Emil Y Sidky

Publications of Emil Y Sidky

• Investigation of discrete imaging models and iterative image reconstruction in differential X-ray phase-contrast tomography.

  Authors: Qiaofeng Xu, Emil Y Sidky, Xiaochuan Pan, Marco Stampanoni, Peter Modregger, Mark A Anastasio

  Optics express. 05/2012; 20(10):10724-49.

  Differential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorptionDifferential X-ray phase-contrast tomography (DPCT) refers to a class of promising methods for reconstructing the X-ray refractive index distribution of materials that present weak X-ray absorption contrast. The tomographic projection data in DPCT, from which an estimate of the refractive index distribution is reconstructed, correspond to one-dimensional (1D) derivatives of the two-dimensional (2D) Radon transform of the refractive index distribution. There is an important need for the development of iterative image reconstruction methods for DPCT that can yield useful images from few-view projection data, thereby mitigating the long data-acquisition times and large radiation doses associated with use of analytic reconstruction methods. In this work, we analyze the numerical and statistical properties of two classes of discrete imaging models that form the basis for iterative image reconstruction in DPCT. We also investigate the use of one of the models with a modern image reconstruction algorithm for performing few-view image reconstruction of a tissue specimen.

• Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm.

  Authors: Emil Y Sidky, Jakob H Jørgensen, Xiaochuan Pan

  Physics in medicine and biology. 04/2012; 57(10):3065-3091.

  The primal-dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1-26) is applied to various convex optimization problems of interest in computed tomographyThe primal-dual optimization algorithm developed in Chambolle and Pock (CP) (2011 J. Math. Imag. Vis. 40 1-26) is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in this paper, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity x-ray illumination is presented.

• Ensuring convergence in total-variation-based reconstruction for accurate microcalcification imaging in breast X-ray CT

  Authors: Jakob H. Jørgensen, Emil Y Sidky, Xiaochuan Pan

  11/2011;

  Breast X-ray CT imaging is being considered in screening as an extension to mammography. As a large fraction of the population will be exposed to radiation, low-dose imaging is essential. IterativeBreast X-ray CT imaging is being considered in screening as an extension to mammography. As a large fraction of the population will be exposed to radiation, low-dose imaging is essential. Iterative image reconstruction based on solving an optimization problem, such as Total-Variation minimization, shows potential for reconstruction from sparse-view data. For iterative methods it is important to ensure convergence to an accurate solution, since important image features, such as presence of microcalcifications indicating breast cancer, may not be visible in a non-converged reconstruction, and this can have clinical significance. To prevent excessively long computational times, which is a practical concern for the large image arrays in CT, it is desirable to keep the number of iterations low, while still ensuring a sufficiently accurate reconstruction for the specific imaging task. This motivates the study of accurate convergence criteria for iterative image reconstruction. In simulation studies with a realistic breast phantom with microcalcifications we compare different convergence criteria for reliable reconstruction. Our results show that it can be challenging to ensure a sufficiently accurate microcalcification reconstruction, when using standard convergence criteria. In particular, the gray level of the small microcalcifications may not have converged long after the background tissue is reconstructed uniformly. We propose the use of the individual objective function gradient components to better monitor possible regions of non-converged variables. For microcalcifications we find empirically a large correlation between nonzero gradient components and non-converged variables, which occur precisely within the microcalcifications. This supports our claim that gradient components can be used to ensure convergence to a sufficiently accurate reconstruction.

• Quantification of admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT

  Authors: Jakob H. Jørgensen, Emil Y. Sidky, Xiaochuan Pan

  09/2011;

  Iterative image reconstruction (IIR) with sparsity-exploiting methods proposed in compressive sensing (CS) claim potentially large reductions in sampling requirements. Quantifying this claim forIterative image reconstruction (IIR) with sparsity-exploiting methods proposed in compressive sensing (CS) claim potentially large reductions in sampling requirements. Quantifying this claim for computed tomography (CT) is difficult, because both full sampling and the reduction in sampling admitted by sparsity-exploiting methods are ill-defined. CS does not provide answers, aside from designing the optimization problem, because the CT imaging model does not belong to any class of measurement matrices for which CS provides theoretical guarantees. This article addresses quantification of admissible undersampling through sparsity-exploiting methods. Four sufficient-sampling conditions (SSCs) are introduced and their use as a reference of full sampling is discussed. The derived SSCs are based only on the condition number of the system matrix. In numerical simulation studies in the setting of breast CT the SSCs are evaluated for quantifying undersampling admitted by total variation minimization. A direct connection between sparsity and admitted undersampling is found.

• Accelerated gradient methods for total-variation-based CT image reconstruction

  Authors: Jakob Heide Jørgensen, Tobias Lindstrøm Jensen, Per Christian Hansen, Søren Holdt Jensen, Emil Y Sidky, Xiaochuan Pan

  05/2011;

  Total-variation (TV)-based Computed Tomography (CT) image reconstruction has shown experimentally to be capable of producing accurate reconstructions from sparse-view data. In particular TV-basedTotal-variation (TV)-based Computed Tomography (CT) image reconstruction has shown experimentally to be capable of producing accurate reconstructions from sparse-view data. In particular TV-based reconstruction is very well suited for images with piecewise nearly constant regions. Computationally, however, TV-based reconstruction is much more demanding, especially for 3D imaging, and the reconstruction from clinical data sets is far from being close to real-time. This is undesirable from a clinical perspective, and thus there is an incentive to accelerate the solution of the underlying optimization problem. The TV reconstruction can in principle be found by any optimization method, but in practice the large-scale systems arising in CT image reconstruction preclude the use of memory-demanding methods such as Newton's method. The simple gradient method has much lower memory requirements, but exhibits slow convergence. In the present work we consider the use of two accelerated gradient-based methods, GPBB and UPN, for reducing the number of gradient method iterations needed to achieve a high-accuracy TV solution in CT image reconstruction. The former incorporates several heuristics from the optimization literature such as Barzilai-Borwein (BB) step size selection and nonmonotone line search. The latter uses a cleverly chosen sequence of auxiliary points to achieve a better convergence rate. The methods are memory efficient and equipped with a stopping criterion to ensure that the TV reconstruction has indeed been found. An implementation of the methods (in C with interface to Matlab) is available for download from http://www2.imm.dtu.dk/~pch/TVReg/. We compare the proposed methods with the standard gradient method, applied to a 3D test problem with synthetic few-view data. We find experimentally that for realistic parameters the proposed methods significantly outperform the gradient method.

• Toward optimal X-ray flux utilization in breast CT

  Authors: Jakob H. Joergensen, Per Christian Hansen, Emil Y Sidky, Ingrid S. Reiser, Xiaochuan Pan

  04/2011;

  A realistic computer-simulation of a breast computed tomography (CT) system and subject is constructed. The model is used to investigate the optimal number of views for the scan given a fixed totalA realistic computer-simulation of a breast computed tomography (CT) system and subject is constructed. The model is used to investigate the optimal number of views for the scan given a fixed total X-ray fluence. The reconstruction algorithm is based on accurate solution to a constrained, TV-minimization problem, which has received much interest recently for sparse-view CT data.

• High resolution image reconstruction with constrained, total-variation minimization

  Authors: Emil Y Sidky, Rick Chartrand, Yuval Duchin, Christer Ullberg, Xiaochuan Pan

  04/2011;

  This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systemsThis work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image reconstruction, because a very fine image grid is needed to realize the resolution inherent in such scanners. These image arrays lead to under-determined imaging models whose inversion is unstable and can result in undesirable artifacts and noise patterns. There are many possibilities to stabilize the imaging model, and this work proposes a method which may have an advantage in terms of algorithm efficiency. The proposed method introduces additional constraints in the optimization problem; these constraints set to zero high spatial frequency components which are beyond the sensing capability of the detector. The method is demonstrated with an actual CT data set and compared with another method based on projection up-sampling.

• Algorithm-Enabled Low-Dose Micro-CT Imaging.

  Authors: Xiao Han, Junguo Bian, Diane R. Eaker, Timothy Kline, Emil Y. Sidky, Erik L. Ritman, Xiaochuan Pan

  IEEE Trans. Med. Imaging. 01/2011; 30:606-620.

• Frequency extrapolation by nonconvex compressive sensing.

  Authors: Rick Chartrand, Emil Y. Sidky, Xiaochuan Pan

  Proceedings of the 8th IEEE International Symposium on Biomedical Imaging: From Nano to Macro, ISBI 2011, March 30 - April 2, 2011, Chicago, Illinois, USA; 01/2011

• A constrained, total-variation minimization algorithm for low-intensity X-ray CT

  Authors: Emil Y Sidky, Yuval Duchin, Christer Ullberg, Xiaochuan Pan

  11/2010;

  Purpose: We develop an iterative image-reconstruction algorithm for application to low-intensity computed tomography (CT) projection data, which is based on constrained, total-variation (TV)Purpose: We develop an iterative image-reconstruction algorithm for application to low-intensity computed tomography (CT) projection data, which is based on constrained, total-variation (TV) minimization. The algorithm design focuses on recovering structure on length scales comparable to a detector-bin width. Method: Recovering the resolution on the scale of a detector bin, requires that pixel size be much smaller than the bin width. The resulting image array contains many more pixels than data, and this undersampling is overcome with a combination of Fourier upsampling of each projection and the use of constrained, TV-minimization, as suggested by compressive sensing. The presented pseudo-code for solving constrained, TV-minimization is designed to yield an accurate solution to this optimization problem within 100 iterations. Results: The proposed image-reconstruction algorithm is applied to a low-intensity scan of a rabbit with a thin wire, to test resolution. The proposed algorithm is compared with filtered back-projection (FBP). Conclusion: The algorithm may have some advantage over FBP in that the resulting noise-level is lowered at equivalent contrast levels of the wire. Comment: This article has been submitted to "Medical Physics" on 9/13/2010

• Evaluation of sparse-view reconstruction from flat-panel-detector cone-beam CT.

  Authors: Junguo Bian, Jeffrey H Siewerdsen, Xiao Han, Emil Y Sidky, Jerry L Prince, Charles A Pelizzari, Xiaochuan Pan

  Physics in medicine and biology. 10/2010; 55(22):6575-99.

  Flat-panel-detector x-ray cone-beam computed tomography (CBCT) is used in a rapidly increasing host of imaging applications, including image-guided surgery and radiotherapy. The purpose of the workFlat-panel-detector x-ray cone-beam computed tomography (CBCT) is used in a rapidly increasing host of imaging applications, including image-guided surgery and radiotherapy. The purpose of the work is to investigate and evaluate image reconstruction from data collected at projection views significantly fewer than what is used in current CBCT imaging. Specifically, we carried out imaging experiments using a bench-top CBCT system that was designed to mimic imaging conditions in image-guided surgery and radiotherapy; we applied an image reconstruction algorithm based on constrained total-variation (TV)-minimization to data acquired with sparsely sampled view-angles and conducted extensive evaluation of algorithm performance. Results of the evaluation studies demonstrate that, depending upon scanning conditions and imaging tasks, algorithms based on constrained TV-minimization can reconstruct images of potential utility from a small fraction of the data used in typical, current CBCT applications. A practical implication of the study is that the optimization of algorithm design and implementation can be exploited for considerably reducing imaging effort and radiation dose in CBCT.

• Image reconstruction exploiting object sparsity in boundary-enhanced X-ray phase-contrast tomography.

  Authors: Emil Y Sidky, Mark A Anastasio, Xiaochuan Pan

  Optics express. 05/2010; 18(10):10404-22.

  Propagation-based X-ray phase-contrast tomography (PCT) seeks to reconstruct information regarding the complex-valued refractive index distribution of an object. In many applications, aPropagation-based X-ray phase-contrast tomography (PCT) seeks to reconstruct information regarding the complex-valued refractive index distribution of an object. In many applications, a boundary-enhanced image is sought that reveals the locations of discontinuities in the real-valued component of the refractive index distribution. We investigate two iterative algorithms for few-view image reconstruction in boundary-enhanced PCT that exploit the fact that a boundary-enhanced PCT image, or its gradient, is often sparse. In order to exploit object sparseness, the reconstruction algorithms seek to minimize the l(1)-norm or TV-norm of the image, subject to data consistency constraints. We demonstrate that the algorithms can reconstruct accurate boundary-enhanced images from highly incomplete few-view projection data.

• Consistency Conditions for Cone-Beam CT Data Acquired with a Straight-Line Source Trajectory.

  Authors: Margo S Levine, Emil Y Sidky, Xiaochuan Pan

  Tsinghua science and technology. 02/2010; 15(1):56-61.

  A consistency condition is developed for computed tomography (CT) projection data acquired from a straight-line X-ray source trajectory. The condition states that integrals of normalized projectionA consistency condition is developed for computed tomography (CT) projection data acquired from a straight-line X-ray source trajectory. The condition states that integrals of normalized projection data along detector lines parallel to the X-ray path must be equal. The projection data is required to be untruncated only along the detector lines parallel to the X-ray path, a less restrictive requirement compared to Fourier conditions that necessitate completely untruncated data. The condition is implemented numerically on simple image functions, a discretization error bound is estimated, and detection of motion inconsistencies is demonstrated. The results show that the consistency condition may be used to quantitatively compare the quality of projection data sets obtained from different scans of the same image object.

• Region of Interest Imaging for a General Trajectory with the Rebinned BPF Algorithm.

  Authors: Junguo Bian, Dan Xia, Emil Y Sidky, Xiaochuan Pan

  Tsinghua science and technology. 02/2010; 15(1):68-73.

  The back-projection-filtration (BPF) algorithm has been applied to image reconstruction for cone-beam configurations with general source trajectories. The BPF algorithm can reconstruct 3-DThe back-projection-filtration (BPF) algorithm has been applied to image reconstruction for cone-beam configurations with general source trajectories. The BPF algorithm can reconstruct 3-D region-of-interest (ROI) images from data containing truncations. However, like many other existing algorithms for cone-beam configurations, the BPF algorithm involves a back-projection with a spatially varying weighting factor, which can result in the non-uniform noise levels in reconstructed images and increased computation time. In this work, we propose a BPF algorithm to eliminate the spatially varying weighting factor by using a rebinned geometry for a general scanning trajectory. This proposed BPF algorithm has an improved noise property, while retaining the advantages of the original BPF algorithm such as minimum data requirement.

• Investigation of Sparse Data Mouse Imaging Using Micro-CT with a Carbon-Nanotube-Based X-ray Source.

  Authors: Junguo Bian, Xiao Han, Emil Y Sidky, Guohua Cao, Jianping Lu, Otto Zhou, Xiaochuan Pan

  Tsinghua science and technology. 02/2010; 15(1):74-78.

  There has been a renewed interest in algorithm development for image reconstruction from highly incomplete data in computed tomography (CT). Such algorithms may lead to reduced imaging dose and time,There has been a renewed interest in algorithm development for image reconstruction from highly incomplete data in computed tomography (CT). Such algorithms may lead to reduced imaging dose and time, and to the design of innovative configurations tailored to specific imaging tasks. In recent years, a carbon-nanotube (CNT)-based field-emission x-ray source has been developed, which offers easy electronic control of radiation and thus can be an ideal candidate for gated imaging. We have recently proposed algorithms for image reconstruction from fan- and cone-beam data collected at highly sparse angular views through minimization of the total-variation (TV) of the image subject to the condition that the estimated data are consistent with the measured data. In this work, we investigate and demonstrate the application of the TV-minimization algorithm to reconstructing images from mouse data acquired with a CNT-based CT scanner at a number of views much lower than what is used in conventional CT imaging. The results demonstrate that the TV-minimization algorithm can yield images with quality comparable to those obtained from a large number of views by use of the conventional algorithms. The significance of the work may lie in that the substantial reduction of projection views promised by the TV-minimization algorithm can be exploited for reducing imaging dose and time or for improving temporal resolution in tasks such as dynamic imaging.

• Dual-Energy Technique at Low Tube Voltages for Small Animal Imaging.

  Authors: Seungryong Cho, Emil Y Sidky, Junguo Bian, Xiaochuan Pan

  Tsinghua science and technology. 02/2010; 15(1):79-86.

  We investigate the feasibility of dual-energy method for image contrast enhancement in small animal studies using a low kV X-ray radiographic system. A robust method for X-ray spectrum estimationWe investigate the feasibility of dual-energy method for image contrast enhancement in small animal studies using a low kV X-ray radiographic system. A robust method for X-ray spectrum estimation from transmission measurements, based on expectation-maximization (EM) method, is applied to an X-ray specimen radiographic system for dual energy imaging of a mouse. From transmission measurements of two known attenuators at two different X-ray tube voltages, the X-ray energy spectra are reconstructed using the EM-based method. From the spectra information thus obtained, the transmission data for bone and soft tissue in terms of various thicknesses are generated. Two polynomial functions of transmission data are then sought for to fit the inverted thicknesses of bone and soft-tissue. Scatters in cone-beam projection data acquired at two X-ray energies were corrected. From the scatter-corrected data, a bone thickness map is separated from a soft-tissue thickness map by use of the polynomial functions.

• Enhanced imaging of microcalcifications in digital breast tomosynthesis through improved image-reconstruction algorithms.

  Authors: Emil Y Sidky, Xiaochuan Pan, Ingrid S. Reiser, Robert M Nishikawa, Richard H Moore, Daniel B Kopans

  Medical physics. 11/2009; 36(11):4920-32.

  PURPOSE: The authors develop a practical, iterative algorithm for image-reconstruction in undersampled tomographic systems, such as digital breast tomosynthesis (DBT). METHODS: The algorithm controlsPURPOSE: The authors develop a practical, iterative algorithm for image-reconstruction in undersampled tomographic systems, such as digital breast tomosynthesis (DBT). METHODS: The algorithm controls image regularity by minimizing the image total p variation (TpV), a function that reduces to the total variation when p = 1.0 or the image roughness when p = 2.0. Constraints on the image, such as image positivity and estimated projection-data tolerance, are enforced by projection onto convex sets. The fact that the tomographic system is undersampled translates to the mathematical property that many widely varied resultant volumes may correspond to a given data tolerance. Thus the application of image regularity serves two purposes: (1) Reduction in the number of resultant volumes out of those allowed by fixing the data tolerance, finding the minimum image TpV for fixed data tolerance, and (2) traditional regularization, sacrificing data fidelity for higher image regularity. The present algorithm allows for this dual role of image regularity in undersampled tomography. RESULTS: The proposed image-reconstruction algorithm is applied to three clinical DBT data sets. The DBT cases include one with microcalcifications and two with masses. CONCLUSIONS: Results indicate that there may be a substantial advantage in using the present image-reconstruction algorithm for microcalcification imaging.

• Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT

  Authors: Emil Y Sidky, Chien-Min Kao, Xiaochuan Pan

  05/2009;

  In practical applications of tomographic imaging, there are often challenges for image reconstruction due to under-sampling and insufficient data. In computed tomography (CT), for example, imageIn practical applications of tomographic imaging, there are often challenges for image reconstruction due to under-sampling and insufficient data. In computed tomography (CT), for example, image reconstruction from few views would enable rapid scanning with a reduced x-ray dose delivered to the patient. Limited-angle problems are also of practical significance in CT. In this work, we develop and investigate an iterative image reconstruction algorithm based on the minimization of the image total variation (TV) that applies to divergent-beam CT. Numerical demonstrations of our TV algorithm are performed with various insufficient data problems in fan-beam CT. The TV algorithm can be generalized to cone-beam CT as well as other tomographic imaging modalities.

• Analysis of image-reconstruction algorithms for circular, cone-beam CT by Hotelling observer performance on a detection task.

  Authors: Emil Y Sidky, Xiaochuan Pan

  Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Conference. 01/2009; 1:997-9.

  We apply task-based evaluation methods to image-reconstruction in circular cone-beam CT. The particular task considered is that of detection of a micro-calcification of known location in a knownWe apply task-based evaluation methods to image-reconstruction in circular cone-beam CT. The particular task considered is that of detection of a micro-calcification of known location in a known background; namely a signal-known-exactly/background-known-exactly (SKE/BKE) detection task. The image-reconstruction algorithms are evaluated based on efficiency for detection. This task-based metric can be applied to any linear image-reconstruction algorithm, such as the FDK algorithm or other more recent approximate methods for image-reconstruction in circular, cone-beam CT.

• Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?

  Authors: Xiaochuan Pan, Emil Y Sidky, Michael Vannier

  Inverse problems. 01/2009; 25(12):1230009.

  Despite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtuallyDespite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtually constant for the past 25 years-the reconstruction algorithm. Fundamental advances have been made in the solution of inverse problems, especially tomographic reconstruction, but these works have not been translated into clinical and related practice. The reasons are not obvious and seldom discussed. This review seeks to examine the reasons for this discrepancy and provides recommendations on how it can be resolved. We take the example of field of compressive sensing (CS), summarizing this new area of research from the eyes of practical medical physicists and explaining the disconnection between theoretical and application-oriented research. Using a few issues specific to CT, which engineers have addressed in very specific ways, we try to distill the mathematical problem underlying each of these issues with the hope of demonstrating that there are interesting mathematical problems of general importance that can result from in depth analysis of specific issues. We then sketch some unconventional CT-imaging designs that have the potential to impact on CT applications, if the link between applied mathematicians and engineers/physicists were stronger. Finally, we close with some observations on how the link could be strengthened. There is, we believe, an important opportunity to rapidly improve the performance of CT and related tomographic imaging techniques by addressing these issues.