Posts tagged Interior Tomography
We are pleased to announce a 2012 NSF CAREER Award Winner: Dr. Hengyong Yu
While classic computed tomography (CT) theory targets exact reconstruction of a whole cross-section or entire volume from complete projections, biomedical applications often focus on relatively small internal region-of-interests (ROIs). However, traditional CT theory cannot exactly reconstruct an internal ROI only from truncated projections associated with x-rays through the ROI because this interior problem does not have a unique solution in an unconstrained setting. In 2007, the PI and his collaborators proved that the interior problem can be exactly and stably solved if a sub-region is known inside the ROI. Inspired by the compressive sensing (CS) theory, in 2009 the PI proposed the concept of CS-based interior tomography and proved that exact interior reconstruction is achievable with an interior scan if the ROI is piecewise constant, which is subsequently extended to the case of piecewise polynomial ROI.
The goal of this CAREER proposal is to advance the CS-based interior tomography theory and algorithms, and make a paradigm shift from traditional global filtered back-projection (FBP) to contemporary interior reconstruction.
The three objectives are to 1) perform mathematical analysis on a general scarcity constraint model to establish uniqueness, exactness and stability, as well as the properties of the corresponding discrete scheme; 2) develop and optimize novel interior reconstruction algorithms in a general POCS framework incorporating the split-Bregman and statistical reconstruction methods; 3) verify the theoretical findings and validate the proposed algorithms via numerical simulation, and demonstrate its utility by solving the big patient problem.
The research will be closely integrated with educational and outreach activities including creating a Medical Image Reconstruction course at both graduate and undergraduate levels at the Virginia Tech-Wake Forest University School of Biomedical Engineering and Sciences (SBES).
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….
Interior Tomography and Instant Tomography by Reconstruction from Truncated Limited-angle Projection Data by Dr. Ge Wang, Yangbo Ye, and Hengyong Yu.
A system and method for tomographic image reconstruction using truncated limited-angle projection data that allows exact interior reconstruction (interior tomography) of a region of interest (ROI) based on linear attenuation coefficient distribution of a subregion within the ROI, thereby improving image quality while reducing radiation dosage. In addition, the method includes parallel interior tomography using multiple sources beamed at multiple angles through an ROI and that enables higher temporal resolution. Click here for full text…
Medical Imagers Lower the Dose
Radiation-lowering techniques were in the works even before studies showed a danger
By Neil Savage / March 2010
Recent research documenting that CT scans increase the risk of cancer has biomedical engineers looking for new ways to reduce patients’ exposure to ionizing radiation. 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, 20100
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….
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, 20090
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, 20090
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. 20090
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….
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….
Yu H, Cao G, Burk L, Lee Y, Lu J, Santago P, Zhou O and Wang G; Compressive sampling based interior tomography for dynamic carbon nanotube Micro-CT; Journal of X-ray Science and Technology, 17(4): 295-303, 20090
In the computed tomography (CT) field, one recent invention is the so-called carbon nanotube (CNT) based field emission x-ray technology. On the other hand, compressive sampling (CS) based interior tomography is a new innovation. Combining the strengths of these two novel subjects, we apply the interior tomography technique to local mouse cardiac imaging using respiration and cardiac gating with a CNT based micro-CT scanner. The major features of our method are: (1) it does not need exact prior knowledge inside an ROI; and (2) two orthogonal scout projections are employed to regularize the reconstruction. Both numerical simulations and in vivo mouse studies are performed to demonstrate the feasibility of our methodology. Click here for full article….
Wang G, Yu H, Ye Y; A scheme for multi-source interior tomography; Medical Physics, 36(8):3575-3581, 20090
Currently, x-ray computed tomography (CT) requires source scanning so that projections can be collected from various orientations for image reconstruction. Limited by the scanning time, temporal resolution of CT is often inadequate when rapid dynamics is involved in an object to be reconstructed. To meet this challenge, here we propose a scheme of multi-source interior tomography for ultrafast imaging that reconstructs a relatively small region of interest (ROI). Specifically, such an ROI is irradiated in parallel with narrow x-ray beams defined by many source-detector pairs for data acquisition. This ROI can be then reconstructed using our interior tomography approach. To demonstrate the merits of this approach, we report interior reconstruction from in vivo lung CT data at much reduced radiation dose, which is roughly proportional to the ROI size. Our results suggest a scheme for ultrafast tomography (such as with a limited number of sources and in a scanning mode) to shorten data acquisition time and suppress motion blurring. Click here for full article….