Biomedical Imaging Division, VT / WFU SBES
Computed Tomography
Cong W, Wang G, Higher-order phase shift reconstruction approach, Med. Phys. 37, 5238-5242, 2010
02 years ago
Biological soft tissues encountered in clinical and preclinical imaging mainly consists of atoms of light elements with low atomic numbers and their elemental composition is nearly uniform with little density variation. Hence, x-ray attenuation contrast is relatively poor and cannot achieve satisfactory sensitivity and specificity. In contrast, x-ray phase-contrast provides a new mechanism for soft tissue imaging. The x-ray phase shift of soft tissues is about a thousand times greater than the x-ray absorption over the diagnostic x-ray energy range, yielding a higher signal-to-noise ratio than the attenuation contrast counterpart. Thus, phase-contrast imaging is a promising technique to
reveal detailed structural variation in soft tissues, offering a high contrast resolution between healthy and malignant tissues. Here the authors develop a novel phase retrieval method to reconstruct the phase image on the object plane from the intensity measurements. The reconstructed phase image is a projection of the phase shift induced by an object and serves as input to reconstruct the 3D refractive index distribution inside the object using a tomographic reconstruction algorithm. Such x-ray refractive index images can reveal structural features in soft tissues, with excellent resolution differentiating healthy and malignant tissues.Click here for full article…
Hengyong Yu, Changguo Ji, and Ge Wang, SART-Type Image Reconstruction from Overlapped Projections, International Journal of Biomedical Imaging, vol. 2011, Article ID 549537, 7 pages, 2010 [PMCID: PMC2943093]
02 years ago
To maximize the time-integrated X-ray flux from multiple X-ray sources and shorten the data acquisition process, a promising way is to allow overlapped projections from multiple sources being simultaneously on without involving the source multiplexing technology. The most challenging task in this configuration is to perform image reconstruction effectively and efficiently from overlapped projections. Inspired by the single-source simultaneous algebraic reconstruction technique (SART), we hereby develop a multisource SART-type reconstruction algorithm regularized by a sparsity-oriented constraint in the soft-threshold filtering framework to reconstruct images from overlapped projections. Our numerical simulation results verify the correctness of the proposed algorithm and demonstrate the advantage of image reconstruction from overlapped projections.Click here for full article…
Yuchuan Wei, Hengyong Yu, and Ge Wang, Inverse Fourier Transform in the Gamma Coordinate System, International Journal of Biomedical Imaging, vol. 2011, Article ID 285130, 16 pages, 2010 [PMCID: PMC2964910]
02 years ago
This paper provides auxiliary results for our general scheme of computed tomography. In 3D parallel-beam geometry, we first demonstrate that the inverse Fourier transform in different coordinate systems leads to different reconstruction formulas and explain why the Radon formula cannot directly work with truncated projection data. Also, we introduce a gamma coordinate system, analyze its properties, compute the Jacobian of the coordinate transform, and define weight functions for the inverse Fourier transform assuming a simple scanning model. Then, we generate Orlov’s theorem and a weighted Radon formula from the inverse Fourier transform in the new system. Furthermore, we present the motion equation of the frequency plane and the conditions for sharp points of the instantaneous rotation axis. Our analysis on the motion of the frequency plane is related to the Frenet-Serret theorem in the differential geometry.Click here for full article…
Lu Y, Yu H, Cao G, Zhao J, Wang G, Zhou O: Multi-beam field emission x-ray system and its reconstruction algorithm. Medical Physics 37:3773-3781, 2010
02 years ago
In this article, the authors propose a multibeam field emission x-ray MBFEX system along with a half-scan fan-beam reconstruction algorithm. The proposed system consists of a linear CNT-based MBFEX source array, a single large
area detector that is divided into same number of segments as the number of x-ray beams, a multihole collimator that aligns each beam with a corresponding detector segment, and a sample rotation stage. The collimator is placed between the source and the object to restrict the x-ray radiations through the target object only. In this design, all the x-ray beams are activated simultaneously to provide multiple projection views of the object. The detector is virtually segmented and synchronized with the x-ray exposure and the physiological signals when gating is involved. The
transmitted x-ray intensity from each beam is collected by the corresponding segment on the detector. After each exposure, the object is rotated by a step angle until sufficient data set is collected. The half-scan reconstruction formula for MBFEX system is derived from the conventional filtered backprojection algorithm. To demonstrate the advantages of the system and method in reducing motion artifacts, the authors performed simulations with both standard and dynamic Shepp–Logan phantoms.Click here for full article…
Yu H, Wang G, A soft-threshold filtering approach for reconstruction from a limited number of projections, Physics in Medicine and Biology, vol. 55, pg 3905-3916, 2010
02 years ago
In the medical imaging field, discrete gradient transform (DGT) is widely used as a sparsifying operator to define the total variation (TV). Recently, TV minimization has become a hot topic in image reconstruction and is usually
implemented using the steepest descent method (SDM). Since TV minimization with the SDM takes a long computational time, here we construct a pseudoinverse of the DGT and adapt a soft-threshold filtering algorithm, whose convergence and efficiency have been theoretically proven. Also, we construct a pseudo-inverse of the discrete difference transform (DDT) and design an algorithm for L1 minimization of the total difference. These two methods are evaluated in numerical simulation. The results demonstrate the merits of the proposed techniques.
Li L, Chen Z, Jin X, Yu H, Wang G, Experimental measurement of human head motion for high-resolution computed tomography system design, Optical Engineering, vol. 49, n. 6, 2010
02 years ago
Human head motion has been experimentally measured for high-resolution computed tomography (CT) design using a Canon digital camera. Our goal is to identify the minimal movements of the human head under ideal conditions without rigid fixation. In our experiments, all the 19 healthy volunteers were lying down with strict self-control. All of them were asked to be calm without pressures. Our results showed that the mean absolute value of the measured translation excursion was about 0.35 mm, which was much less than the measurements on real patients. Furthermore, the head motions in different directions were correlated. These results are useful for the design of the new instant CT system for in vivo high-resolution imaging (about 40 µm). Click here for full article….
Wang G, Yu H, Can interior tomography outperform lambda tomography, PNAS, vol. 107, n.22, 2010 [PMCID: PMC2890447]
02 years ago
Whereas classic computed tomography (CT) theory targets the exact reconstruction of a whole cross-section or entire volume from complete projections, a real-world application often focuses on a region of interest (ROI). It has been a long-standing challenge to reconstruct an internal ROI only from truncated projections collected with a radiative beam through the ROI because this “interior problem” does not have a unique solution.Click here for full article…
Wang G, Yu H, Can interior tomography outperform lambda tomography, PNAS, vol. 107, n.22, 2010
02 years ago
Whereas classic computed tomography (CT) theory targets the exact reconstruction of a whole cross-section or entire volume from complete projections, a real-world application often focuses on a region of interest (ROI). It has been a long-standing challenge to reconstruct an internal ROI only from truncated projections collected with a radiative beam through the ROI because this “interior problem” does not have a unique solution (1). When a traditional CT algorithm such as “filtered backprojection” is applied for an interior reconstruction from truncated projections, features outside the ROI may create artifacts overlapping inside features, rendering the images inaccurate or useless. On the other hand, over past decades, lambda tomography has been developed as a branch of applied mathematics that recovers gradient-like features within an ROI from truncated projections. With lambda tomography, the outcomes are not always the most appealing because of their non-quantitative nature. Recently, Quinto et al. (2) demonstrated the utility and limitation of electron lambda tomography and pointed out that “unless prior knowledge is being used…structures in the specimen cannot be exactly recovered even if we have access to noise-free continuum data….” Click here for full article….
Yang L, Lu Y, Wang G, Compressed sensing inspired image reconstruction from overlapped projections, International Journal of Biomedical Imaging, vol. 2010, Article ID 284073, 2010
03 years ago
The key idea discussed in this paper is to reconstruct an image from overlapped projections so that the data acquisition process can be shortened while the image quality remains essentially uncompromised. To perform image reconstruction from overlapped projections, the conventional reconstruction approach (e.g., filtered backprojection (FBP) algorithms) cannot be directly used because of two problems. First, overlapped projections represent an imaging system in terms of summed exponentials, which cannot be transformed into a linear form. Second, the overlapped measurement carries less information than the traditional line integrals. To meet these challenges, we propose a compressive sensing-(CS-) based iterative algorithm for reconstruction from overlapped data. This algorithm starts with a good initial guess, relies on adaptive linearization, and minimizes the total variation (TV). Then, we demonstrated the feasibility of this algorithm in numerical tests. Click here for full article….
Lu Y, Katsevich A, Zhao J, Yu H, Wang G: Fast exact/quasi-exact FBP algorithms for triple-source helical cone-beam CT. IEEE Trans. Medical Imaging 29:756-770, 2010
03 years ago
Cardiac computed tomography (CT) has been improved over past years, but it still needs improvement for higher temporal resolution in the cases of high or irregular cardiac rates. Given successful applications of dual-source cardiac CT scanners, triple-source cone-beam CT seems a promising mode for cardiac CT. In this paper, we propose two filtered-backprojection algorithms for triple-source helical cone-beam CT. The first algorithm utilizes two families of filtering lines. These lines are parallel to the tangent of the scanning trajectory and the so-called L lines. The second algorithm utilizes two families of filtering lines tangent to the boundaries of the Zhao window and L lines, respectively, but it eliminates the filtering paths along the tangent of the scanning trajectory, thus reducing the required detector size greatly. The first algorithm is theoretically exact for r < 0.265 R and quasi-exact for 0.265 R ≤ r < 0.495 R, and the second algorithm is quasi-exact for r < 0.495 R, where and denote the object radius and the trajectory radius, respectively. Both algorithms are computationally efficient. Numerical results are presented to verify and showcase the proposed algorithms. Click here for full article….
Yang JS, Yu HY, Jiang M, Wang G: High-order total variation minimization for interior tomography. Inverse Problems 26:1-29, 2010
03 years ago
Recently, an accurate solution to the interior problem was proposed based on the total variation (TV) minimization, assuming that a region of interest (ROI) is piecewise constant. In this paper, we generalize that assumption to allow a piecewise polynomial ROI, introduce the high-order TV (HOT), and prove that an ROI can be accurately reconstructed from projection data associated with x-rays through the ROI via the HOT minimization if the ROI is piecewise polynomial. Then, we verify our theoretical results in numerical simulation. Click here for full article….
Yu H, Wang G: SART-type image reconstruction from a limited number of projections with the sparsity constraint; International Journal of Biomedical Imaging, Vol. 2010, Article ID: 934847, 2010
03 years ago
Based on the recent mathematical findings on solving the linear inverse problems with sparsity constraints by Daubechiesx et al., here we adapt a simultaneous algebraic reconstruction technique (SART) for image reconstruction from a limited number of projections subject to a sparsity constraint in terms of an invertible compression transform. The algorithm is implemented with an exemplary Haar wavelet transform and tested with a modified Shepp-Logan phantom. Our preliminary results demonstrate that the sparsity constraint helps effectively improve the quality of reconstructed images and reduce the number of necessary projections. Click here for full article…
Yu H, Wang G, SART-Type Image Reconstruction froma Limited Number of Projections with the Sparsity Constraint, IJBMI 2010
03 years ago
Based on the recent mathematical findings on solving the linear inverse problems with sparsity constraints by Daubechiesx et al., here we adapt a simultaneous algebraic reconstruction technique (SART) for image reconstruction from a limited number of projections subject to a sparsity constraint in terms of an invertible compression transform. The algorithm is implemented with an exemplary Haar wavelet transform and tested with a modified Shepp-Logan phantom. Our preliminary results demonstrate that the sparsity constraint helps effectively improve the quality of reconstructed images and reduce the number of necessary projections.Click here for full article…
Yu H, Wang G, A soft-threshold filtering approach for reconstruction from a limited number of projections, Physics in Medicine and Biology, vol. 55, pg 3905-3916, 2010
03 years ago
In the medical imaging field, discrete gradient transform (DGT) is widely used as a sparsifying operator to define the total variation (TV). Recently, TV minimization has become a hot topic in image reconstruction and is usually implemented using the steepest descent method (SDM). Since TV minimization with the SDM takes a long computational time, here we construct a pseudo-inverse of the DGT and adapt a soft-threshold filtering algorithm, whose convergence and efficiency have been theoretically proven. Also, we construct a pseudo-inverse of the discrete difference transform (DDT) and design an algorithm for L1 minimization of the total difference. These two methods are evaluated in numerical simulation. The results demonstrate the merits of the proposed techniques. Click here for full article….
Bharkhada D, Yu HY, Dixon R, Wei YC, Carr JJ, Bourland D, Hogan R, Wang G: Demonstration of dose and scatter reduction for interior tomography. J Comput Assist Tomogr.,33(6):967-72, 2009
03 years ago
With continuing developments in computed tomography (CT) technology and its increasing use of CT imaging, the ionizing radiation dose from CT is becoming a major public concern particularly for high-dose applications such as cardiac imaging. We recently proposed a novel interior tomography approach for x-ray dose reduction that is very different from all the previously proposed methods. Our method only uses the projection data for the rays passing through the desired region of interest. This method not only reduces x-ray dose but scatter as well. In this paper, we quantify the reduction in the amount of x-ray dose and scattered radiation that could be achieved using this method. Results indicate that interior tomography may reduce the x-ray dose by 18% to 58% and scatter to the detectors by 19% to 59% as the FOV is reduced from 50 to 8.6 cm. Click here for full article….
Han W, Yu H, Wang G: A general total variation minimization theorem for compressed sensing based interior tomography; International Journal of Biomedical Imaging, Article ID: 125871, 2009
03 years ago
Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu andWang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical tool to prove this result is functional analysis without involving the Dirac delta function, which was heuristically used by Yu andWang (2009). Click here for full article….
Yu H, Yang JS, Jiang M, Wang G: Supplemental analysis on compressed sensing based interior tomography, Physics in Medicine and Biology, 54(18):N425-N432. 2009
03 years ago
Recently, in the compressed sensing framework we proved that an interior ROI can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant. In the proofs, we implicitly utilized the property that if an artifact image assumes a constant value within the ROI, then this constant must be zero. Here we prove this property in the space of square integrable functions. Click here for full article….
Ye L, Yu H, Wang G: Determination of exact reconstruction Regions in Composite-circling cone-beam tomography. Medical Physics, .36(8):3448-3454, 2009
03 years ago
Image reconstruction of a short portion of a long object using longitudinally truncated cone-beam data is important for major medical computed tomography (CT) applications, especially cardiac CT. Cardiac CT is an essential imaging tool for the diagnosis and therapeutic assessment of heart defects, cardiovascular diseases, and lung diseases, but it is still limited by suboptimal image quality. Recently, saddle-curve and composite-circling scanning modes have been proposed to solve this problem using exact reconstruction formulas. However, saddle-curve scanning involves both circular and linear motions, while composite-circling scanning conveniently involves just circular motions. Because saddle-curve scanning is difficult to implement mechanically, composite-circling scanning provides another, hopefully easier, approach: An x-ray focal spot in an x-ray tube is rotated on a plane facing the heart, while the x-ray tube and possibly the detector are simultaneously rotated on the gantry plane. This article determines regions for chord-based exact reconstruction in the composite-circling scanning mode and compares them to those in the saddle-curve scanning mode. For different scanning parameter combinations, this article finds the largest sphere centered at the origin that can be embedded inside the exact reconstruction region. This article also shows that the embedded spheres become larger when the x-ray focal spot rotates at variable speeds, allowing the scanning curve to cover a larger object. In summary, this article derives guidelines for prototyping a new cardiac CT scanner to meet the goals of reducing radiation dose and increasing spatial and temporal resolution. Click here for full article….
Bharkhada D, Yu H, Shuping G, Carr J, Wang G: Cardiac CT dose reduction using interior reconstruction algorithm with the aorta and vertebra as known information. Journal of Computer Assisted Tomography, 33(3), 338-347, 2009
03 years ago
High x-ray radiation dose is a major public concern with the increasing use of multidetector computed tomography (CT) for diagnosis of cardiovascular diseases. This issue must be effectively addressed by dose-reduction techniques. Recently, our group proved that an internal region of interest (ROI) can be exactly reconstructed solely from localized projections if a small subregion within the ROI is known. In this article, we propose to use attenuation values of the blood in aorta and vertebral bone to serve as the known information for localized cardiac CT. First, we describe a novel interior tomography approach that backprojects differential fan-beam or parallel-beam projections to obtain the Hilbert transform and then reconstructs the original image in an ROI using the iterative projection onto convex sets algorithm. Then, we develop a numerical phantom based on clinical cardiac CT images for simulations. Our results demonstrate that it is feasible to use practical prior information and exactly reconstruct cardiovascular structures only from projection data along x-ray paths through the ROI. Click here for full article….
Yu HY, Wang G: Compressive sensing based interior tomography. Phys. Med. Biol. 54, 2791–2805, 2009
04 years ago
While conventional wisdom is that the interior problem does not have a unique solution, by analytic continuation we recently showed that the interior problem can be uniquely and stably solved if we have a known sub-region inside a region of interest (ROI). However, such a known sub-region is not always readily available, and it is even impossible to find in some cases. Based on compressed sensing theory, here we prove that if an object under reconstruction is essentially piecewise constant, a local ROI can be exactly and stably reconstructed via the total variation minimization. Because many objects in computed tomography (CT) applications can be approximately modeled as piecewise constant, our approach is practically useful and suggests a new research direction for interior tomography. To illustrate the merits of our finding, we develop an iterative interior reconstruction algorithm that minimizes the total variation of a reconstructed image and evaluate the performance in numerical simulation. Click here for full article….