Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis-Representation Tensor Sparsity Regularization

Image-spectral decomposition extended-learning assisted by sparsity for multi-energy computed tomography reconstruction

Background

Multi-energy computed tomography (CT) provides multiple channel-wise reconstructed images, and they can be used for material identification and k-edge imaging. Nonetheless, the projection datasets are frequently corrupted by various noises (e.g., electronic, Poisson) in the acquisition process, resulting in lower signal-noise-ratio (SNR) measurements. Multi-energy CT images have local sparsity, nonlocal self-similarity in spatial dimension, and correlation in spectral dimension.

Methods

In this paper, we propose an image-spectral decomposition extended-learning assisted by sparsity (IDEAS) method to fully exploit these intrinsic priors for multi-energy CT image reconstruction. Particularly, a nonlocal low-rank Tucker decomposition (TD) is employed to utilize the correlation and nonlocal self-similarity priors. Moreover, considering the advantages of multi-task tensor dictionary learning (TDL) in sparse representation, an adaptive spatial dictionary and an adaptive spectral dictionary are trained during the iterative reconstruction process. Furthermore, a weighted total variation (TV) regularization term is employed to encourage local sparsity.

Results

Numerical simulation, physical phantom, and preclinical mouse experiments are performed to validate the proposed IDEAS algorithm. Specifically, in the simulation experiments, the proposed IDEAS reconstructed high-quality images that are very close to the references. For example, the root mean square error (RMSE) of IDEAS image in energy bin 1 is as low as 0.0672, while the RMSE of other methods are higher than 0.0843. Besides, the structural similarity (SSIM) of IDEAS reconstructed image in energy bin 1 is greater than 0.98. For material decomposition, the RMSE of IDEAS bone component is as low as 0.0152, and other methods are higher than 0.0199. In addition, the computational cost of IDEAS is as low as 98.8 s for one iteration, and the competing tensor decomposition method is higher than 327 s.

Conclusions

To further improve the quality of the reconstructed multi-energy CT images, multiple prior regularizations are introduced to the multi-energy CT reconstructed model, leading to an IDEAS method. Both qualitative and quantitative evaluation of our results confirm the outstanding performance of the proposed algorithm compared to the state-of-the-arts.

Spectral CT reconstruction via Spectral-Image Tensor and Bidirectional Image-gradient minimization

It is challenging to obtain good image quality in spectral computed tomography (CT) as the photon-number for the photon-counting detectors is limited for each narrow energy bin. This results in a lower signal to noise ratio (SNR) for the projections. To handle this issue, we first formulate the weight bidirectional image gradient with L₀-norm constraint of spectral CT image. Then, as a new regularizer, bidirectional image gradient with L₀-norm constraint is introduced into the tensor decomposition model, generating the Spectral-Image Tensor and Bidirectional Image-gradient Minimization (SITBIM) algorithm. Finally, the split-Bregman method is employed to optimize the proposed SITBIM mathematical model. The experiments on the numerical mouse phantom and real mouse experiments are designed to validate and evaluate the SITBIM method. The results demonstrate that the SITBIM can outperform other state-of-the-art methods (including TVM, TV + LR, SSCMF and NLCTF). INDEX TERMS: -spectral CT, image reconstruction, tensor decomposition, unidirectional image gradient, image similarity.

[Nonlocal low-rank and sparse matrix decomposition for low-dose cerebral perfusion CT image restoration]

OBJECTIVE

To present a nonlocal low-rank and sparse matrix decomposition (NLSMD) method for low-dose cerebral perfusion CT image restoration.

METHODS

Low-dose cerebral perfusion CT images were first partitioned into a matrix, and the low- rank and sparse matrix decomposition model was constructed to obtain high-quality low-dose cerebral perfusion CT images. The cerebral hemodynamic parameters were calculated from the restored high-quality CT images.

RESULTS

In the phantom study, the average structured similarity (SSIM) value of the sequential images obtained by filtered back-projection (FBP) algorithm was 0.9438, which was increased to 0.9765 using the proposed algorithm; the SSIM values of cerebral blood flow (CBF) and cerebral blood volume (CBV) map obtained by FBP algorithm were 0.7005 and 0.6856, respectively, which were increased using the proposed algorithm to 0.7871 and 0.7972, respectively.

CONCLUSION

The proposed method can effectively suppress noises in low-dose cerebral perfusion CT images to obtain accurate cerebral hemodynamic parameters.

Basis and current state of computed tomography perfusion imaging: a review

Computed tomography perfusion (CTP) is a functional imaging that allows for providing capillary-level hemodynamics information of the desired tissue in clinics. In this paper, we aim to offer insight into CTP imaging which covers the basics and current state of CTP imaging, then summarize the technical applications in the CTP imaging as well as the future technological potential. At first, we focus on the fundamentals of CTP imaging including systematically summarized CTP image acquisition and hemodynamic parameter map estimation techniques. A short assessment is presented to outline the clinical applications with CTP imaging, and then a review of radiation dose effect of the CTP imaging on the different applications is presented. We present a categorized methodology review on known and potential solvable challenges of radiation dose reduction in CTP imaging. To evaluate the quality of CTP images, we list various standardized performance metrics. Moreover, we present a review on the determination of infarct and penumbra. Finally, we reveal the popularity and future trend of CTP imaging.

Noise modelling of perfusion CT images for robust hemodynamic parameter estimations

Objective. The radiation dose of cerebral perfusion computed tomography (CPCT) imaging can be reduced by lowering the milliampere-second or kilovoltage peak. However, dose reduction can decrease image quality due to excessive x-ray quanta fluctuation and reduced detector signal relative to system electronic noise, thereby influencing the accuracy of hemodynamic parameters for patients with acute stroke. Existing low-dose CPCT denoising methods, which mainly focus on specific temporal and spatial prior knowledge in low-dose CPCT images, not take the noise distribution characteristics of low-dose CPCT images into consideration. In practice, the noise of low-dose CPCT images can be much more complicated. This study first investigates the noise properties in low-dose CPCT images and proposes a perfusion deconvolution model based on the noise properties. Approach. To characterize the noise distribution in CPCT images properly, we analyze noise properties in low-dose CPCT images and find that the intra-frame noise distribution may vary in the different areas and the inter-frame noise also may vary in low-dose CPCT images. Thus, we attempt the first-ever effort to model CPCT noise with a non-independent and identical distribution (i.i.d.) mixture-of-Gaussians (MoG) model for noise assumption. Furthermore, we integrate the noise modeling strategy into a perfusion deconvolution model and present a novel perfusion deconvolution method by using self-relative structural similarity information and MoG model (named as SR-MoG) to estimate the hemodynamic parameters accurately. In the presented SR-MoG method, the self-relative structural similarity information is obtained from preprocessed low-dose CPCT images. Main results. The results show that the presented SR-MoG method can achieve promising gains over the existing deconvolution approaches. In particular, the average root-mean-square error (RMSE) of cerebral blood flow (CBF), cerebral blood volume, and mean transit time was improved by 40.3%, 69.1%, and 40.8% in the digital phantom study, and the average RMSE of CBF can be improved by 81.0% in the clinical data study, compared with tensor total variation regularization deconvolution method. Significance. The presented SR-MoG method can estimate high-accuracy hemodynamic parameters andachieve promising gains over the existing deconvolution approaches.

Convex optimization algorithms in medical image reconstruction - in the age of AI

The past decade has seen the flourish of model based image reconstruction (MBIR) algorithms, which are often applications or adaptations of convex optimization algorithms from the optimization community. We review some state-of-the-art algorithms that have enjoyed wide popularity in medical image reconstruction, emphasize known connections between different algorithms, and discuss practical issues such as computation and memory cost. More recently, deep learning (DL) has forayed into medical imaging, where the latest development tries to exploit the synergy between DL and MBIR to elevate the MBIR's performance. We present existing approaches and emerging trends in DL-enhanced MBIR methods, with particular attention to the underlying role of convexity and convex algorithms on network architecture. We also discuss how convexity can be employed to improve the generalizability and representation power of DL networks in general.

Iterative reconstruction for low-dose cerebral perfusion computed tomography using prior image induced diffusion tensor

Cerebral perfusion computed tomography (CPCT) can depict the functional status of cerebral circulation at the tissue level; hence, it has been increasingly used to diagnose patients with cerebrovascular disease. However, there is a significant concern that CPCT scanning protocol could expose patients to excessive radiation doses. Although reducing the x-ray tube current when acquiring CPCT projection data is an effective method for reducing radiation dose, this technique usually results in degraded image quality. To enhance the image quality of low-dose CPCT, we present a prior image induced diffusion tensor (PIDT) for statistical iterative reconstruction, based on the penalized weighted least-squares (PWLS) criterion, which we referred to as PWLS-PIDT, for simplicity. Specifically, PIDT utilizes the geometric features of pre-contrast scanned high-quality CT image as a structure prior for PWLS reconstruction; therefore, the low-dose CPCT images are enhanced while preserving important features in the target image. An effective alternating minimization algorithm is developed to solve the associated objective function in the PWLS-PIDT reconstruction. We conduct qualitative and quantitative studies to evaluate the PWLS-PIDT reconstruction with a digital brain perfusion phantom and patient data. With this method, the noise in the reconstructed CPCT images is more substantially reduced than that of other competing methods, without sacrificing structural details significantly. Furthermore, the CPCT sequential images reconstructed via the PWLS-PIDT method can derive more accurate hemodynamic parameter maps than those of other competing methods.

Learning non-local perfusion textures for high-quality computed tomography perfusion imaging

Background. Computed tomography perfusion (CTP) imaging plays a critical role in the acute stroke syndrome assessment due to its widespread availability, speed of image acquisition, and relatively low cost. However, due to its repeated scanning protocol, CTP imaging involves a substantial radiation dose, which might increase potential cancer risks.Methods. In this work, we present a novel deep learning model called non-local perfusion texture learning network (NPTN) for high-quality CTP imaging at low-dose cases. Specifically, considering abundant similarities in the CTP images, i.e. latent self-similarities within the non-local region in the CTP images, we firstly search the most similar pixels from the adjacent frames within a fixed search window to obtain the non-local similarities and to construct non-local textures vector. Then, both the low-dose frame and these non-local textures from adjacent frames are fed into a convolution neural network to predict high-quality CTP images, which can help better characterize the structure details and contrast variants in the targeted CTP image rather than simply utilizing the targeted frame itself. The residual learning strategy and batch normalization are utilized to boost the performance of the convolution neural network. In the experiment, the CTP images of 31 patients with suspected stroke disease are collected to demonstrate the performance of the presented NPTN method.Results. The results show the presented NPTN method obtains superior performance compared with the competing methods. From numerical value, at all dose levels, the presented NPTN method has achieved around 3.0 dB improvement of average PSNR, an increase of around 1.4% of average SSIM, and a decrease of around 4.8% of average RMSE in the low-dose CTP reconstruction task, and also has achieved an increase of around 3.4% of average SSIM and a decrease of around 61.1% of average RMSE in the cerebral blood flow (CBF) estimation task.Conclusions. The presented NPTN method can obtain high-quality CTP images and estimate high-accuracy CBF map by characterizing more structure details and contrast variants in the CTP image and outperform the competing methods at low-dose cases.

Whole Brain Myelin Water Mapping in One Minute Using Tensor Dictionary Learning With Low-Rank Plus Sparse Regularization

The quantification of myelin water content in the brain can be obtained by the multi-echo [Formula: see text] weighted images ( [Formula: see text]WIs). To accelerate the long acquisition, a novel tensor dictionary learning algorithm with low-rank and sparse regularization (TDLLS) is proposed to reconstruct the [Formula: see text]WIs from the undersampled data. The proposed algorithm explores the local and nonlocal similarity and the global temporal redundancy in the real and imaginary parts of the complex relaxation signals. The joint application of the low-rank constraints on the dictionaries and the sparse constraints on the core coefficient tensors improves the performance of the tensor-based recovery. Parallel imaging is incorporated into the TDLLS algorithm (pTDLLS) for further acceleration. A pulse sequence is proposed to prospectively undersample the Ky-t space to obtain the whole brain high-quality myelin water fraction (MWF) maps within 1 minute at an undersampling rate (R) of 6.

Reconstruction of Optical Coherence Tomography Images Using Mixed Low Rank Approximation and Second Order Tensor Based Total Variation Method

This paper proposes a mixed low-rank approximation and second-order tensor-based total variation (LRSOTTV) approach for the super-resolution and denoising of retinal optical coherence tomography (OCT) images through effective utilization of nonlocal spatial correlations and local smoothness properties. OCT imaging relies on interferometry, which explains why OCT images suffer from a high level of noise. In addition, data subsampling is conducted during OCT A-scan and B-scan acquisition. Therefore, using effective super-resolution algorithms is necessary for reconstructing high-resolution clean OCT images. In this paper, a low-rank regularization approach is proposed for exploiting nonlocal self-similarity prior to OCT image reconstruction. To benefit from the advantages of the redundancy of multi-slice OCT data, we construct a third-order tensor by extracting the nonlocal similar three-dimensional blocks and grouping them by applying the k-nearest-neighbor method. Next, the nuclear norm is used as a regularization term to shrink the singular values of the constructed tensor in the non-local correlation direction. Further, the regularization approaches of the first-order tensor-based total variation (FOTTV) and SOTTV are proposed for better preservation of retinal layers and suppression of artifacts in OCT images. The alternative direction method of multipliers (ADMM) technique is then used to solve the resulting optimization problem. Our experiments show that integrating SOTTV instead of FOTTV into a low-rank approximation model can achieve noticeably improved results. Our experimental results on the denoising and super-resolution of OCT images demonstrate that the proposed model can provide images whose numerical and visual qualities are higher than those obtained by using state-of-the-art methods.

Multi-energy CT reconstruction using tensor nonlocal similarity and spatial sparsity regularization

Background

Multi-energy computed tomography (MECT) based on a photon-counting detector is an emerging imaging modality that collects projections at several energy bins with a single scan. However, the limited number of photons collected into the divided, narrow energy bins results in high quantum noise levels in reconstructed images. This study aims to improve MECT image quality by minimizing noise levels while retaining image details.

Methods

A novel MECT reconstruction method was proposed by exploiting the nonlocal tensor similarity among interchannel images and spatial sparsity in single-channel images. Similar patches were initially extracted from the interchannel images in spectral and spatial domains, then stacked into a new three-order tensor. Intrinsic tensor sparsity regularization that combined the Tuker and canonical polyadic (CP) low-rank decomposition techniques were applied to exploit the nonlocal similarity of the formulated tensor. Spatial sparsity in single-channel images was modeled by total variation (TV) regularization that utilizes the compressibility of gradient image. A new MECT reconstruction model was established by simultaneously incorporating the intrinsic tensor sparsity and TV regularizations. The iterative alternating minimization method was utilized to solve the reconstruction model based on a flexible framework.

Results

The proposed method was applied to the digital phantom and real mouse data to assess its feasibility and reliability. The reconstruction and decomposition results in the mouse data were encouraging and demonstrated the ability of the proposed method in noise suppression while preserving image details, not observed with other methods. Imaging data from the digital phantom illustrated this method as achieving the best intuitive reconstruction and decomposition results among all compared methods. They reduced the root mean square error (RMSE) by 89.75%, 50.75%, and 36.54% on the reconstructed images compared with analytic, TV-based, and tensor-based methods, respectively. This phenomenon was also observed with decomposition results, where the RMSE was also reduced by 97.96%, 67.74%, 72.05%, respectively.

Conclusions

In this study, we proposed a reconstruction method for photon counting detector-based MECT, using the intrinsic tensor sparsity and TV regularizations. Improvements in noise suppression and detail preservation in the digital phantom and real mouse data were validated by the qualitative and quantitative evaluations on the reconstruction and decomposition results, verifying the potential of the proposed method in MECT reconstruction.

Contrast-Medium Anisotropy-Aware Tensor Total Variation Model for Robust Cerebral Perfusion CT Reconstruction with Low-Dose Scans

Perfusion computed tomography (PCT) is critical in detecting cerebral ischemic lesions. PCT examination with low-dose scans can effectively reduce radiation exposure to patients at the cost of degraded images with severe noise and artifacts. Tensor total variation (TTV) models are powerful tools that can encode the regional continuous structures underlying a PCT object. In a TTV model, the sparsity structures of the contrast-medium concentration (CMC) across PCT frames are assumed to be isotropic with identical and independent distribution. However, this assumption is inconsistent with practical PCT tasks wherein the sparsity has evident variations and correlations. Such modeling deviation hampers the performance of TTV-based PCT reconstructions. To address this issue, we developed a novel contrast-medium anisotropy-aware tensor total variation (CMAA-TTV) model to describe the intrinsic anisotropy sparsity of the CMC in PCT imaging tasks. Instead of directly on the difference matrices, the CMAA-TTV model characterizes sparsity on a low-rank subspace of the difference matrices which are calculated from the input data adaptively, thus naturally encoding the intrinsic variant and correlated anisotropy sparsity structures of the CMC. We further proposed a robust and efficient PCT reconstruction algorithm to improve low-dose PCT reconstruction performance using the CMAA-TTV model. Experimental studies using a digital brain perfusion phantom, patient data with low-dose simulation and clinical patient data were performed to validate the effectiveness of the presented algorithm. The results demonstrate that the CMAA-TTV algorithm can achieve noticeable improvements over state-of-the-art methods in low-dose PCT reconstruction tasks.

VVBP-Tensor in the FBP Algorithm: Its Properties and Application in Low-Dose CT Reconstruction

For decades, commercial X-ray computed tomography (CT) scanners have been using the filtered backprojection (FBP) algorithm for image reconstruction. However, the desire for lower radiation doses has pushed the FBP algorithm to its limit. Previous studies have made significant efforts to improve the results of FBP through preprocessing the sinogram, modifying the ramp filter, or postprocessing the reconstructed images. In this paper, we focus on analyzing and processing the stacked view-by-view backprojections (named VVBP-Tensor) in the FBP algorithm. A key challenge for our analysis lies in the radial structures in each backprojection slice. To overcome this difficulty, a sorting operation was introduced to the VVBP-Tensor in its z direction (the direction of the projection views). The results show that, after sorting, the tensor contains structures that are similar to those of the object, and structures in different slices of the tensor are correlated. We then analyzed the properties of the VVBP-Tensor, including structural self-similarity, tensor sparsity, and noise statistics. Considering these properties, we have developed an algorithm using the tensor singular value decomposition (named VVBP-tSVD) to denoise the VVBP-Tensor for low-mAs CT imaging. Experiments were conducted using a physical phantom and clinical patient data with different mAs levels. The results demonstrate that the VVBP-tSVD is superior to all competing methods under different reconstruction schemes, including sinogram preprocessing, image postprocessing, and iterative reconstruction. We conclude that the VVBP-Tensor is a suitable processing target for improving the quality of FBP reconstruction, and the proposed VVBP-tSVD is an effective algorithm for noise reduction in low-mAs CT imaging. This preliminary work might provide a heuristic perspective for reviewing and rethinking the FBP algorithm.

Non-Local Low-Rank Cube-Based Tensor Factorization for Spectral CT Reconstruction

Spectral computed tomography (CT) reconstructs material-dependent attenuation images from the projections of multiple narrow energy windows, which is meaningful for material identification and decomposition. Unfortunately, the multi-energy projection datasets usually have lower signal-noise ratios (SNR). Very recently, a spatial-spectral cube matching frame (SSCMF) was proposed to explore the non-local spatial-spectral similarities for spectral CT. This method constructs a group by clustering up a series of non-local spatial-spectral cubes. The small size of spatial patches for such a group makes the SSCMF fail to fully encode the sparsity and low-rank properties. The hard-thresholding and collaboration filtering in the SSCMF also cause difficulty in recovering the image features and spatial edges. While all the steps are operated on 4-D group, the huge computational cost and memory load might not be affordable in practice. To avoid the above limitations and further improve the image quality, we first formulate a non-local cube-based tensor instead of group to encode the sparsity and low-rank properties. Then, as a new regularizer, the Kronecker-basis-representation tensor factorization is employed into a basic spectral CT reconstruction model to enhance the capability of image feature extraction and spatial edge preservation, generating a non-local low-rank cube-based tensor factorization (NLCTF) method. Finally, the split-Bregman method is adopted to solve the NLCTF model. Both numerical simulations and preclinical mouse studies are performed to validate and evaluate the NLCTF algorithm. The results show that the NLCTF method outperforms the other state-of-the-art competing algorithms.

Multi-energy computed tomography reconstruction using a nonlocal spectral similarity model

Multi-energy computed tomography (MECT) is able to acquire simultaneous multi-energy measurements from one scan. In addition, it allows material differentiation and quantification effectively. However, due to the limited energy bin width, the number of photons detected in an energy-specific channel is smaller than that in traditional CT, which results in image quality degradation. To address this issue, in this work, we develop a statistical iterative reconstruction algorithm to acquire high-quality MECT images and high-accuracy material-specific images. Specifically, this algorithm fully incorporates redundant self-similarities within nonlocal regions in the MECT image at one bin and rich spectral similarities among MECT images at all bins. For simplicity, the presented algorithm is referred to as 'MECT-NSS'. Moreover, an efficient optimization algorithm is developed to solve the MECT-NSS objective function. Then, a comprehensive evaluation of parameter selection for the MECT-NSS algorithm is conducted. In the experiment, the datasets include images from three phantoms and one patient to validate and evaluate the MECT-NSS reconstruction performance. The qualitative and quantitative results demonstrate that the presented MECT-NSS can successfully yield better MECT image quality and more accurate material estimation than the competing algorithms.

Statistical CT reconstruction using region-aware texture preserving regularization learning from prior normal-dose CT image

In some clinical applications, prior normal-dose CT (NdCT) images are available, and the valuable textures and structure features in them may be used to promote follow-up low-dose CT (LdCT) reconstruction. This study aims to learn texture information from the NdCT images and leverage it for follow-up LdCT image reconstruction to preserve textures and structure features. Specifically, the proposed reconstruction method first learns the texture information from those patches with similar structures in NdCT image, and the similar patches can be clustered by searching context features efficiently from the surroundings of the current patch. Then it utilizes redundant texture information from the similar patches as a priori knowledge to describe specific regions in the LdCT image. The advanced region-aware texture preserving prior is termed as 'RATP'. The main advantage of the PATP prior is that it can properly learn the texture features from available NdCT images and adaptively characterize the region-specific structures in the LdCT image. The experiments using patient data were performed to evaluate the performance of the proposed method. The proposed RATP method demonstrated superior performance in LdCT imaging compared to the filtered back projection (FBP) and statistical iterative reconstruction (SIR) methods using Gaussian regularization, Huber regularization and the original texture preserving regularization.

Iterative quality enhancement via residual-artifact learning networks for low-dose CT

Radiation exposure and the associated risk of cancer for patients in computed tomography (CT) scans have been major clinical concerns. The radiation exposure can be reduced effectively via lowering the x-ray tube current (mA). However, this strategy may lead to excessive noise and streak artifacts in the conventional filtered back-projection reconstructed images. To address this issue, some deep convolutional neural network (ConvNet) based approaches have been developed for low-dose CT imaging inspired by the recent development of machine learning. Nevertheless, some of the image textures reconstructed by the ConvNet could be corrupted by the severe streaks, especially in ultra-low-dose cases, which could be close to prostheses and hamper diagnosis. Therefore, in this work, we propose an iterative residual-artifact learning ConvNet (IRLNet) approach to improve the reconstruction performance over the ConvNet based approaches. Specifically, the proposed IRLNet estimates the high-frequency details within the noise and then removes them iteratively; after eliminating severe streaks in the low-dose CT images, the residual low-frequency details can be processed through the conventional network. Moreover, the proposed IRLNet scheme can be extended for robust handling of quantitative dual energy CT/cerebral perfusion CT imaging, and statistical iterative reconstruction. Real patient data are used to evaluate the proposed IRLNet, and the experimental results demonstrate that the proposed IRLNet approach outperforms the previous ConvNet based approaches in reducing the image noise and streak artifacts efficiently at the same time as preserving edge details well, suggesting that the proposed IRLNet approach can be used to improve the CT image quality, especially in ultra-low-dose cases.