spatial domains, and stacked to form a third-order tensor after vectorization along the energy channels. Second, the framelet tensor nuclear norm (FTNN) is introduced and applied to construct the regularization to exploit the sparsity embedded in nonlocal similarity of spectral images, and thus the reconstruction problem is modeled as a constrained optimization. Third, an iterative algorithm is proposed by utilizing the alternating direction method of multipliers framework in which efficient solvers are developed for each subproblem.

RESULTS

Both numerical simulations and real data verifications were performed to evaluate and validate the proposed FTNN based method. Compared to the analytic, TV-based, and the state-of-the-art tensor-based methods, the proposed method achieves higher numerical accuracy on both reconstructed CT images and decomposed material maps in the mouse data indicating the capability in noise suppression and detail preservation of the proposed method.

CONCLUSIONS

A framelet tensor sparsity-based iterative algorithm is proposed for spectral reconstruction. The qualitative and quantitative comparisons show a promising improvement of image quality, indicating its promising potential in spectral CT imaging. This article is protected by copyright. All rights reserved.

Tensor Dictionary Learning with an Enhanced Sparsity Constraint for Sparse-View Spectral CT Reconstruction

Spectral computed tomography (CT) can divide collected photons into multi-energy channels and gain multi-channel projections synchronously by using photon-counting detectors. However, reconstructed images usually contain severe noise due to the limited number of photons in the corresponding energy channel. Tensor dictionary learning (TDL)-based methods have achieved better performance, but usually lose image edge information and details, especially from an under-sampling dataset. To address this problem, this paper proposes a method termed TDL with an enhanced sparsity constraint for spectral CT reconstruction. The proposed algorithm inherits the superiority of TDL by exploring the correlation of spectral CT images. Moreover, the method designs a regularization using the L0-norm of the image gradient to constrain images and the difference between images and a prior image in each energy channel simultaneously, further improving the ability to preserve edge information and subtle image details. The split-Bregman algorithm has been applied to address the proposed objective minimization model. Several numerical simulations and realistic preclinical mice are studied to assess the effectiveness of the proposed algorithm. The results demonstrate that the proposed method improves the quality of spectral CT images in terms of noise elimination, edge preservation, and image detail recovery compared to the several existing better methods.

Image-domain Material Decomposition for Spectral CT using a Generalized Dictionary Learning

The spectral computed tomography (CT) has huge advantages by providing accurate material information. Unfortunately, due to the instability or overdetermination of material decomposition model, the accuracy of material decomposition can be compromised in practice. Very recently, the dictionary learning based image-domain material decomposition (DLIMD) can obtain high accuracy for material decompositions from reconstructed spectral CT images. This method can explore the correlation of material components to some extent by training a unified dictionary from all material images. In addition, the dictionary learning based prior as a penalty is applied on material components independently, and many parameters would be carefully elaborated in practice. Because the concentration of contrast agent in clinical applications is low, it can result in data inconsistency for dictionary based representation during the iteration process. To avoid the aforementioned limitations and further improve the accuracy of materials, we first construct a generalized dictionary learning based image-domain material decomposition (GDLIMD) model. Then, the material tensor image is unfolded along the mode-1 to enhance the correlation of different materials. Finally, to avoid the data inconsistency of low iodine contrast, a normalization strategy is employed. Both physical phantom and tissue-synthetic phantom experiments demonstrate the proposed GDLIMD method outperforms the DLIMD and direct inversion (DI) methods.

Dictionary learning based image-domain material decomposition for spectral CT

The potential huge advantage of spectral computed tomography (CT) is that it can provide accurate material identification and quantitative tissue information by material decomposition. However, material decomposition is a typical inverse problem, where the noise can be magnified. To address this issue, we develop a dictionary learning based image-domain material decomposition (DLIMD) method for spectral CT to achieve accurate material components with better image quality. Specifically, a set of image patches are extracted from the mode-1 unfolding of normalized material images decomposed by direct inversion to train a unified dictionary using the K-SVD technique. Then, the DLIMD model is established to explore the redundant similarities of the material images, where the split-Bregman is employed to optimize the model. Finally, more constraints (i.e. volume conservation and the bounds of each pixel within material maps) are integrated into the DLIMD model. Numerical phantom, physical phantom and preclinical experiments are performed to evaluate the performance of the proposed DLIMD in material decomposition accuracy, material image edge preservation and feature recovery.

Deep-learning-based direct inversion for material decomposition

PURPOSE

To develop a convolutional neural network (CNN) that can directly estimate material density distribution from multi-energy computed tomography (CT) images without performing conventional material decomposition.

METHODS

The proposed CNN (denoted as Incept-net) followed the general framework of encoder-decoder network, with an assumption that local image information was sufficient for modeling the nonlinear physical process of multi-energy CT. Incept-net was implemented with a customized loss function, including an in-house-designed image-gradient-correlation (IGC) regularizer to improve edge preservation. The network consisted of two types of customized multibranch modules exploiting multiscale feature representation to improve the robustness over local image noise and artifacts. Inserts with various densities of different materials [hydroxyapatite (HA), iodine, a blood-iodine mixture, and fat] were scanned using a research photon-counting detector (PCD) CT with two energy thresholds and multiple radiation dose levels. The network was trained using phantom image patches only, and tested with different-configurations of full field-of-view phantom and in vivo porcine images. Furthermore, the nominal mass densities of insert materials were used as the labels in CNN training, which potentially provided an implicit mass conservation constraint. The Incept-net performance was evaluated in terms of image noise, detail preservation, and quantitative accuracy. Its performance was also compared to common material decomposition algorithms including least-square-based material decomposition (LS-MD), total-variation regularized material decomposition (TV-MD), and U-net-based method.

RESULTS

Incept-net improved accuracy of the predicted mass density of basis materials compared with the U-net, TV-MD, and LS-MD: the mean absolute error (MAE) of iodine was 0.66, 1.0, 1.33, and 1.57 mgI/cc for Incept-net, U-net, TV-MD, and LS-MD, respectively, across all iodine-present inserts (2.0-24.0 mgI/cc). With the LS-MD as the baseline, Incept-net and U-net achieved comparable noise reduction (both around 95%), both higher than TV-MD (85%). The proposed IGC regularizer effectively helped both Incept-net and U-net to reduce image artifact. Incept-net closely conserved the total mass densities (i.e., mass conservation constraint) in porcine images, which heuristically validated the quantitative accuracy of its outputs in anatomical background. In general, Incept-net performance was less dependent on radiation dose levels than the two conventional methods; with approximately 40% less parameters, the Incept-net achieved relatively improved performance than the comparator U-net, indicating that performance gain by Incept-net was not achieved by simply increasing network learning capacity.

CONCLUSION

Incept-net demonstrated superior qualitative image appearance, quantitative accuracy, and lower noise than the conventional methods and less sensitive to dose change. Incept-net generalized and performed well with unseen image structures and different material mass densities. This study provided preliminary evidence that the proposed CNN may be used to improve the material decomposition quality in multi-energy CT.

Locally linear transform based three-dimensional gradient L 0 -norm minimization for spectral CT reconstruction

PURPOSE

Spectral computed tomography (CT) is proposed by extending the conventional CT along the energy dimension. One newly implementation is to employ an energy-discriminating photon counting detector (PCD), which can distinguish photon energy and divide a whole x-ray spectrum into several energy bins with appropriate post-processing steps. The state-of-the-art PCD-based spectral CT has superior energy resolution and material distinguishability, and it further has a great potential in both medical and industrial applications. To improve the reconstruction quality and decomposition accuracy, in this work, we propose an optimization-based spectral CT reconstruction method with an innovational sparsity constraint.

METHODS

We first employ a locally linear transform to the reconstructed channel images, and the structural similarity along the spectral dimension is effectively converted to a one-dimensional (1D) gradient sparsity. Then, combining the prior knowledge of piecewise constant in the spatial domain (e.g., a two-dimensional (2D) gradient sparsity feature), we unify both spectral and spatial dimensions and establish a joint three-dimensional (3D) gradient sparsity. In addition, we use the L 0 -norm to measure the proposed sparsity and incorporate it as a smoothness constraint to concretize a general optimization framework. Furthermore, we develop the corresponding iterative algorithm to solve the optimization problem.

RESULTS

Both visual results and quantitative indexes of numerical simulations and phantom experiments demonstrate the proposed method outperform the conventional filtered backprojection (FBP), total variation (TV), 2D L₀ -norm (L₀ ), and TV with low rank (TVLR)-based methods. From the image and ROI comparisons, we find the proposed method performs well in noise suppression, detail maintenance, and decomposition accuracy. However, the FBP suffers severe noise, the TV and L₀ are difficult to work consistently among different energy bins, and the TVLR fails to avoid gray value shift. The image quality assessments, such as peak signal-to-noise ratio (PSNR), normal mean absolute deviation (NMAD). and structural similarity (SSIM), also consistently indicate the proposed method can effectively removing noise and keeping fine structures in both channel-wise reconstructions and material decompositions.

CONCLUSIONS

By employing a locally linear transform, the structural similarity among spectral channel images is converted to a 1D gradient sparsity and the gray value shift is effectively avoided when the difference measurement is minimized. The 3D L₀ -norm jointly and uniformly measures the gradient sparsity in both spectral and spatial dimensions. The cooperation of locally linear transform and 3D L₀ -norm well reinforces the global sparse features and keeps the correlation along spectral dimension without bringing gray-value distortions. The corresponding constraint optimization model is fast and stably solved by using an alternative direction technique. Both numerical simulations and phantom experiments confirm the superior performance of the proposed method in noise suppression, structure maintenance, and accurate decomposition.

Block matching frame based material reconstruction for spectral CT

Spectral computed tomography (CT) has a great potential in material identification and decomposition. To achieve high-quality material composition images and further suppress the x-ray beam hardening artifacts, we first propose a one-step material reconstruction model based on Taylor's first-order expansion. Then, we develop a basic material reconstruction method named material simultaneous algebraic reconstruction technique (MSART). Considering the local similarity of each material image, we incorporate a powerful block matching frame (BMF) into the material reconstruction (MR) model and generate a BMF based MR (BMFMR) method. Because the BMFMR model contains the L 0-norm problem, we adopt a split-Bregman method for optimization. The numerical simulation and physical phantom experiment results validate the correctness of the material reconstruction algorithms and demonstrate that the BMF regularization outperforms the total variation and no-local mean regularizations.

Image reconstruction by Mumford-Shah regularization for low-dose CT with multi-GPU acceleration

Mumford-Shah (MS) functional has emerged as a regularization technique in x-ray computed tomography (CT) recently. However, for high-resolution CT applications, the huge size of both projection data and image leads to an implementation difficulty. In this work, we propose an approach to implement and accelerate MS regularization on a multi-GPU platform to resolve the issue of data size and rich onboard memory and computing units. We have established a novel partition scheme of the 3D volume under reconstruction and corresponding multithread parallel acceleration strategy to fully utilize the computing resource of multi-GPUs. Our implementation is highly modularized and can be easily scaled with the configuration of GPUs. Experiment results with simulation data as well as real data demonstrate a superior reconstruction quality in contrast to the total variation regularization approach, especially for the ultra-low-dose case. Moreover, this is the first time that MS regularization is used for 3D reconstruction of huge images up to 3072³ voxels within 12 min.

Low-dose spectral CT reconstruction using image gradient ℓ 0-norm and tensor dictionary

Spectral computed tomography (CT) has a great superiority in lesion detection, tissue characterization and material decomposition. To further extend its potential clinical applications, in this work, we propose an improved tensor dictionary learning method for low-dose spectral CT reconstruction with a constraint of image gradient ℓ ₀-norm, which is named as ℓ ₀TDL. The ℓ ₀TDL method inherits the advantages of tensor dictionary learning (TDL) by employing the similarity of spectral CT images. On the other hand, by introducing the ℓ ₀-norm constraint in gradient image domain, the proposed method emphasizes the spatial sparsity to overcome the weakness of TDL on preserving edge information. The split-bregman method is employed to solve the proposed method. Both numerical simulations and real mouse studies are perform to evaluate the proposed method. The results show that the proposed ℓ ₀TDL method outperforms other competing methods, such as total variation (TV) minimization, TV with low rank (TV+LR), and TDL methods.

Spatial-Spectral Cube Matching Frame for Spectral CT Reconstruction

Spectral computed tomography (CT) reconstructs the same scanned object from projections of multiple narrow energy windows, and it can be used for material identification and decomposition. However, the multi-energy projection dataset has a lower signal-noise-ratio (SNR), resulting in poor reconstructed image quality. To address this thorny problem, we develop a spectral CT reconstruction method, namely spatial-spectral cube matching frame (SSCMF). This method is inspired by the following three facts: i) human body usually consists of two or three basic materials implying that the reconstructed spectral images have a strong sparsity; ii) the same basic material component in a single channel image has similar intensity and structures in local regions. Different material components within the same energy channel share similar structural information; iii) multi-energy projection datasets are collected from the subject by using different narrow energy windows, which means images reconstructed from different energy-channels share similar structures. To explore those information, we first establish a tensor cube matching frame (CMF) for a BM4D denoising procedure. Then, as a new regularizer, the CMF is introduced into a basic spectral CT reconstruction model, generating the SSCMF method. Because the SSCMF model contains an L0-norm minimization of 4D transform coefficients, an effective strategy is employed for optimization. Both numerical simulations and realistic preclinical mouse studies are performed. The results show that the SSCMF method outperforms the state-of-the-art algorithms, including the simultaneous algebraic reconstruction technique, total variation minimization, total variation plus low rank, and tensor dictionary learning.

Iterative spectral CT reconstruction based on low rank and average-image-incorporated BM3D

In a photon counting detector integrated spectral CT scanner, the received photons are counted in several energy channels to generate the corresponding projections. Since the projection in each energy channel is generated using part of the received photons, the reconstructed channel image suffers from severe noise. Therefore, image reconstruction in spectral CT is considered to be a big challenge. Because the inter-channel images are all from the same object but in different energy bins, there exists a strong correlation among these images. Moreover, it is suggested that there are similarities among various patches of CT images in the spatial domain. In this work, we propose average-image-incorporated block-matching and 3D (aiiBM3D) filtering along with low rank regularization for iterative spectral CT reconstruction. The aiiBM3D method is based on filtered 3D data arrays formed by similar 2D blocks using the mapped version of the average image obtained from linear regression. The reconstruction procedure consists of two main steps. First, the alternating direction method of multipliers is employed to solve the problem with low rank regularization where the goal is to exploit the correlation in inter-channel images. Second, our proposed BM3D-based algorithm is applied to all the channel images to make use of the redundant information in the spatial domain and inter-channel. The two steps repeat until the stopping criteria are satisfied. The proposed method is validated on numerically simulated and preclinical datasets. Our results confirm its high performance in terms of signal to noise ratio and structural preservation.