Jiansheng Yang

High Order Total Variation Minimization for Interior Tomography.

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 through the HOT minimization if the ROI is piecewise polynomial. Then, we verify our theoretical results in numerical simulation.

Supplemental analysis on compressed sensing based interior tomography

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.

Determining scientific impact using a collaboration index

Researchers collaborate on scientific projects that are often measured by both the quantity and the quality of the resultant peer-reviewed publications. However, not all collaborators contribute to these publications equally, making metrics such as the total number of publications and the H-index insufficient measurements of individual scientific impact. To remedy this, we use an axiomatic approach to assign relative credits to the coauthors of a given paper, referred to as the A-index for its axiomatic foundation. In this paper, we use the A-index to compute the weighted sums of peer-reviewed publications and journal impact factors, denoted as the C- and P-indexes for collaboration and productivity, respectively. We perform an in-depth analysis of bibliometric data for 186 biomedical engineering faculty members and from extensive simulation. It is found that these axiomatically weighted indexes better capture a researcher’s scientific caliber than do the total number of publications and the H-index, allowing for fairer and sharper evaluation of researchers with diverse collaborative behaviors.

High-order total variation minimization for interior SPECT

Recently, we developed an approach for solving the computed tomography (CT) interior problem based on the high-order TV (HOT) minimization, assuming that a region-of-interest (ROI) is piecewise polynomial. In this paper, we generalize this finding from the CT field to the single-photon emission computed tomography (SPECT) field, and prove that if an ROI is piecewise polynomial, then the ROI can be uniquely reconstructed from the SPECT projection data associated with the ROI through the HOT minimization. Also, we propose a new formulation of HOT, which has an explicit formula for any n-order piecewise polynomial function, while the original formulation has no explicit formula for n ≥ 2. Finally, we verify our theoretical results in numerical simulation, and discuss relevant issues.

Parallel Implementation of Katsevich's FBP Algorithm

For spiral cone-beam CT, parallel computing is an effective approach to resolving the problem of heavy computation burden. It is well known that the major computation time is spent in the backprojection step for either filtered-backprojection (FBP) or backprojected-filtration (BPF) algorithms. By the cone-beam cover method [1], the backprojection procedure is driven by cone-beam projections, and every cone-beam projection can be backprojected independently. Basing on this fact, we develop a parallel implementation of Katsevichs FBP algorithm. We do all the numerical experiments on a Linux cluster. In one typical experiment, the sequential reconstruction time is 781.3 seconds, while the parallel reconstruction time is 25.7 seconds with 32 processors.

A bibliometric analysis of academic publication and NIH funding

Academic productivity and research funding have been hot topics in biomedical research. While publications and their citations are popular indicators of academic productivity, there has been no rigorous way to quantify co-authors’ relative contributions. This has seriously compromised quantitative studies on the relationship between academic productivity and research funding. Here we apply an axiomatic approach and associated bibliometric measures to revisit a recent study by Ginther et al. (Ginther et al., 2011a,b) in which the probability of receiving a U.S. National Institutes of Health (NIH) R01 award was analyzed with respect to the applicants race/ethnicity. Our results provide new insight and suggest that there is no significant racial bias in the NIH review process, in contrast to the conclusion from the study by D. K. Ginther et al. Our axiomatic approach has a potential to be widely used for scientific assessment and management.

Theoretical study on high order interior tomography

In this paper, we study a new type of high order interior problems characterized by high order differential phase shift measurement. This problem is encountered in local x-ray phase-contrast tomography. Here we extend our previous theoretical framework from interior CT to interior differential phase-contrast tomography, and establish the solution uniqueness in this context. We employ the analytic continuation method and high order total variation minimization which we developed in our previous work for interior CT, and prove that an image in a region of interest (ROI) can be uniquely reconstructed from truncated high order differential projection data if the image is known a priori in a sub-region of the ROI or the image is piecewise polynomial in the ROI. Preliminary numerical experiments support the theoretical finding.

Data consistency condition for truncated projections in fan-beam geometry.

It is well known that CT projections are redundant. Over the past decades, significant efforts have been devoted to characterize the data redundancy in different aspects. Very recently, Clackdoyle and Desbat reported a new integral-type data consistency condition (DCC) for truncated 2D parallel-beam projections, which can be applied to a region inside a field of view (FOV) but outside of the convex hull of the compact support of an object. Inspired by their work, here we derive a more general condition for 2D fan-beam geometry with a general scanning trajectory. This extended DCC is verified with simulated projections of the Shepp-Logan phantom and a clinically collected sinogram. Then, we demonstrate an application of the proposed DCC.

Cone-beam reconstruction for the two-circles-plus-one-line trajectory

The Kodak Image Station In-Vivo FX has an x-ray module with cone-beam configuration for radiographic imaging but lacks the functionality of tomography. To introduce x-ray tomography into the system, we choose the two-circles-plus-one-line trajectory by mounting one translation motor and one rotation motor. We establish a reconstruction algorithm by applying the M-line reconstruction method. Numerical studies and preliminary physical phantom experiment demonstrate the feasibility of the proposed design and reconstruction algorithm.

High order total variation method for interior tomography

While classic CT theory targets exact reconstruction of a whole cross-section or an entire object, practical applications often focus on a region of interest (ROI). The long-standing interior problem is well known that an internal ROI cannot be exactly reconstruct only from truncated projection data associated with x-rays through the ROI. Although lambda tomography was developed to target gradient-like features of an internal ROI for the interior problem, it has not been well accepted in the biomedical community. On the other hand, approximate local reconstruction methods are subject to biases and artifacts. Recently, the interior problem is re-visited with appropriate prior knowledge, delivering practical results. First, the interior problem can be exactly and stably solved if a sub-region in an ROI is known. Thereafter, the sub-region knowledge can be replaced by certain rather weak constraints. For local reconstruction, a candidate image can be represented as the sum of the truth and an ambiguity component. Very surprisingly, the ROI image is prove to be the unique minimizer of the total variation (TV) or high order total variation (HOT) functional subject to the measurement, if the ROI is piece-wise constant or polynomial. Interior tomography algorithms based on HOT minimization have been developed for x-ray CT, and then extended for interior SPECT and interior differential phasecontrast tomography, respectively. In this paper, we will summarize the main theoretical and algorithmic results.