Approximate Reconstruction Algorithm Research Articles

Angular and CP-Violation Analyses of B-→D⁎+l-ν-l Decays at Hadron Collider Experiments

The B-→D⁎+l-ν-l branching fractions ratio between muon and tau lepton decay modes R(D⁎) has shown intriguing discrepancies between the Standard Model prediction and measurements performed at BaBar, Belle, and LHCb experiments, a possible sign of beyond the Standard Model physics. Theoretical studies show how observables related to the B-→D⁎+l-ν-l differential decay distribution can be used to further constrain New Physics contributions, but their experimental measurements are lacking to date. This article proposes the measurement of B-→D⁎+l-ν-l angular and CP-violating observables at hadron collider experiments, by exploiting approximate reconstruction algorithms using information from detectable final-state particles only. The resolution on the phase space variables is studied using B-→D⁎+l-ν-l decays simulated in a forward detector geometry like LHCb. A method to correct the observable values for the reconstruction inaccuracies based on detector simulation is successfully tested on simulated data and the decrease in precision with respect to a perfect reconstruction is evaluated. The D⁎+ longitudinal polarization fraction and the AT(2)CP-violating observable can be measured losing a factor of 2 and 5 in precision, respectively. The extraction of angular distributions from the template fit selecting B-→D⁎+l-ν-l decays and associated systematic uncertainties are also discussed.

An adaptive sampling method for high‐dimensional shift‐invariant signals

In this paper, an adaptive method for sampling and reconstructing high‐dimensional shift‐invariant signals is proposed. First, the integrate‐and‐fire sampling scheme and an approximate reconstruction algorithm for one‐dimensional bandlimited signals are generalized to shift‐invariant signals. Then, a high‐dimensional shift‐invariant signal is reduced to be a sequence of one‐dimensional shift‐invariant signals along the trajectories parallel to some coordinate axis, which can be approximately reconstructed by the generalized integrate‐and‐fire sampling scheme. Finally, an approximate reconstruction for the high‐dimensional shift‐invariant signal is obtained by solving a series of stable linear systems of equations. The main result shows that the final reconstructed error is completely determined by the initial threshold in integrate‐and‐fire sampling scheme, which is generally very small. Copyright © 2017 John Wiley & Sons, Ltd.

The inverse problem reconstruction approach for single-photon emission computed tomography imaging

In this paper, we study the inverse problem reconstruction approach for parallel-beam projection in -scheme short-scan SPECT image and obtain approximate reconstruction algorithms if the attenuation is real constant and complex-valued angle-dependent cases and the parallel-beam projection data functions are acquired from -scheme short-scan single-photon emission computed tomography. Finally, we also give an numerical implementation.

An iterative approach to non-overdetermined inverse scattering at fixed energy

We present an iterative approximate reconstruction algorithm for non-overdetermined inverse scattering at fixed energy with incomplete data, where the dimension . In particular, we obtain rapidly converging approximate reconstructions for this inverse scattering for . Bibliography: 38 titles.

Evaluation of Algebraic Iterative Image Reconstruction Methods for Tetrahedron Beam Computed Tomography Systems

Tetrahedron beam computed tomography (TBCT) performs volumetric imaging using a stack of fan beams generated by a multiple pixel X-ray source. While the TBCT system was designed to overcome the scatter and detector issues faced by cone beam computed tomography (CBCT), it still suffers the same large cone angle artifacts as CBCT due to the use of approximate reconstruction algorithms. It has been shown that iterative reconstruction algorithms are better able to model irregular system geometries and that algebraic iterative algorithms in particular have been able to reduce cone artifacts appearing at large cone angles. In this paper, the SART algorithm is modified for the use with the different TBCT geometries and is tested using both simulated projection data and data acquired using the TBCT benchtop system. The modified SART reconstruction algorithms were able to mitigate the effects of using data generated at large cone angles and were also able to reconstruct CT images without the introduction of artifacts due to either the longitudinal or transverse truncation in the data sets. Algebraic iterative reconstruction can be especially useful for dual-source dual-detector TBCT, wherein the cone angle is the largest in the center of the field of view.

Approximate Discrete Reconstruction Algorithm

Discrete tomography deals with tomographic reconstruction of greyscale images for which the set of possible grey levels is discrete and small. Here, we develop a discrete approximate reconstruction algorithm. Our algorithm computes an image that has only grey values belonging to a given finite set. It also guarantees that the difference between the given projections and the projections of the reconstructed discrete image is bounded. The bound, which is computable, is independent of the image size. We present reconstruction experiments for a range of phantom images and a varying number of grey values.

Physical phantom studies of helical cone‐beam CT with exact reconstruction

Onboard cone-beam computed tomography (CBCT) connected to radiotherapy linear accelerators suffers CT number consistency and uniformity problems in addition to limited longitudinal coverage. Such problems have prevented CBCT from being fully utilized in many quantitative applications including tumor response evaluation and daily radiation dose computation. This paper presents a feasibility study on the helical CBCT scan with exact reconstruction that could be a potential solution. A Varian TrueBeam treatment machine was programmed in the research mode to accomplish helical scans that required synchronized gantry circular rotation and couch table linear motion. Two physical phantoms were scanned in both 360° and 720° helical trajectories. A Katsevich exact reconstruction algorithm was implemented and tested with digital phantom simulations. It was further optimized to account for mechanical instabilities of both gantry rotation and couch table motion from the physical phantom measurements. Preprocessing was employed to correct photon scattering, beam hardening, and bowtie filtration. The reconstructed images were compared to those reconstructed from the FDK approximate reconstruction algorithm using the same phantom projections. Comparisons have also been made with the clinical circular CBCT images and the diagnostic helical CT images of the same physical phantoms. Satisfactory reconstruction results were obtained for the Katsevich algorithm in digital phantom study. Physical phantom results demonstrated that a 360° helical scan could provide up to 19 cm longitudinal coverage, which could be increased to 54 cm with a 720° helical scan. Image spatial resolution and soft tissue contrast were sufficient. The Q-value, which combined the spatial frequency response (modulation transfer function) and the image noise, was calculated, and suggested that the Katsevich algorithm was superior to the FDK algorithm. A helical CBCT scan is useful to extend the longitudinal coverage. The Katsevich exact reconstruction algorithm could provide additional advantages in image qualities over the traditional FDK approximate algorithm. The combination of helical CBCT scan with exact reconstruction was proved feasible and would render CBCT more useful in image-guided radiation therapy.

WE-C-351-07: Tetrahedron Beam Computed Tomography: A New Design of Online Imaging System for Image Guided Radiotherapy

Purpose: Cone‐beam computed tomography(CBCT) is an important online imaging modality for image‐guidedradiotherapy(IGRT) as well as other forms of image guided interventions. However, current CBCTimage quality is inferior to that of the diagnostic fan beam CT. We have designed a novel Tetrahedron Beam Computed Tomography (TBCT) imagingsystem that may achieve the same diagnostic quality as helical CT scanners. Method and Materials: The TBCT imagingsystem is comprised of a linear scan x‐ray source and a linear discrete x‐ray detector array. The axis of linear x‐ray tube and the detector array are aligned perpendicular to and within the rotation plane, respectively. The x‐ray beams are narrowly collimated into fan beams and focused to the linear detector.Detector and x‐ray tube rotate slowly while the fan beams scan quickly along the axis. The TBCT reconstruction geometry is similar to CBCT. Approximate and exact reconstruction algorithms can be modified for TBCT reconstruction. Results: TBCT will produce diagnostic quality online images due to its scatter rejection mechanism and the use of high‐performance discrete x‐ray detectors. TBCT also has several other advantages such as larger clearance, ease of performing dynamic field size and mAs controls, etc. Conclusion: TBCT will significantly improve online image quality. Clinical implementation of TBCT would be of importance in IGRT as well as other forms of image guided interventions. This research is partially supported by NCI grant under award number 1R21CA130330‐01A1.

A Fourier reconstruction algorithm with constant attenuation compensation using 180° acquisition data for SPECT

In this paper, we develop an approximate analytical reconstruction algorithm that compensates for uniform attenuation in 2D parallel-beam SPECT with a 180° acquisition. This new algorithm is in the form of a direct Fourier reconstruction. The complex variable central slice theorem is used to derive this algorithm. The image is reconstructed with the following steps: first, the attenuated projection data acquired over 180° are extended to 360° and the value for the uniform attenuator is changed to a negative value. The Fourier transform (FT) of the image in polar coordinates is obtained from the Fourier transform of an analytic function interpolated from an extension of the projection data according to the complex central slice theorem. Finally, the image is obtained by performing a 2D inverse Fourier transform. Computer simulations and comparison studies with a 360° full-scan algorithm are provided.

Cone-beam pseudo-lambda tomography

In this paper, for the first time we define the concept of 3D pseudo-lambda tomography based on the 3D Calderon operator, and formulate an approximate local reconstruction algorithm for cone-beam data collected along an arbitrary scanning curve. The main idea is to rewrite the filtering operator in an exact filtered-backprojection reconstruction formula as a local projection. Simulation using the 3D differentiable Shepp–Logan phantom is performed to demonstrate the utility of this new technique.

Tilted cone-beam reconstruction with row-wise fan-to-parallel rebinning

Reconstruction algorithms for cone-beam CT have been the focus of many studies. Several exact and approximate reconstruction algorithms were proposed for step-and-shoot and helical scanning trajectories to combat cone-beam related artefacts. In this paper, we present a new closed-form cone-beam reconstruction formula for tilted gantry data acquisition. Although several algorithms were proposed in the past to combat errors induced by the gantry tilt, none of the algorithms addresses the scenario in which the cone-beam geometry is first rebinned to a set of parallel beams prior to the filtered backprojection. We show that the image quality advantages of the rebinned parallel-beam reconstruction are significant, which makes the development of such an algorithm necessary. Because of the rebinning process, the reconstruction algorithm becomes more complex and the amount of iso-centre adjustment depends not only on the projection and tilt angles, but also on the reconstructed pixel location. In this paper, we first demonstrate the advantages of the row-wise fan-to-parallel rebinning and derive a closed-form solution for the reconstruction algorithm for the step-and-shoot and constant-pitch helical scans. The proposed algorithm requires the ‘warping’ of the reconstruction matrix on a view-by-view basis prior to the backprojection step. We further extend the algorithm to the variable-pitch helical scans in which the patient table travels at non-constant speeds. The algorithm was tested extensively on both the 16- and 64-slice CT scanners. The efficacy of the algorithm is clearly demonstrated by multiple experiments.

Practical hybrid convolution algorithm for helical CT reconstruction

Great strides have been taken in the last few years in the development of both approximate and exact reconstruction algorithms for helical cone-beam computed tomography (CT). However, it is hard to achieve a good balance between reconstruction speed, flexibility, and image quality. We propose a new algorithm that combines the advantages of many previously published algorithms. It uses the so-called hybrid convolution, which is the sum of the ramp and Hilbert filters. In this work, we evaluate the new algorithm and compare it to other candidates in terms of spatial resolution, noise, and image artifacts. Our evaluation demonstrated that the proposed algorithm outperforms the helical Feldkamp algorithm in terms of image noise uniformity and the cone beam artifact. We also propose a simplified version for the over-scan reconstruction.

An Approximate Cone Beam Reconstruction Algorithm for Gantry-Tilted CT Using Tangential Filtering

FDK algorithm is a well-known 3D (three-dimensional) approximate algorithm for CT (computed tomography) image reconstruction and is also known to suffer from considerable artifacts when the scanning cone angle is large. Recently, it has been improved by performing the ramp filtering along the tangential direction of the X-ray source helix for dealing with the large cone angle problem. In this paper, we present an FDK-type approximate reconstruction algorithm for gantry-tilted CT imaging. The proposed method improves the image reconstruction by filtering the projection data along a proper direction which is determined by CT parameters and gantry-tilted angle. As a result, the proposed algorithm for gantry-tilted CT reconstruction can provide more scanning flexibilities in clinical CT scanning and is efficient in computation. The performance of the proposed algorithm is evaluated with turbell clock phantom and thorax phantom and compared with FDK algorithm and a popular 2D (two-dimensional) approximate algorithm. The results show that the proposed algorithm can achieve better image quality for gantry-tilted CT image reconstruction.

Three‐dimensional fluorescence lifetime tomography

Near-infrared fluorescence tomography using molecularly targeted lifetime-sensitive, fluorescent contrast agents have applications for early-stage cancer diagnostics. Yet, although the measurement of fluorescent lifetime imaging microscopy (FLIM) is extensively used in microscopy and spectroscopy applications, demonstration of fluorescence lifetime tomography for medical imaging is limited to two-dimensional studies. Herein, the feasibility of three-dimensional fluorescence-lifetime tomography on clinically relevant phantom volumes is established, using (i) a gainmodulated intensified charge coupled device (CCD) and modulated laser diode imaging system, (ii) two fluorescent contrast agents, e.g., Indocyanine green and 3-3'-Diethylthiatricarbocyanine iodide differing in their fluorescence lifetime by 0.62 ns, and (iii) a two stage approximate extended Kalman filter reconstruction algorithm. Fluorescence measurements of phase and amplitude were acquired on the phantom surface under different target to background fluorescence absorption (70:1, 100:1) and fluorescence lifetime (1:1, 2.1:1) contrasts at target depths of 1.4-2 cm. The Bayesian tomography algorithm was employed to obtain three-dimensional images of lifetime and absorption owing to the fluorophores.