Rebinning Algorithm Research Articles

Study of large axial space rebinning algorithm in γ-photon industrial tomography image reconstruction

The accuracy of the existing single slice and Fourier rebinning algorithms depends on the projection angle of the line of response. The increase of such projection angle with the detector size, typical in the large axial space of γ-photon industrial detection, and the loss of some projection data after rebinning, result in the degradation of the image quality. In addition, those algorithms consider the probability of positron annihilation equally distributed along the line of response, which prevents to estimate accurately the positions of the annihilation point, and can originate artifacts and noise in the reconstructed image. In this work, we propose an alternative large axial space rebinning algorithm. In that algorithm, initially the line of response is divided into transverse and axial components. Then, each line of response is uniformly rebinned into all the 2D sinogram data intersecting with it. To improve the accuracy of the estimate of the annihilation point location and suppress the noise effectively, we assign a Gaussian weight coefficient to the projection data, and optimise the rebinning algorithm with it. Finally, we reconstruct the image on the basis of the 2D sinograms with the optimised weights. On the computational side, the algorithm is also accelerated by making use of parallel computing. Both simulation and experimental results show that the proposed method improves the contrast and spatial resolution of 2D reconstructed images. Furthermore, the reconstruction time is not affected by the new method, which is therefore expected to meet the demand of γ-photon industrial inspection imaging.

High resolution reconstruction of PET images using the iterative OSEM algorithm

Improvement of the spatial resolution in positron emission tomography (PET) by incorporation of the image-forming characteristics of the scanner into the process of iterative image reconstruction. All measurements were performed at the whole-body PET system ECAT EXACT HR(+) in 3D mode. The acquired 3D sinograms were sorted into 2D sinograms by means of the Fourier rebinning (FORE) algorithm, which allows the usage of 2D algorithms for image reconstruction. The scanner characteristics were described by a spatially variant line-spread function (LSF), which was determined from activated copper-64 line sources. This information was used to model the physical degradation processes in PET measurements during the course of 2D image reconstruction with the iterative OSEM algorithm. To assess the performance of the high-resolution OSEM algorithm, phantom measurements performed at a cylinder phantom, the hotspot Jaszczack phantom, and the 3D Hoffmann brain phantom as well as different patient examinations were analyzed. Scanner characteristics could be described by a Gaussian-shaped LSF with a full-width at half-maximum increasing from 4.8 mm at the center to 5.5 mm at a radial distance of 10.5 cm. Incorporation of the LSF into the iteration formula resulted in a markedly improved resolution of 3.0 and 3.5 mm, respectively. The evaluation of phantom and patient studies showed that the high-resolution OSEM algorithm not only lead to a better contrast resolution in the reconstructed activity distributions but also to an improved accuracy in the quantification of activity concentrations in small structures without leading to an amplification of image noise or even the occurrence of image artifacts. The spatial and contrast resolution of PET scans can markedly be improved by the presented image restauration algorithm, which is of special interest for the examination of both patients with brain disorders and small animals.

Fan-beam geometry based inversion algorithm in computed tomography (CT) for imaging of composite materials

The investigation is concerned first with reconstruction of the density function of an object from computed tomography data. The projection (Fourier Slice) theorem is discussed for fan-beam geometry. A rebinning algorithm, based on the slant stacking approach, is introduced in order to transform fan-beam geometry data into its parallel-beam counterpart. The density function is reconstructed using a filtered back-projection algorithm. The sampling criteria for fan beam computed tomography are also derived. The MATLAB package has been utilized to implement these algorithms for the simulation of Shepp–Logan head phantom and implementation of the discrete normal Radon transform based on fan-beam geometry. The reconstruction of transverse cross-sectional micro-structures of fiber reinforced composite material test specimens has also been discussed. In addition, the MATLAB package has been utilized to demonstrate the image reconstruction of the cross-section of a two-phase composite material using parallel beam geometry (Radon transform).

The usefulness of fully three-dimensional OSEM algorithm on lymph node metastases from lung cancer with 18F-FDG PET/CT

This work assessed the usefulness of fully three-dimensional ordered subset expectation maximization (3D-OSEM) algorithm for lymph node (LN) metastases from lung cancer. 3D-OSEM images were evaluated by comparing them with those reconstructed by conventional algorithms, such as conventional OSEM algorithm (2D-OSEM) for 2D acquisition and Fourier rebinning plus conventional OSEM algorithm (FORE + OSEM) for 3D acquisition. In a phantom study, the contrast ratio, the image noise and the signal-to-noise ratio (SNR) were calculated, and the detectability and the image quality of these images were visually evaluated. In a clinical study, 14 patients suffering from lung cancer with LN metastases were evaluated. The image quality and the malignancy, and the detectability were visually evaluated. The contrast ratio was significantly improved using 3D-OSEM as compared with FORE + OSEM, and it was similar to 2D-OSEM. The image noise and SNR in 3D-OSEM images were significantly improved compared with those by other algorithms (p < 0.001). In the visual assessment, the image quality was significantly improved in 3D-OSEM images compared with those by 2D-OSEM and FORE + OSEM (p < 0.001, p = 0.001, respectively). In the clinical study, the image quality and the detectability of LN metastases were improved in 3D-OSEM images compared with those by FORE + OSEM (p < 0.001, p = 0.006, respectively), and image quality and detectability were similar to those of 2D-OSEM images. 3D-OSEM algorithm successfully improved the diagnostic accuracy of LN metastases in 3D-PET tests.

Advancements to the planogram frequency–distance rebinning algorithm

In this paper we consider the task of image reconstruction in positron emission tomography (PET) with the planogram frequency–distance rebinning (PFDR) algorithm. The PFDR algorithm is a rebinning algorithm for PET systems with panel detectors. The algorithm is derived in the planogram coordinate system which is a native data format for PET systems with panel detectors. A rebinning algorithm averages over the redundant four-dimensional set of PET data to produce a three-dimensional set of data. Images can be reconstructed from this rebinned three-dimensional set of data. This process enables one to reconstruct PET images more quickly than reconstructing directly from the four-dimensional PET data. The PFDR algorithm is an approximate rebinning algorithm. We show that implementing the PFDR algorithm followed by the (ramp) filtered backprojection (FBP) algorithm in linogram coordinates from multiple views reconstructs a filtered version of our image. We develop an explicit formula for this filter which can be used to achieve exact reconstruction by means of a modified FBP algorithm applied to the stack of rebinned linograms and can also be used to quantify the errors introduced by the PFDR algorithm. This filter is similar to the filter in the planogram filtered backprojection algorithm derived by Brasse et al. The planogram filtered backprojection and exact reconstruction with the PFDR algorithm require complete projections which can be completed with a reprojection algorithm. The PFDR algorithm is similar to the rebinning algorithm developed by Kao et al. By expressing the PFDR algorithm in detector coordinates, we provide a comparative analysis between the two algorithms. Numerical experiments using both simulated data and measured data from a positron emission mammography/tomography (PEM/PET) system are performed. Images are reconstructed by PFDR+FBP (PFDR followed by 2D FBP reconstruction), PFDRX (PFDR followed by the modified FBP algorithm for exact reconstruction) and planogram filtered backprojection image reconstruction algorithms. We show that the PFDRX algorithm produces images that are nearly as accurate as images reconstructed with the planogram filtered backprojection algorithm and more accurate than images reconstructed with the PFDR+FBP algorithm. Both the PFDR+FBP and PFDRX algorithms provide a dramatic improvement in computation time over the planogram filtered backprojection algorithm.

Continuous and Discrete Data Rebinning in Time-of-Flight PET

This paper investigates data compression methods for time-of-flight (TOF) positron emission tomography (PET), which rebin the 3-D TOF measurements into a set of 2-D TOF data for a stack of transaxial slices. The goal of this work is to develop rebinning algorithms that are more accurate than the TOF single-slice-rebinning (TOF-SSRB) method proposed by Mullani in 1982. Two approaches are explored. The first one is based on a partial differential equation, which expresses a consistency condition for TOF-PET data with a Gaussian TOF profile. From this equation we derive an analytical rebinning algorithm, which is unbiased in the limit of continuous sampling. The second approach is discrete: each 2-D rebinned data sample is calculated as a linear combination of the 3-D TOF samples in the same axial plane parallel to the axis of the scanner. The coefficients of the linear combination are precomputed by optimizing a cost function which enforces both accuracy and good variance reduction, models the TOF profile, the axial PSF of the LORs, and the specific sampling scheme of the scanner. Measurements of a thorax phantom on a prototype TOF-PET scanner with a resolution of 550 ps show that the proposed discrete method improves the bias-variance trade-off and is a promising alternative to TOF-SSRB when data compression is required to achieve clinically acceptable reconstruction time.

Planogram rebinning with the frequency-distance relationship

We present an efficient rebinning algorithm for positron emission tomography (PET) systems with panel detectors. The rebinning algorithm is derived in the planogram coordinate system which is the native data format for PET systems with panel detectors and is the 3-D extension of the 2-D linogram transform developed by Edholm. Theoretical error bounds and numerical results are included.

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.

Fourier rebinning of time-of-flight PET data

This paper explores fast reconstruction strategies for 3D time-of-flight (TOF) positron emission tomography (PET), based on 2D data rebinning. Starting from pre-corrected 3D TOF data, a rebinning algorithm estimates for each transaxial slice the 2D TOF sinogram that would have been acquired by a single-ring scanner. The rebinned sinograms can then be reconstructed using any algorithm for 2D TOF reconstruction. We introduce TOF-FORE, an approximate rebinning algorithm obtained by extending the Fourier rebinning method for non-TOF data. In addition, we identify two partial differential equations that must be satisfied by consistent 3D TOF data, and use them to derive exact rebinning algorithms and to characterize the degree of the approximation in TOF-FORE. Numerical simulations demonstrate that TOF-FORE is more accurate than two different TOF extensions of the single-slice rebinning method, and suggest that TOF-FORE will be a valuable tool for practical TOF PET in the range of axial apertures and time resolutions typical of current scanners.

Image reconstruction based on Fourier-rebinning for a novel high resolution ClearPET Neuro scanner

At present a high-resolution PET scanner (ClearPET Neuro) is constructed at the Research Centre Jülich. While human PET systems have a spatial resolution of 5–7 mm, high resolution PET needs a resolution of < 2 mm and a high sensitivity which is achieved e.g. by taking data in fully 3D mode. The Fourier- Rebinning algorithm (FORE) is a procedure that sorts the 3D data into a 2D data set. The 3D image is then recovered by applying a 2D reconstruction method to each slice, such as filtered back projection. FORE is approximate, but allows an efficient implementation, based on the 2D Fourier transformation of the data [M. Defrise, et al., Exact and approximate rebinning algorithms for 3-D PET Data, IEEE Trans. Med. Imag. 16 (1997) 145–158] and speeds up the reconstruction time significantly.

Respiratory reordered UNFOLD perfusion imaging

To propose a respiratory reordered UNFOLD (RR-UNFOLD) imaging sequence to significantly reduce the amount of k-space data required for first-pass MR myocardial perfusion imaging. Rapid acquisition of high-resolution imaging data is essential to detailed quantitative analysis of first-pass myocardial perfusion. Existing MR sequences have explored the full capacity of the imaging hardware to reduce the acquisition window within each cardiac cycle while maintaining the desired spatial resolution. Further improvement in perfusion imaging will require a more efficient use of the information content of the k-space data. The method uses prospective diaphragmatic navigator echoes to ensure that temporal filtering of UNFOLD is carried out on a series of images that are spatially registered. An adaptive real-time rebinning algorithm is developed for the creation of static image subseries related to different levels of respiratory motion. Issues concerning the temporal smoothing of tracer kinetic signals are discussed, and a solution based on oversampling of the central k-space is provided. The method is assessed in 10 normal subjects without the administration of contrast agent, and further validated by administration of Gd-DTPA in 10 patients at rest. The results of this study show that RR-UNFOLD significantly extends the applicability of UNFOLD to perfusion imaging, which yields a 40% reduction in image artifact when the same amount of k-space information is used. The scan efficiency achieved can be used in combination with MR hardware improvements for extending the three-dimensional spatial coverage and shortening the data acquisition window to provide detailed information on regional myocardial perfusion abnormalities.

High resolution reconstruction of PET images using the iterative OSEM algorithm

Summary Aim: Improvement of the spatial resolution in positron emission tomography (PET) by incorporation of the image-forming characteristics of the scanner into the process of iterative image reconstruction. Methods: All measurements were performed at the whole-body PET system ECAT EXACT HR+ in 3D mode. The acquired 3D sinograms were sorted into 2D sinograms by means of the Fourier rebinning (FORE) algorithm, which allows the usage of 2D algorithms for image reconstruction. The scanner characteristics were described by a spatially variant line-spread function (LSF), which was determined from activated copper-64 line sources. This information was used to model the physical degradation processes in PET measurements during the course of 2D image reconstruction with the iterative OSEM algorithm. To assess the performance of the high-resolution OSEM algorithm, phantom measurements performed at a cylinder phantom, the hotspot Jaszczack phantom, and the 3D Hoffmann brain phantom as well as different patient examinations were analyzed. Results: Scanner characteristics could be described by a Gaussian-shaped LSF with a full-width at half-maximum increasing from 4.8 mm at the center to 5.5 mm at a radial distance of 10.5 cm. Incorporation of the LSF into the iteration formula resulted in a markedly improved resolution of 3.0 and 3.5 mm, respectively. The evaluation of phantom and patient studies showed that the high-resolution OSEM algorithm not only lead to a better contrast resolution in the reconstructed activity distributions but also to an improved accuracy in the quantification of activity concentrations in small structures without leading to an amplification of image noise or even the occurrence of image artifacts. Conclusion: The spatial and contrast resolution of PET scans can markedly be improved by the presented image restauration algorithm, which is of special interest for the examination of both patients with brain disorders and small animals.

Improved two-dimensional rebinning of helical cone-beam computerized tomography datausing John’s equation

This paper deals with three-dimensional (3D) image reconstruction for helical computerizedtomography with multi-row detectors. We describe a method to improve the accuracy ofthe rebinning algorithms, which separate 3D reconstruction into independent 2Dreconstructions for a set of oblique slices. Each oblique slice is reconstructed from anestimate of its 2D Radon transform obtained from the cone-beam projections acquiredwhile the x-ray source moves along a segment of the helix. Because this helixsegment is not contained within the oblique slice, the estimated 2D Radon transformis approximate. In theory, exact rebinning could be achieved by solving John’spartial differential equation to virtually move the x-ray source within the obliqueslice. In contrast with previous work by Patch (2002 IEEE Trans. Med. Imaging 21801–13), we do not attempt to solve John’s equation exactly. Instead, we use John’sequation to compute a first order correction to the rebinning algorithm. Testswith simulated data demonstrate a significant improvement of image quality,obtained with a negligible increase of the computation time and of the sensitivity tonoise.

Favorable noise uniformity properties of Fourier-based interpolation and reconstruction approaches in single-slice helical computed tomography.

Volumes reconstructed by standard methods from single-slice helical computed tomography (CT) data have been shown to have noise levels that are highly nonuniform relative to those in conventional CT. These noise nonuniformities can affect low-contrast object detectability and have also been identified as the cause of the zebra artifacts that plague maximum intensity projection (MIP) images of such volumes. While these spatially variant noise levels have their root in the peculiarities of the helical scan geometry, there is also a strong dependence on the interpolation and reconstruction algorithms employed. In this paper, we seek to develop image reconstruction strategies that eliminate or reduce, at its source, the nonuniformity of noise levels in helical CT relative to that in conventional CT. We pursue two approaches, independently and in concert. We argue, and verify, that Fourier-based longitudinal interpolation approaches lead to more uniform noise ratios than do the standard 360LI and 180LI approaches. We also demonstrate that a Fourier-based fan-to-parallel rebinning algorithm, used as an alternative to fanbeam filtered backprojection for slice reconstruction, also leads to more uniform noise ratios, even when making use of the 180LI and 360LI interpolation approaches.

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.

A fast rebinning algorithm for 3D positron emission tomography using John's equation

Volume imaging in positron emission tomography (PET) requires the inversion of the three-dimensional (3D) x-ray transform. The usual solution to this problem is based on 3D filtered-backprojection (FBP), but is slow. Alternative methods have been proposed which factor the 3D data into independent 2D data sets corresponding to the 2D Radon transforms of a stack of parallel slices. Each slice is then reconstructed using 2D FBP. These so-called rebinning methods are numerically efficient but are approximate. In this paper a new exact rebinning method is derived by exploiting the fact that the 3D x-ray transform of a function is the solution to the second-order partial differential equation first studied by John. The method is proposed for two sampling schemes, one corresponding to a pair of infinite plane detectors and another one corresponding to a cylindrical multi-ring PET scanner. The new FORE-J algorithm has been implemented for this latter geometry and was compared with the approximate Fourier rebinning algorithm FORE and with another exact rebinning algorithm, FOREX. Results with simulated data demonstrate a significant improvement in accuracy compared to FORE, while the reconstruction time is doubled. Compared to FOREX, the FORE-J algorithm is slightly less accurate but more than three times faster.

Data processing and image reconstruction methods for the HEAD PENN-PET scanner

Methods of reconstruction and quantitation are developed for a 3D system and are evaluated on the septa-less HEAD PENN-PET scanner, which has a very large axial acceptance angle (/spl theta//sub max/=/spl plusmn/28/spl deg/ in the center) and large axial field-of-view of 256 mm. To overcome the difficulties of data storage and reconstruction time with 3D reconstruction, the authors have reduced the size of the 4-D projection matrix required for 3D-RP reconstruction, and compared the results to the Fourier rebinning (FORE) algorithm. Both approaches achieve a favorable tradeoff in data storage requirements, reconstruction time, and accuracy that are suitable for clinical use. The authors have also studied the application of the FORE algorithm to transmission scans acquired with a single point source (/sup 137/Cs) so that data quantitation can be performed.

Combination of Wiener filtering and singular value decomposition filtering for volume imaging PET

Although the three-dimensional (3D) multi-slice rebinning (MSRB) algorithm in PET is fast and practical, and provides an accurate reconstruction, the MSRB image, in general, suffers from the noise amplified by its singular value decomposition (SVD) filtering operation in the axial direction. Our aim in this study is to combine the use of the Wiener filter (WF) with the SVD to decrease the noise and improve the image quality. The SVD filtering deconvolves the spatially variant axial response function while the WF suppresses the noise and reduces the blurring not modeled by the axial SVD filter but included in the system modulation transfer function. Therefore, the synthesis of these two techniques combines the advantages of both filters. We applied this approach to the volume imaging HEAD PENN-PET brain scanner with an axial extent of 256 mm. This combined filter was evaluated in terms of spatial resolution, image contrast, and signal-to-noise ratio with several phantoms, such as a cold sphere phantom and 3D brain phantom. Specifically, we studied both the SVD filter with an axial Wiener filter and the SVD filter with a 3D Wiener filter, and compared the filtered images to those from the 3D reprojection (3DRP) reconstruction algorithm. Our results indicate that the Wiener filter increases the signal to noise ratio and also improves the contrast. For the MSRB images of the 3D brain phantom, after 3D WF, both the Gray/White and Gray/Ventricle ratios were improved from 1.8 to 2.8 and 2.1 to 4.1, respectively. In addition, the image quality with the MSRB algorithm is close to that of the 3DRP algorithm with 3D WF applied to both image reconstructions. >