Advanced Single-slice Rebinning Research Articles

A Practical Statistical Approach to the Reconstruction Problem Using a Single Slice Rebinning Method

Abstract The paper presented here describes a new practical approach to the reconstruction problem applied to 3D spiral x-ray tomography. The concept we propose is based on a continuous-to-continuous data model, and the reconstruction problem is formulated as a shift invariant system. This original reconstruction method is formulated taking into consideration the statistical properties of signals obtained by the 3D geometry of a CT scanner. It belongs to the class of nutating reconstruction methods and is based on the advanced single slice rebinning (ASSR) methodology. The concept shown here significantly improves the quality of the images obtained after reconstruction and decreases the complexity of the reconstruction problem in comparison with other approaches. Computer simulations have been performed, which prove that the reconstruction algorithm described here does indeed significantly outperforms conventional analytical methods in the quality of the images obtained.

Анализ трехмерных алгоритмов реконструкции в рентгеновской компьютерной томографии

The article analyzes the existing three-dimensional image reconstruction algorithms in conebeam X-ray computed tomography with a spiral trajectory of the source. The main approaches to the design of the reconstruction algorithms are considered, their brief classification is given. The focus is on approximate Feldcamp-type algorithms and methods of rebinning cone data to parallel geometry. The extended parallel backprojection and advanced single-slice rebinning algorithms, their advantages and disadvantages are described. The authors have considered the exact methods for solving image reconstruction problem for the 3D data set in cone-beam CT. The author describes the additional conditions imposed on the projection data, the computational efficiency of the algorithms, and the quality of the images. The emphasis is on relation between the cone beam and Radon transform and the classical 3D Radon transform inversion. The general scheme for constructing inversion algorithms for cone beam CT is described. The algorithm of cone-beam reconstruction by backprojection and filtering is considered. The advantages and disadvantages of exact reconstruction algorithms are presented.

К вопросу разработки методов реконструкции изображений в рентгеновской компьютерной томографии с конусным пучком излучения

The article reflects the main task of the X-ray computed tomography and its mathematical description. Direct and inverse Radon transform are given. The methods of image reconstruction in X-ray computed tomography are presented. Their brief classification are given. The author have reviewed classical problem of two-dimensional computed tomography and basics approaches to its solution. Emphasis is placed on back projection algorithm with filtering convolution. The derivation of the algorithm for parallel and fan-beam reconstruction are given. The analysis of the problem of three-dimensional reconstruction are presented. The author describes the additional conditions imposed on the projection data, the computational efficiency of the algorithms and the quality of the images. The basic trajectory of the X-ray source, providing the condition Tuy, are considered. The article gives an overview of existing methods of three-dimensional reconstruction with cone-beam geometry, their advantages, disadvantages, clinical applications. Their brief classification are given. Approximate algorithms of three-dimensional reconstruction are presented. The Feldkamp algorithm, the extended parallel backprojection, and the advanced single-slice rebinning are described. The author raises the question of developing approaches and methods for obtaining images with three-dimensional reconstruction for cone-beam spiral CT.

Radiation dose reduction in medical x‐ray CT via Fourier‐based iterative reconstruction

A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

Variable Pitch Reconstruction Using John's Equation

We present an algorithm to reconstruct helical cone beam computed tomography (CT) data acquired at variable pitch. The algorithm extracts a halfscan segment of projections using an extended version of the advanced single slice rebinning (ASSR) algorithm. ASSR rebins constant pitch cone beam data to fan beam projections that approximately lie on a plane that is tilted to optimally fit the source helix. For variable pitch, the error between the tilted plane chosen by ASSR and the source helix increases, resulting in increased image artifacts. To reduce the artifacts, we choose a reconstruction plane, which is tilted and shifted relative to the source trajectory. We then correct rebinned fan beam data using John's equation to virtually move the source into the tilted and shifted reconstruction plane. Results obtained from simulated phantom images and scanner images demonstrate the applicability of the proposed algorithm.

Optoelectronic implementation of helical cone-beam computed tomography algorithms

This paper presents a hybrid processor dedicated to the reconstruction algorithm in multislice spiral computed tomography. The described architecture focuses on the advanced single-slice rebinning algorithm, which is a basic 2-D-to-3-D rebinning method developed in 2000. The hybrid processor is composed of four cores (rebinning, filtering, backprojection, and interpolation), including an optical processor for the backprojection. The system is modeled with a multi-abstraction-level approach. The model permits one to evaluate the dependence of both the reconstruction quality and the computation time with different parameters (reconstruction parameters, device features, etc.). It is used in a substantial simulation process allowing the identification of predominant degradation sources and the evaluation of their impact, and leading to the specification of each subsystem. A prototype of each core has been realized. The optical core has been identified as the most critical element, although results are very encouraging. This study has underlined that a computational speedup of more than two orders of magnitude could be reached. This is expected to be very useful for future challenging applications in the field of image-guided computer-assisted surgery, where the reconstruction rate would become critical to ensuring acceptable responsiveness.

AAPM Recognizes Contributions to Medical Physics

The American Association of Physicists in Medicine presented its awards for 2001 at its annual meeting held in Salt Lake City, Utah, in July. Ravinder Nath, a professor and chief of the department of therapeutic radiology at the Yale University School of Medicine, received the William D. Coolidge Award. This award is the society’s highest honor, given in recognition of a distinguished career in medical physics. The citation praised Nath for his significant contributions to advances in radiation medicine, to AAPM and other organizations that deal with medical applications of physics, and to the medical physics literature.The Farrington Daniels Award, given for the best paper on radiation dosimetry published in Medical Physics during the previous year, went to Iwan Kawrakow for his paper entitled “Accurate Condensed History Monte Carlo Simulation of Electron Transport I: EGSnrc, The New EGS4 Version.” Kawrakow is a research officer in the ionizing radiation standards department at the National Research Council’s Institute for National Measurement Standards in Ottawa, Ontario.Two Sylvia Sorkin Greenfield Awards, given for the best paper (other than radiation dosimetry) published in Medical Physics during the previous year, were presented at the meeting. The first was shared by Marc Kachelriess, Stefan Schaller, and Willi Kalender for their paper entitled “Advanced Single-Slice Rebinning in Cone-Beam Spiral CT.” Schaller is head of applications pre-development in the computer tomography division at Siemens in Forchheim, Germany. Kalender is director of, and a professor of medical physics at, the Institute of Medical Physics at the University of Erlangen-Nürnberg in Germany. Kachelriess is a physicist at the same institute.The second Greenfield Award went to David Jaffray and Jeffrey Siewerdsen for their paper entitled “Cone-Beam Computed Tomography with a Flat-Panel Imager: Initial Performance Characterization.” Jaffray is a staff physicist and Siewerdsen is a senior research scientist in the radiation oncology department at William Beaumont Hospital in Royal Oak, Michigan. Nath PPT|High resolution© 2001 American Institute of Physics.

Advanced single-slice rebinning for tilted spiral cone-beam CT.

Future medical CT scanners and today's micro CT scanners demand cone-beam reconstruction algorithms that are capable of reconstructing data acquired from a tilted spiral trajectory where the vector of rotation is not necessarily parallel to the vector of table increment. For the medical CT scanner this case of nonparallel object motion is met for nonzero gantry tilt: the table moves into a direction that is not perpendicular to the plane of rotation. Since this is not a special application of medical CT but rather a daily routine in head exams, there is a strong need for corresponding reconstruction algorithms. In contrast to medical CT, where the special case of nonperpendicular motion is used on purpose, micro CT scanners cannot avoid aberrations of the rotational axis and the table increment vector due to alignment problems. Especially for those micro CT scanners that have the lifting stage mounted on the rotation table (in contrast to setups where the lifting stage holds the rotation table), this kind of misalignment is equivalent to a gantry tilt. We therefore generalize the advanced single-slice rebinning algorithm (ASSR), which is considered a very promising approach for medical cone-beam reconstruction due to its high image quality and its high reconstruction speed [Med. Phys. 27, 754-772 (2000)], to the case of tilted gantries. We evaluate this extended ASSR approach (which we will denote as ASSR+, for convenience) in comparison to the original ASSR algorithm using simulated phantom data for reconstruction. For the case of nonparallel object motion ASSR+ shows significant improvements over ASSR, however, its computational complexity is slightly increased due to the broken symmetry of the spiral trajectory.

Advanced single-slice rebinning in cone-beam spiral CT.

To achieve higher volume coverage at improved z-resolution in computed tomography (CT), systems with a large number of detector rows are demanded. However, handling an increased number of detector rows, as compared to today's four-slice scanners, requires to accounting for the cone geometry of the beams. Many so-called cone-beam reconstruction algorithms have been proposed during the last decade. None met all the requirements of the medical spiral cone-beam CT in regard to the need for high image quality, low patient dose and low reconstruction times. We therefore propose an approximate cone-beam algorithm which uses virtual reconstruction planes tilted to optimally fit 180 degrees spiral segments, i.e., the advanced single-slice rebinning (ASSR) algorithm. Our algorithm is a modification of the single-slice rebinning algorithm proposed by Noo et al. [Phys. Med. Biol. 44, 561-570 (1999)] since we use tilted reconstruction slices instead of transaxial slices to approximate the spiral path. Theoretical considerations as well as the reconstruction of simulated phantom data in comparison to the gold standard 180 degrees LI (single-slice spiral CT) were carried out. Image artifacts, z-resolution as well as noise levels were evaluated for all simulated scanners. Even for a high number of detector rows the artifact level in the reconstructed images remains comparable to that of 180 degrees LI. Multiplanar reformations of the Defrise phantom show none of the typical cone-beam artifacts usually appearing when going to larger cone angles. Image noise as well as the shape of the respective slice sensitivity profiles are equivalent to the single-slice spiral reconstruction, z-resolution is slightly decreased. The ASSR has the potential to become a practical tool for medical spiral cone-beam CT. Its computational complexity lies in the order of standard single-slice CT and it allows to use available 2D backprojection hardware.

Single-slice rebinning reconstruction in spiral cone-beam computed tomography.

At the advent of multislice computed tomography ICT) a variety of approximate cone-beam algorithms have been proposed suited for reconstruction of small cone-angle CT data in a spiral mode of operation. The goal of this study is to identify a practical and efficient approximate cone-beam method, extend its potential for medical use, and demonstrate its performance at medium cone-angles required for area detector CT. We will investigate two different approximate single-slice rebinning algorithms for cone-beam CT: the multirow Fourier reconstruction (MFR) and an extension of the advanced single-slice rebinning method (ASSR), which combines the idea of ASSR with a z-filtering approach. Thus, both algorithms, MFR and ASSR, are formulated in the framework of z-filtering using optimized spiral interpolation algorithms. In each view, X-ray samples to be used for reconstruction are identified, which describe an approximation to a virtual reconstruction plane. The performance of approximate reconstruction should improve as the virtual reconstruction plane better fits the spiral focus path. The image quality of the respective reconstruction will be assessed with respect to image artifacts, spatial resolution, contrast resolution, and image noise. It turns out that the ASSR method using tilted reconstruction planes is a practical and efficient algorithm, providing image quality comparable to that of a single-row scanning system even with a 46-row detector at a table feed of 64 mm. Both algorithms tolerate any table feed below the maximum value associated to the detector height. Due to the z-filter approach, all detector data sampled can be used for image reconstruction.