Statistical interior tomography

Hybrid source translation scanning mode for interior tomography

Interior tomography is a promising technique that can be used to image large objects with high acquisition efficiency. However, it suffers from truncation artifacts and attenuation value bias due to the contribution from the parts of the object outside the ROI, which compromises its ability of quantitative evaluation in material or biological studies. In this paper, we present a hybrid source translation scanning mode for interior tomography, called hySTCT-where the projections inside the ROI and outside the ROI are finely sampled and coarsely sampled respectively to mitigate truncation artifacts and value bias within the ROI. Inspired by our previous work-virtual projection-based filtered backprojection (V-FBP) algorithm, we develop two reconstruction methods-interpolation V-FBP (iV-FBP) and two-step V-FBP (tV-FBP)-based on the linearity property of the inverse Radon transform for hySTCT reconstruction. The experiments demonstrate that the proposed strategy can effectively suppress truncated artifacts and improve the reconstruction accuracy within the ROI.

Statistical Interior Tomography via L1 Norm Dictionary Learning without Assuming an Object Support

Interior tomography of X-ray computed tomography (CT) has many advantages, such as a lower radiation dose and lower detector hardware cost compared to traditional CT. However, this imaging technique only uses the projection data passing through the region of interest (ROI) for imaging; accordingly, the projection data are truncated at both ends of the detector, so the traditional analytical reconstruction algorithm cannot satisfy the demand of clinical diagnosis. To solve the above limitations, in this paper we propose a high-quality statistical iterative reconstruction algorithm that uses the zeroth-order image moment as novel prior knowledge; the zeroth-order image moment can be estimated in the projection domain using the Helgason–Ludwig consistency condition. Then, the L1norm of sparse representation, in terms of dictionary learning, and the zeroth-order image moment constraints are incorporated into the statistical iterative reconstruction framework to construct an objective function. Finally, the objective function is minimized using an alternating minimization iterative algorithm. The chest CT image simulated and CT real data experimental results demonstrate that the proposed approach can remove shift artifacts effectively and has superior performance in removing noise and persevering fine structures than the total variation (TV)-based approach.

Data Extrapolation From Learned Prior Images for Truncation Correction in Computed Tomography

Data truncation is a common problem in computed tomography (CT). Truncation causes cupping artifacts inside the field-of-view (FOV) and anatomical structures missing outside the FOV. Deep learning has achieved impressive results in CT reconstruction from limited data. However, its robustness is still a concern for clinical applications. Although the image quality of learning-based compensation schemes may be inadequate for clinical diagnosis, they can provide prior information for more accurate extrapolation than conventional heuristic extrapolation methods. With extrapolated projection, a conventional image reconstruction algorithm can be applied to obtain a final reconstruction. In this work, a general plug-and-play (PnP) method for truncation correction is proposed based on this idea, where various deep learning methods and conventional reconstruction algorithms can be plugged in. Such a PnP method integrates data consistency for measured data and learned prior image information for truncated data. This shows to have better robustness and interpretability than deep learning only. To demonstrate the efficacy of the proposed PnP method, two state-of-the-art deep learning methods, FBPConvNet and Pix2pixGAN, are investigated for truncation correction in cone-beam CT in noise-free and noisy cases. Their robustness is evaluated by showing false negative and false positive lesion cases. With our proposed PnP method, false lesion structures are corrected for both deep learning methods. For FBPConvNet, the root-mean-square error (RMSE) inside the FOV can be improved from 92HU to around 30HU by PnP in the noisy case. Pix2pixGAN solely achieves better image quality than FBPConvNet solely for truncation correction in general. PnP further improves the RMSE inside the FOV from 42HU to around 27HU for Pix2pixGAN. The efficacy of PnP is also demonstrated on real clinical head data.

Spectral CT Reconstruction via Low-Rank Representation and Region-Specific Texture Preserving Markov Random Field Regularization

Photon-counting spectral computed tomography (CT) is capable of material characterization and can improve diagnostic performance over traditional clinical CT. However, it suffers from photon count starving for each individual energy channel which may cause severe artifacts in the reconstructed images. Furthermore, since the images in different energy channels describe the same object, there are high correlations among different channels. To make full use of the inter-channel correlations and minimize the count starving effect while maintaining clinically meaningful texture information, this paper combines a region-specific texture model with a low-rank correlation descriptor as an a priori regularization to explore a superior texture preserving Bayesian reconstruction of spectral CT. Specifically, the inter-channel correlations are characterized by the low-rank representation, and the inner-channel regional textures are modeled by a texture preserving Markov random field. In other words, this paper integrates the spectral and spatial information into a unified Bayesian reconstruction framework. The widely-used Split-Bregman algorithm is employed to minimize the objective function because of the non-differentiable property of the low-rank representation. To evaluate the tissue texture preserving performance of the proposed method for each channel, three references are built for comparison: one is the traditional CT image from energy integration detection. The second one is spectral images from dual-energy CT. The third one is individual channels images from custom-made photon-counting spectral CT. As expected, the proposed method produced promising results in terms of not only preserving texture features but also suppressing image noise in each channel, comparing to existing methods of total variation (TV), low-rank TV and tensor dictionary learning, by both visual inspection and quantitative indexes of root mean square error, peak signal to noise ratio, structural similarity and feature similarity.

Interior photon counting computed tomography for quantification of coronary artery calcium: pre-clinical phantom study

Computed tomography (CT) is the reference method for cardiac imaging, but concerns have been raised regarding the radiation dose of CT examinations. Recently, photon counting detectors (PCDs) and interior tomography, in which the radiation beam is limited to the organ-of-interest, have been suggested for patient dose reduction. In this study, we investigated interior PCD-CT (iPCD-CT) for non-enhanced quantification of coronary artery calcium (CAC) using an anthropomorphic torso phantom and ex vivo coronary artery samples. We reconstructed the iPCD-CT measurements with filtered back projection (FBP), iterative total variation (TV) regularization, padded FBP, and adaptively detruncated FBP and adaptively detruncated TV. We compared the organ doses between conventional CT and iPCD-CT geometries, assessed the truncation and cupping artifacts with iPCD-CT, and evaluated the CAC quantification performance of iPCD-CT. With approximately the same effective dose between conventional CT geometry (0.30 mSv) and interior PCD-CT with 10.2 cm field-of-view (0.27 mSv), the organ dose of the heart was increased by 52.3% with interior PCD-CT when compared to CT. Conversely, the organ doses to peripheral and radiosensitive organs, such as the stomach (55.0% reduction), were often reduced with interior PCD-CT. FBP and TV did not sufficiently reduce the truncation artifact, whereas padded FBP and adaptively detruncated FBP and TV yielded satisfactory truncation artifact reduction. Notably, the adaptive detruncation algorithm reduced truncation artifacts effectively when it was combined with reconstruction detrending. With this approach, the CAC quantification accuracy was good, and the coronary artery disease grade reclassification rate was particularly low (5.6%). Thus, our results confirm that CAC quantification can be performed with the interior CT geometry, that the artifacts are effectively reduced with suitable interior reconstruction methods, and that interior tomography provides efficient patient dose reduction.

A Soft-Threshold Filtering Approach for Tomography Reconstruction from a Limited Number of Projections with Bilateral Edge Preservation

In X-ray tomography image reconstruction, one of the most successful approaches involves a statistical approach with l2 norm for fidelity function and some regularization function with lp norm, 1<p<2. Among them stands out, both for its results and the computational performance, a technique that involves the alternating minimization of an objective function with l2 norm for fidelity and a regularization term that uses discrete gradient transform (DGT) sparse transformation minimized by total variation (TV). This work proposes an improvement to the reconstruction process by adding a bilateral edge-preserving (BEP) regularization term to the objective function. BEP is a noise reduction method and has the purpose of adaptively eliminating noise in the initial phase of reconstruction. The addition of BEP improves optimization of the fidelity term and, as a consequence, improves the result of DGT minimization by total variation. For reconstructions with a limited number of projections (low-dose reconstruction), the proposed method can achieve higher peak signal-to-noise ratio (PSNR) and structural similarity index measurement (SSIM) results because it can better control the noise in the initial processing phase.

K-edge-based interior tomography

Interior tomography reconstructs a region of interest using truncated projection data, but it is subject to the ill-posedness of interior tomography. With the photon-counting detector, K-edge imaging uses data in the low and high energy bins around the K-edge of a contrast agent, and can faithfully recover true image contrast for improved diagnosis. The purpose of this paper is to reconstruct a region of interest inside a patient assuming the existence of a known K-edge material. In this case, there is a significant difference in x-ray attenuation around the K-edge, but these attenuation coefficients are inter-related to guide updating an intermediate reconstruction until a stopping criterion is satisfied. In our study, new interior tomography algorithms were developed without any major computational overhead, and several phantoms were used to validate the algorithms. The proposed methods are advantageous relative to the existing interior tomography algorithms, because of the available spectral information in the form of a known K-edge material.

Adaptive non-local means on local principle neighborhood for noise/artifacts reduction in low-dose CT images

PURPOSE

Low-dose CT (LDCT) technique can reduce the x-ray radiation exposure to patients at the cost of degraded images with severe noise and artifacts. Non-local means (NLM) filtering has shown its potential in improving LDCT image quality. However, currently most NLM-based approaches employ a weighted average operation directly on all neighbor pixels with a fixed filtering parameter throughout the NLM filtering process, ignoring the non-stationary noise nature of LDCT images. In this paper, an adaptive NLM filtering scheme on local principle neighborhoods (PC-NLM) is proposed for structure-preserving noise/artifacts reduction in LDCT images.

METHODS

Instead of using neighboring patches directly, in the PC-NLM scheme, the principle component analysis (PCA) is first applied on local neighboring patches of the target patch to decompose the local patches into uncorrelated principle components (PCs), then a NLM filtering is used to regularize each PC of the target patch and finally the regularized components is transformed to get the target patch in image domain. Especially, in the NLM scheme, the filtering parameter is estimated adaptively from local noise level of the neighborhood as well as the signal-to-noise ratio (SNR) of the corresponding PC, which guarantees a "weaker" NLM filtering on PCs with higher SNR and a "stronger" filtering on PCs with lower SNR. The PC-NLM procedure is iteratively performed several times for better removal of the noise and artifacts, and an adaptive iteration strategy is developed to reduce the computational load by determining whether a patch should be processed or not in next round of the PC-NLM filtering.

RESULTS

The effectiveness of the presented PC-NLM algorithm is validated by experimental phantom studies and clinical studies. The results show that it can achieve promising gain over some state-of-the-art methods in terms of artifact suppression and structure preservation.

CONCLUSIONS

With the use of PCA on local neighborhoods to extract principal structural components, as well as adaptive NLM filtering on PCs of the target patch using filtering parameter estimated based on the local noise level and corresponding SNR, the proposed PC-NLM method shows its efficacy in preserving fine anatomical structures and suppressing noise/artifacts in LDCT images.

Optimization-based region-of-interest reconstruction for X-ray computed tomography based on total variation and data derivative

Region-of-interest (ROI) and interior reconstructions for computed tomography (CT) have drawn much attention and can be of practical value for potential applications in reducing radiation dose and hardware cost. The conventional wisdom is that the exact reconstruction of an interior ROI is very difficult to be obtained by only using data associated with lines through the ROI. In this study, we propose and investigate optimization-based methods for ROI and interior reconstructions based on total variation (TV) and data derivative. Objective functions are built by the image TV term plus the data finite difference term. Different data terms in the forms of L1-norm, L2-norm, and Kullback-Leibler divergence are incorporated and investigated in the optimizations. Efficient algorithms are developed using the proximal alternating direction method of multipliers (ADMM) for each program. All sub-problems of ADMM are solved by using closed-form solutions with high efficiency. The customized optimizations and algorithms based on the TV and derivative-based data terms can serve as a powerful tool for interior reconstructions. Simulations and real-data experiments indicate that the proposed methods can be of practical value for CT imaging applications.

Low dose CT reconstruction via L1 norm dictionary learning using alternating minimization algorithm and balancing principle

Excessive radiation exposure in computed tomography (CT) scans increases the chance of developing cancer and has become a major clinical concern. Recently, statistical iterative reconstruction (SIR) with l0-norm dictionary learning regularization has been developed to reconstruct CT images from the low dose and few-view dataset in order to reduce radiation dose. Nonetheless, the sparse regularization term adopted in this approach is l0-norm, which cannot guarantee the global convergence of the proposed algorithm. To address this problem, in this study we introduced the l1-norm dictionary learning penalty into SIR framework for low dose CT image reconstruction, and developed an alternating minimization algorithm to minimize the associated objective function, which transforms CT image reconstruction problem into a sparse coding subproblem and an image updating subproblem. During the image updating process, an efficient model function approach based on balancing principle is applied to choose the regularization parameters. The proposed alternating minimization algorithm was evaluated first using real projection data of a sheep lung CT perfusion and then using numerical simulation based on sheep lung CT image and chest image. Both visual assessment and quantitative comparison using terms of root mean square error (RMSE) and structural similarity (SSIM) index demonstrated that the new image reconstruction algorithm yielded similar performance with l0-norm dictionary learning penalty and outperformed the conventional filtered backprojection (FBP) and total variation (TV) minimization algorithms.

Quest for the ultimate cardiac CT scanner

PURPOSE

To quantitatively evaluate and compare six proposed system architectures for cardiac CT scanning.

METHODS

Starting from the clinical requirements for cardiac CT, we defined six dedicated cardiac CT architectures. We selected these architectures based on a previous screening study and defined them in sufficient detail to comprehensively analyze their cost and performance. We developed rigorous comparative evaluation methods for the most important aspects of performance and cost, and we applied these evaluation criteria to the defined cardiac CT architectures.

RESULTS

We found that CT system architectures based on the third-generation geometry provide nearly linear performance improvement versus the increased cost of additional beam lines (i.e., source-detector pairs), although similar performance improvement could be achieved with advanced motion-correction algorithms. The third-generation architectures outperform even the most promising of the proposed architectures that deviate substantially from the traditional CT system architectures.

CONCLUSION

This work confirms the validity of the current trend in commercial CT scanner design. However, we anticipate that over time, CT hardware and software technologies will evolve, the relative importance of the performance criteria will change, the relative costs of components will vary, some of the remaining challenges will be addressed, and perhaps new candidate architectures will be identified; therefore, the conclusion of a comparative analysis like this may change. The evaluation methods that we used can provide a framework for other researchers to analyze their own proposed CT architectures.

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

Low-dose CT via convolutional neural network

In order to reduce the potential radiation risk, low-dose CT has attracted an increasing attention. However, simply lowering the radiation dose will significantly degrade the image quality. In this paper, we propose a new noise reduction method for low-dose CT via deep learning without accessing original projection data. A deep convolutional neural network is here used to map low-dose CT images towards its corresponding normal-dose counterparts in a patch-by-patch fashion. Qualitative results demonstrate a great potential of the proposed method on artifact reduction and structure preservation. In terms of the quantitative metrics, the proposed method has showed a substantial improvement on PSNR, RMSE and SSIM than the competing state-of-art methods. Furthermore, the speed of our method is one order of magnitude faster than the iterative reconstruction and patch-based image denoising methods.

Interior tomography with curvelet-based regularization

The interior problem, i.e. reconstruction from local truncated projections in computed tomography (CT), is common in practical applications. However, its solution is non-unique in a general unconstrained setting. To solve the interior problem uniquely and stably, in recent years both the prior knowledge- and compressive sensing (CS)-based methods have been developed. Those theoretically exact solutions for the interior problem are called interior tomography. Along this direction, we propose here a new CS-based method for the interior problem based on the curvelet transform. A curvelet is localized in both radial and angular directions in the frequency domain. A two-dimensional (2D) image can be represented in a curvelet frame. We employ the curvelet transform coefficients to regularize the interior problem and obtain a curvelet frame based regularization method (CFRM) for interior tomography. The curvelet coefficients of the reconstructed image are split into two sets according to their visibility from the interior data, and different regularization parameters are used for these two sets. We also presents the results of numerical experiments, which demonstrate the feasibility of the proposed approach.

Fast iterative reconstruction of data in full interior tomography

This paper introduces two novel strategies for iterative reconstruction of full interior tomography (FINT) data, i.e. when the field of view is entirely inside the object support and knowledge of the object support itself or the attenuation coefficients inside specific regions of interest are not available. The first approach is based on data edge-padding. The second technique creates an intermediate virtual sinogram, which is, then, reconstructed by a standard iterative algorithm. Both strategies are validated in the framework of the alternate direction method of multipliers plug-and-play with gridding projectors that provide a speed-up of three orders of magnitude with respect to standard operators implemented in real space. The proposed methods are benchmarked on synchrotron-based X-ray tomographic microscopy datasets of mouse lung alveoli. Compared with analytical techniques, the proposed methods substantially improve the reconstruction quality for FINT underconstrained datasets, facilitating subsequent post-processing steps.

An adaptive reconstruction algorithm for spectral CT regularized by a reference image

The photon counting detector based spectral CT system is attracting increasing attention in the CT field. However, the spectral CT is still premature in terms of both hardware and software. To reconstruct high quality spectral images from low-dose projections, an adaptive image reconstruction algorithm is proposed that assumes a known reference image (RI). The idea is motivated by the fact that the reconstructed images from different spectral channels are highly correlated. If a high quality image of the same object is known, it can be used to improve the low-dose reconstruction of each individual channel. This is implemented by maximizing the patch-wise correlation between the object image and the RI. Extensive numerical simulations and preclinical mouse study demonstrate the feasibility and merits of the proposed algorithm. It also performs well for truncated local projections, and the surrounding area of the region- of-interest (ROI) can be more accurately reconstructed. Furthermore, a method is introduced to adaptively choose the step length, making the algorithm more feasible and easier for applications.

A two-step filtering-based iterative image reconstruction method for interior tomography

The optimization-based method that utilizes the additional sparse prior of region-of-interest (ROI) image, such as total variation, has been the subject of considerable research in problems of interior tomography reconstruction. One challenge for optimization-based iterative ROI image reconstruction is to build the relationship between ROI image and truncated projection data. When the reconstruction support region is smaller than the original object, an unsuitable representation of data fidelity may lead to bright truncation artifacts in the boundary region of field of view. In this work, we aim to develop an iterative reconstruction method to suppress the truncation artifacts and improve the image quality for direct ROI image reconstruction. A novel reconstruction approach is proposed based on an optimization problem involving a two-step filtering-based data fidelity. Data filtering is achieved in two steps: the first takes the derivative of projection data; in the second step, Hilbert filtering is applied in the differentiated data. Numerical simulations and real data reconstructions have been conducted to validate the new reconstruction method. Both qualitative and quantitative results indicate that, as theoretically expected, the proposed method brings reasonable performance in suppressing truncation artifacts and preserving detailed features. The presented local reconstruction method based on the two-step filtering strategy provides a simple and efficient approach for the iterative reconstruction from truncated projections.

Interior tomographic imaging of mouse heart in a carbon nanotube micro-CT

BACKGROUND

The relatively high radiation dose from micro-CT is a cause for concern in preclinical research involving animal subjects. Interior region-of-interest (ROI) imaging was proposed for dose reduction, but has not been experimentally applied in micro-CT.

OBJECTIVE

Our aim is to implement interior ROI imaging in a carbon nanotube (CNT) x-ray source based micro-CT, and present the ROI image quality and radiation dose reduction for interior cardiac micro-CT imaging of a mouse heart in situ.

METHODS

An aperture collimator was mounted at the source-side to induce a small-sized cone beam (10 mm width) at the isocenter. Interior in situ micro-CT scans were conducted on a mouse carcass and several micro-CT phantoms. A GPU-accelerated hybrid iterative reconstruction algorithm was employed for volumetric image reconstruction. Radiation dose was measured for the same system operated at the interior and global micro-CT modes.

RESULTS

Visual inspection demonstrated comparable image quality between two scan modes. Quantitative evaluation demonstrated high structural similarity index (up to 0.9614) with improved contrast-noise-ratio (CNR) on interior micro-CT mode. Interior micro-CT mode yielded significant reduction (up to 83.9%) for dose length product (DLP).

CONCLUSIONS

This work demonstrates the applicability of using CNT x-ray source based interior micro-CT for preclinical imaging with significantly reduced radiation dose.

Statistical iterative reconstruction using adaptive fractional order regularization

In order to reduce the radiation dose of the X-ray computed tomography (CT), low-dose CT has drawn much attention in both clinical and industrial fields. A fractional order model based on statistical iterative reconstruction framework was proposed in this study. To further enhance the performance of the proposed model, an adaptive order selection strategy, determining the fractional order pixel-by-pixel, was given. Experiments, including numerical and clinical cases, illustrated better results than several existing methods, especially, in structure and texture preservation.

Recovery of CT stroke hypodensity--An adaptive variational approach

The present research was directed to effective image restoration with the extraction of ischemic edema signs. Computerized support of hyperacute stroke diagnosis based on routinely used computerized tomography (CT) scans was optimized to visualize the infarct extent more precisely. In particular, a beneficial support of time-limited appropriate decision of whether to treat the patient by thrombolysis is expected. Because of a limited accuracy in determining the area of core infarction, particularly in the early hours of symptoms' onset, a variational approach to sensed data recovery was applied. Proposed methodology adjusts fidelity norms and regularization priors integrated with simulated sensing procedures in a compressed sensing framework. Experimental study confirmed almost perfect recognition of ischemic stroke in a test set of over 500 CT scans.

Tensor-based dictionary learning for dynamic tomographic reconstruction

In dynamic computed tomography (CT) reconstruction, the data acquisition speed limits the spatio-temporal resolution. Recently, compressed sensing theory has been instrumental in improving CT reconstruction from far few-view projections. In this paper, we present an adaptive method to train a tensor-based spatio-temporal dictionary for sparse representation of an image sequence during the reconstruction process. The correlations among atoms and across phases are considered to capture the characteristics of an object. The reconstruction problem is solved by the alternating direction method of multipliers. To recover fine or sharp structures such as edges, the nonlocal total variation is incorporated into the algorithmic framework. Preclinical examples including a sheep lung perfusion study and a dynamic mouse cardiac imaging demonstrate that the proposed approach outperforms the vectorized dictionary-based CT reconstruction in the case of few-view reconstruction.

Median prior constrained TV algorithm for sparse view low-dose CT reconstruction

It is known that lowering the X-ray tube current (mAs) or tube voltage (kVp) and simultaneously reducing the total number of X-ray views (sparse view) is an effective means to achieve low-dose in computed tomography (CT) scan. However, the associated image quality by the conventional filtered back-projection (FBP) usually degrades due to the excessive quantum noise. Although sparse-view CT reconstruction algorithm via total variation (TV), in the scanning protocol of reducing X-ray tube current, has been demonstrated to be able to result in significant radiation dose reduction while maintain image quality, noticeable patchy artifacts still exist in reconstructed images. In this study, to address the problem of patchy artifacts, we proposed a median prior constrained TV regularization to retain the image quality by introducing an auxiliary vector m in register with the object. Specifically, the approximate action of m is to draw, in each iteration, an object voxel toward its own local median, aiming to improve low-dose image quality with sparse-view projection measurements. Subsequently, an alternating optimization algorithm is adopted to optimize the associative objective function. We refer to the median prior constrained TV regularization as "TV_MP" for simplicity. Experimental results on digital phantoms and clinical phantom demonstrated that the proposed TV_MP with appropriate control parameters can not only ensure a higher signal to noise ratio (SNR) of the reconstructed image, but also its resolution compared with the original TV method.

Interior micro-CT with an offset detector

PURPOSE

The size of field-of-view (FOV) of a microcomputed tomography (CT) system can be increased by offsetting the detector. The increased FOV is beneficial in many applications. All prior investigations, however, have been focused to the case in which the increased FOV after offset-detector acquisition can cover the transaxial extent of an object fully. Here, the authors studied a new problem where the FOV of a micro-CT system, although increased after offset-detector acquisition, still covers an interior region-of-interest (ROI) within the object.

METHODS

An interior-ROI-oriented micro-CT scan with an offset detector poses a difficult reconstruction problem, which is caused by both detector offset and projection truncation. Using the projection completion techniques, the authors first extended three previous reconstruction methods from offset-detector micro-CT to offset-detector interior micro-CT. The authors then proposed a novel method which combines two of the extended methods using a frequency split technique. The authors tested the four methods with phantom simulations at 9.4%, 18.8%, 28.2%, and 37.6% detector offset. The authors also applied these methods to physical phantom datasets acquired at the same amounts of detector offset from a customized micro-CT system.

RESULTS

When the detector offset was small, all reconstruction methods showed good image quality. At large detector offset, the three extended methods gave either visible shading artifacts or high deviation of pixel value, while the authors' proposed method demonstrated no visible artifacts and minimal deviation of pixel value in both the numerical simulations and physical experiments.

CONCLUSIONS

For an interior micro-CT with an offset detector, the three extended reconstruction methods can perform well at a small detector offset but show strong artifacts at a large detector offset. When the detector offset is large, the authors' proposed reconstruction method can outperform the three extended reconstruction methods by suppressing artifacts and maintaining pixel values.

Hybrid spectral micro-CT: system design, implementation, and preliminary results

Spectral CT has proven an important development in biomedical imaging, and there have been several publications in the past years demonstrating its merits in pre-clinical and clinical applications. In 2012, Xu reported that near-term implementation of spectral micro-CT could be enhanced by a hybrid architecture: a narrow-beam spectral “interior” imaging chain integrated with a traditional wide-beam “global” imaging chain. This hybrid integration coupled with compressive sensing (CS)-based interior tomography demonstrated promising results for improved contrast resolution, and decreased system cost and radiation dose. The motivation for the current study is implementation and evaluation of the hybrid architecture with a first-of-its-kind hybrid spectral micro-CT system. Preliminary results confirm improvements in both contrast and spatial resolution. This technology is shown to merit further investigation and potential application in future spectral CT scanner design.

Study of scan protocol for exposure reduction in hybrid spectral micro-CT

The hybrid spectral micro-computed tomography (CT) architecture integrates a conventional imaging chain and an interior spectral imaging chain, and has been proven to be an important development in spectral CT. The motivation for this study is to minimize X-ray exposure for hybrid spectral micro-CT using both simulated and experimental scan data while maintaining the spectral fidelity of the reconstruction. Three elements of the hybrid scan protocol are investigated: truncation of the interior spectral chain and the numbers of projections for each of the global and interior imaging chains. The effect of these elements is quantified by analyzing how each affects the reconstructed spectral accuracy. The results demonstrate that there is significant scope for reduction of radiation exposure in the hybrid scan protocol. It appears decreasing the number of conventional projections offers the most potential for exposure reduction, while further reduction is possible by decreasing the interior FOV and number of spectral projections.

Radial differential interior tomography and its image reconstruction with differentiated backprojection and projection onto convex sets

PURPOSE

Interior tomography has been recognized as one of the most effective approaches in computed tomography (CT) to reduce radiation dose rendered to patients. In this work, the authors propose and evaluate an imaging method of radial differential interior tomography.

METHODS

In interior tomography, an x-ray beam is collimated to only irradiate the region of interest (ROI) with suspected lesions while the surrounding area∕volume of normal tissues∕organs is spared. In the proposed imaging method of radial differential interior tomography, the outcome is a ROI image that has gone through a radial differential filtering. The image reconstruction algorithm for the radial differential interior tomography is kept in the fashion of differentiated backprojection and projection onto convex sets, but the required a priori knowledge in a small round area becomes zero and may be more readily available in practice.

RESULTS

Using the projection data simulated by computer and acquired by CT scanner, the authors evaluate and verify the performance of the proposed radial differential interior tomography method and its associated image reconstruction algorithm. The preliminary results show that the proposed imaging method can generate an image that is the radial differentiation of a conventional tomographic image and is robust over noise that inevitably exist in practice.

CONCLUSIONS

It is believed that the proposed imaging method may find its utility in advanced clinical applications wherein a ROI-based image processing and analysis is required for lesion visualization, characterization, and diagnosis.

Conceptual design and simulation study of an ROI-focused panel-PET scanner

Positron emission tomography (PET) is an important imaging modality for clincial use. Conventionally, the PET scanner is generally built to provide a roomy enough transverse field-of-view (FOV) for imaging most adults’ torsos. However, in many cases, the region-of-interest (ROI) for imaging is usually a small area inside the human body. Therefore, to fulfill a PET system which provides an FOV comparable in size to the target ROI seems appealing and more cost effective. Meanwhile, such a PET system has the potential for portable or bedside application with the reduced system size. In this work, we have investigated the feasibility of using dual-headed panel-detectors to build an ROI-focused PET scanner. A novel windowed list-mode ordered subset expectation maximization method was developed to perform the ROI image reconstruction. With this method, the ROI of the object can be reconstructed from the coincidences whose position determined by time-of-flight (TOF) measurements was inside the ROI. Monte Carlo simulation demonstrates the feasibility of detecting lesions not less than 1 cm in diameter, with a 300 ps full width at half maximum timing resolution. As a critical system performance, the impact of TOF information on image quality has been studied and the required TOF capability was assessed. With enhanced timing resolution, the distortions and artifacts were reduced effectively. The further improved TOF capability also shows a noticeable improvement of detection performance for low uptake lesions, as well as the recovery speed of lesion contrast, which is of practical significance in the lesion detection task.

The meaning of interior tomography

The classic imaging geometry for computed tomography is for the collection of un-truncated projections and the reconstruction of a global image, with the Fourier transform as the theoretical foundation that is intrinsically non-local. Recently, interior tomography research has led to theoretically exact relationships between localities in the projection and image spaces and practically promising reconstruction algorithms. Initially, interior tomography was developed for x-ray computed tomography. Then, it was elevated to have the status of a general imaging principle. Finally, a novel framework known as 'omni-tomography' is being developed for a grand fusion of multiple imaging modalities, allowing tomographic synchrony of diversified features.

Image reconstruction for sparse-view CT and interior CT-introduction to compressed sensing and differentiated backprojection

New designs of future computed tomography (CT) scanners called sparse-view CT and interior CT have been considered in the CT community. Since these CTs measure only incomplete projection data, a key to put these CT scanners to practical use is a development of advanced image reconstruction methods. After 2000, there was a large progress in this research area briefly summarized as follows. In the sparse-view CT, various image reconstruction methods using the compressed sensing (CS) framework have been developed towards reconstructing clinically feasible images from a reduced number of projection data. In the interior CT, several novel theoretical results on solution uniqueness and solution stability have been obtained thanks to the discovery of a new class of reconstruction methods called differentiated backprojection (DBP). In this paper, we mainly review this progress including mathematical principles of the CS image reconstruction and the DBP image reconstruction for readers unfamiliar with this area. We also show some experimental results from our past research to demonstrate that this progress is not only theoretically elegant but also works in practical imaging situations.

Piecewise-constant-model-based interior tomography applied to dentin tubules

Dentin is a hierarchically structured biomineralized composite material, and dentin's tubules are difficult to study in situ. Nano-CT provides the requisite resolution, but the field of view typically contains only a few tubules. Using a plate-like specimen allows reconstruction of a volume containing specific tubules from a number of truncated projections typically collected over an angular range of about 140°, which is practically accessible. Classical computed tomography (CT) theory cannot exactly reconstruct an object only from truncated projections, needless to say a limited angular range. Recently, interior tomography was developed to reconstruct a region-of-interest (ROI) from truncated data in a theoretically exact fashion via the total variation (TV) minimization under the condition that the ROI is piecewise constant. In this paper, we employ a TV minimization interior tomography algorithm to reconstruct interior microstructures in dentin from truncated projections over a limited angular range. Compared to the filtered backprojection (FBP) reconstruction, our reconstruction method reduces noise and suppresses artifacts. Volume rendering confirms the merits of our method in terms of preserving the interior microstructure of the dentin specimen.

Medipix-based Spectral Micro-CT

Since Hounsfield's Nobel Prize winning breakthrough decades ago, X-ray CT has been widely applied in the clinical and preclinical applications - producing a huge number of tomographic gray-scale images. However, these images are often insufficient to distinguish crucial differences needed for diagnosis. They have poor soft tissue contrast due to inherent photon-count issues, involving high radiation dose. By physics, the X-ray spectrum is polychromatic, and it is now feasible to obtain multi-energy, spectral, or true-color, CT images. Such spectral images promise powerful new diagnostic information. The emerging Medipix technology promises energy-sensitive, high-resolution, accurate and rapid X-ray detection. In this paper, we will review the recent progress of Medipix-based spectral micro-CT with the emphasis on the results obtained by our team. It includes the state- of-the-art Medipix detector, the system and method of a commercial MARS (Medipix All Resolution System) spectral micro-CT, and the design and color diffusion of a hybrid spectral micro-CT.

Interior tomography with continuous singular value decomposition

The long-standing interior problem has important mathematical and practical implications. The recently developed interior tomography methods have produced encouraging results. A particular scenario for theoretically exact interior reconstruction from truncated projections is that there is a known sub-region in the ROI. In this paper, we improve a novel continuous singular value decomposition (SVD) method for interior reconstruction assuming a known sub-region. First, two sets of orthogonal eigen-functions are calculated for the Hilbert and image spaces respectively. Then, after the interior Hilbert data are calculated from projection data through the ROI, they are projected onto the eigen-functions in the Hilbert space, and an interior image is recovered by a linear combination of the eigen-functions with the resulting coefficients. Finally, the interior image is compensated for the ambiguity due to the null space utilizing the prior sub-region knowledge. Experiments with simulated and real data demonstrate the advantages of our approach relative to the POCS type interior reconstructions.

Low-dose X-ray CT reconstruction via dictionary learning

Although diagnostic medical imaging provides enormous benefits in the early detection and accuracy diagnosis of various diseases, there are growing concerns on the potential side effect of radiation induced genetic, cancerous and other diseases. How to reduce radiation dose while maintaining the diagnostic performance is a major challenge in the computed tomography (CT) field. Inspired by the compressive sensing theory, the sparse constraint in terms of total variation (TV) minimization has already led to promising results for low-dose CT reconstruction. Compared to the discrete gradient transform used in the TV method, dictionary learning is proven to be an effective way for sparse representation. On the other hand, it is important to consider the statistical property of projection data in the low-dose CT case. Recently, we have developed a dictionary learning based approach for low-dose X-ray CT. In this paper, we present this method in detail and evaluate it in experiments. In our method, the sparse constraint in terms of a redundant dictionary is incorporated into an objective function in a statistical iterative reconstruction framework. The dictionary can be either predetermined before an image reconstruction task or adaptively defined during the reconstruction process. An alternating minimization scheme is developed to minimize the objective function. Our approach is evaluated with low-dose X-ray projections collected in animal and human CT studies, and the improvement associated with dictionary learning is quantified relative to filtered backprojection and TV-based reconstructions. The results show that the proposed approach might produce better images with lower noise and more detailed structural features in our selected cases. However, there is no proof that this is true for all kinds of structures.

Volume-of-change cone-beam CT for image-guided surgery

C-arm cone-beam CT (CBCT) can provide intraoperative 3D imaging capability for surgical guidance, but workflow and radiation dose are the significant barriers to broad utilization. One main reason is that each 3D image acquisition requires a complete scan with a full radiation dose to present a completely new 3D image every time. In this paper, we propose to utilize patient-specific CT or CBCT as prior knowledge to accurately reconstruct the aspects of the region that have changed by the surgical procedure from only a sparse set of x-rays. The proposed methods consist of a 3D-2D registration between the prior volume and a sparse set of intraoperative x-rays, creating digitally reconstructed radiographs (DRRs) from the registered prior volume, computing difference images by subtracting DRRs from the intraoperative x-rays, a penalized likelihood reconstruction of the volume of change (VOC) from the difference images, and finally a fusion of VOC reconstruction with the prior volume to visualize the entire surgical field. When the surgical changes are local and relatively small, the VOC reconstruction involves only a small volume size and a small number of projections, allowing less computation and lower radiation dose than is needed to reconstruct the entire surgical field. We applied this approach to sacroplasty phantom data obtained from a CBCT test bench and vertebroplasty data with a fresh cadaver acquired from a C-arm CBCT system with a flat-panel detector. The VOCs were reconstructed from a varying number of images (10-66 images) and compared to the CBCT ground truth using four different metrics (mean squared error, correlation coefficient, structural similarity index and perceptual difference model). The results show promising reconstruction quality with structural similarity to the ground truth close to 1 even when only 15-20 images were used, allowing dose reduction by the factor of 10-20.

Image reconstruction for hybrid true-color micro-CT

X-ray micro-CT is an important imaging tool for biomedical researchers. Our group has recently proposed a hybrid "true-color" micro-CT system to improve contrast resolution with lower system cost and radiation dose. The system incorporates an energy-resolved photon-counting true-color detector into a conventional micro-CT configuration, and can be used for material decomposition. In this paper, we demonstrate an interior color-CT image reconstruction algorithm developed for this hybrid true-color micro-CT system. A compressive sensing-based statistical interior tomography method is employed to reconstruct each channel in the local spectral imaging chain, where the reconstructed global gray-scale image from the conventional imaging chain served as the initial guess. Principal component analysis was used to map the spectral reconstructions into the color space. The proposed algorithm was evaluated by numerical simulations, physical phantom experiments, and animal studies. The results confirm the merits of the proposed algorithm, and demonstrate the feasibility of the hybrid true-color micro-CT system. Additionally, a "color diffusion" phenomenon was observed whereby high-quality true-color images are produced not only inside the region of interest, but also in neighboring regions. It appears harnessing that this phenomenon could potentially reduce the color detector size for a given ROI, further reducing system cost and radiation dose.

A splitting-based iterative algorithm for accelerated statistical X-ray CT reconstruction

Statistical image reconstruction using penalized weighted least-squares (PWLS) criteria can improve image-quality in X-ray computed tomography (CT). However, the huge dynamic range of the statistical weights leads to a highly shift-variant inverse problem making it difficult to precondition and accelerate existing iterative algorithms that attack the statistical model directly. We propose to alleviate the problem by using a variable-splitting scheme that separates the shift-variant and ("nearly") invariant components of the statistical data model and also decouples the regularization term. This leads to an equivalent constrained problem that we tackle using the classical method-of-multipliers framework with alternating minimization. The specific form of our splitting yields an alternating direction method of multipliers (ADMM) algorithm with an inner-step involving a "nearly" shift-invariant linear system that is suitable for FFT-based preconditioning using cone-type filters. The proposed method can efficiently handle a variety of convex regularization criteria including smooth edge-preserving regularizers and nonsmooth sparsity-promoting ones based on the l(1)-norm and total variation. Numerical experiments with synthetic and real in vivo human data illustrate that cone-filter preconditioners accelerate the proposed ADMM resulting in fast convergence of ADMM compared to conventional (nonlinear conjugate gradient, ordered subsets) and state-of-the-art (MFISTA, split-Bregman) algorithms that are applicable for CT.

Practical interior tomography with radial Hilbert filtering and a priori knowledge in a small round area

PURPOSES

Interior tomography problem can be solved using the so-called differentiated backprojection-projection onto convex sets (DBP-POCS) method, which requires a priori knowledge within a small area interior to the region of interest (ROI) to be imaged. In theory, the small area wherein the a priori knowledge is required can be in any shape, but most of the existing implementations carry out the Hilbert filtering either horizontally or vertically, leading to a vertical or horizontal strip that may be across a large area in the object. In this work, we implement a practical DBP-POCS method with radial Hilbert filtering and thus the small area with the a priori knowledge can be roughly round (e.g., a sinus or ventricles among other anatomic cavities in human or animal body). We also conduct an experimental evaluation to verify the performance of this practical implementation.

METHODS

We specifically re-derive the reconstruction formula in the DBP-POCS fashion with radial Hilbert filtering to assure that only a small round area with the a priori knowledge be needed (namely radial DBP-POCS method henceforth). The performance of the practical DBP-POCS method with radial Hilbert filtering and a priori knowledge in a small round area is evaluated with projection data of the standard and modified Shepp-Logan phantoms simulated by computer, followed by a verification using real projection data acquired by a computed tomography (CT) scanner.

RESULTS

The preliminary performance study shows that, if a priori knowledge in a small round area is available, the radial DBP-POCS method can solve the interior tomography problem in a more practical way at high accuracy.

CONCLUSIONS

In comparison to the implementations of DBP-POCS method demanding the a priori knowledge in horizontal or vertical strip, the radial DBP-POCS method requires the a priori knowledge within a small round area only. Such a relaxed requirement on the availability of a priori knowledge can be readily met in practice, because a variety of small round areas (e.g., air-filled sinuses or fluid-filled ventricles among other anatomic cavities) exist in human or animal body. Therefore, the radial DBP-POCS method with a priori knowledge in a small round area is more feasible in clinical and preclinical practice.