Analytical Reconstruction Algorithm Research Articles

CdZnTe strip detector SPECT imaging with a slit collimator

In this paper, we propose a CdZnTe rotating and spinning gamma camera attached with a slit collimator. This imaging system acquires convergent planar integrals of a radioactive distribution. Two analytical image reconstruction algorithms are proposed. Preliminary phantom studies show that our small CdZnTe camera with a slit collimator outperforms a larger NaI(Tl) camera with a pinhole collimator in terms of spatial resolution in the reconstructed images. The main application of this system is small animal SPECT imaging.

Effect of compensation for scattering angular uncertainty in analytical Compton camera reconstruction

In Compton cameras, the measured scattering angle is associated with an uncertainty which becomes larger as the incident gamma-ray energy decreases. Since this uncertainty degrades the spatial resolution of reconstructed images, Hirasawa and Tomitani (2003 Phys. Med. Biol. 48 1009–26) previously revised their analytical reconstruction algorithm to compensate for it. As the new algorithm improved the spatial resolution in effect, they expected an enhancement of the statistical noise. In this paper, the effect of this compensation has been analysed in view of spatial resolution (the FWHM of the noise-free reconstructed image for a point source distribution), statistical noise (the relative standard deviation of reconstructed images for an isotropic source distribution) and image quality (the roughness of reconstructed images for a phantom). The results describe not only the effect of the compensation, but also the relation between the statistical noise and three parameters, i.e., the incident gamma-ray energy, the spatial resolution and the measured total event numbers, in reconstruction with compensation. This relation should be taken into account for the design of Compton cameras with good quality images, i.e., useful image, output.

Analytical image reconstruction of cone-beam projections from limited-angle Compton camera data

Since the integration of gamma-rays on a cone is measured with Compton cameras, some sort of image reconstruction method is necessary. Parra (2000) developed an analytical reconstruction algorithm based on a spherical harmonics expansion of projection data that covers the entire scattering-angle range. The measurable scattering angle range is limited due to the electrical noise of the detector and to the finite detector configuration. In this article, a reconstruction algorithm from the projection of a limited scattering angle range is presented. The algorithm was based on an inversion of the summed backprojection. The variance of the reconstructed image of a uniform source was calculated and found proportional to the third power of the number of expansion terms. Thus, window functions were introduced to suppress noise at the cost of spatial resolution. The dependency of the spatial resolution on the number of expansion terms was analyzed. From this, the dependency of the variance on the spatial resolution was found to be variance/spl prop/(spatial resolution)/sup -3/.

An analytical image reconstruction algorithm to compensate for scattering angle broadening in Compton cameras

Compton cameras have been developed for use in gamma-ray astronomy and nuclear medicine. Their defining merit is that they do not need collimators; however, on the demerit side, they need inversion procedures for image reconstruction, since a measured datum is proportional to the integration of incident gamma rays along a cone surface with the same Compton scattering angle. First, an iteration method was adopted for this task. Later, analytical methods were found under restricted conditions. Parra (2000 IEEE Trans. Nucl. Sci. 47 1543–50) deduced a purely analytical reconstruction algorithm for a complete set of scattering-projection data that include data at all the scattering angles. Tomitani and Hirasawa (2002 Phys. Med. Biol. 47 2129–45) found that by making a slight modification, Parra's algorithm could be extended to the scattering-projection data in limited scattering angles. However, their algorithm neglected the effects of practical problems that cause the degradation of spatial resolution. Sources of degradation were identified as noise in the energy signal of their front detector and the Doppler effect in the scattering process. In this paper, we first analyse the effects of these sources on the angular resolution of the scattering-projection data and then present a revised reconstruction algorithm in which these two factors are incorporated. Simulation studies on digital phantoms reveal that the algorithm can reconstruct images even when these two factors are included.

Analytic reconstruction algorithms in emission tomography with variable attenuation

Analytic reconstruction algorithms in emission tomography with variable attenuation

Rotating slant-hole single-photon emission-computed tomography

This dissertation presents a detailed investigation of the use of rotating slant-hole (RSH) collimators in single-photon emission-computed tomography(SPECT). We propose RSH SPECT as an alternative imaging technique, which may have advantages over more traditional SPECT techniques, in certain imaging applications. The basic imaging properties of RSH collimators are derived. This includes the derivation of expressions for the size and location of the common volume of view and the geometric resolution and efficiency. In addition, we derive an analytical expression for the geometric response and transfer functions of RSH collimators. The theoretical expressions for the aforementioned imaging characteristics are verified via Monte Carlo simulations and phantom experiments. Next, we present the development of a three-dimensional (3-D) analytic reconstruction algorithm for RSH SPECT. This includes the derivation of both a backprojection of the filtered projections and a filtering of the simple backprojections (BpjF) algorithm. The relationship between the derived 3-D RSH reconstruction filter and a number of other reconstruction filters is discussed. In addition, the implementation of the BpjF reconstruction algorithm is described and its performance is demonstrated via simulations and phantom experiments. We have also implemented an iterative ordered-subsets expectation-maximization (OS-EM) reconstruction algorithm for RSH SPECT. A detailed description of the development of the projector/backprojector employed by the OS-EM algorithm is provided. Simulation and phantom experiments are again used to demonstrate the performance of the projector/backprojector and the iterative OS-EM reconstruction algorithm. Rotating slant-hole SPECT has potential applications in cardiac and breast imaging. Thus, we demonstrate the feasibility, advantages, and disadvantages of using RSH SPECT via a comparison with conventional SPECT in a cardiac and breast imaging phantom experiment. In conclusion, we summarize the results presented and discuss their implications on the current and future state of RSH SPECT research.

Attenuation and scatter correction of list-mode data driven iterative and analytic image reconstruction algorithms for rotating 3D PET systems

Image reconstruction directly from list-mode data requires different data correction techniques to standard projection-data based reconstruction, particularly in the case of iterative reconstruction. Attenuation and scatter correction techniques have been developed for two list-mode data driven reconstruction algorithms (FAIR-B (iterative) and Atrax (analytic/iterative)) recently proposed by the authors, and the results compared with two fast projection-data based algorithms (FORE+OSEM (iterative) and FORE+FBP (analytic)). List-mode data driven algorithms require event-by-event correction schemes, or alternatively image space procedures, as no direct operations to the completely sampled projection data set can be practically carried out. The methods developed in this work allow correction of list-mode data driven EM-ML type algorithms, such as FAIR, as well as analytic list-mode algorithms. The correction schemes have been applied to simulated data from various activity and attenuating medium distributions for a rotating 3D PET system. Both list-mode algorithms show some improvements in noise-contrast behaviour compared to the projection-data based methods.

Iterative and analytical reconstruction algorithms for varying-focal-length cone-beam projections

In single photon emission computed tomography (SPECT), a varying-focal-length cone-beam collimator can be used to reduce the truncation problem and to maintain sensitivity when imaging the organ of interest. The collimator is constructed so that the collimator holes focus to a circular symmetric, spatially varying, focal point function. The focal length increases radially from the shortest focal length at the centre to the longest focal length at the periphery of the collimator. This paper describes a 3D backprojection-filtering (BF) algorithm for this varying-focal-length cone-beam geometry. The proposed algorithm is compared to an iterative ML-EM (maximum likelihood-expectation maximization) algorithm. The 3D Hoffman brain phantom and Defrise phantom are used in computer simulations. Since the maximum tilt angle of the projection rays is small for most realistic imaging geometries, the proposed algorithm provides a good approximation. When a circular orbit is used, the BF algorithm gives an exact reconstruction of the central slice.

Comparative Study on Analytical Reconstruction Algorithm of SPECT

Comparative Study on Analytical Reconstruction Algorithm of SPECT

A multifocal collimator with circularly distributed focal points for SPECT imaging

Proposes a new circular multifocal collimator which has multiple axial focal points distributed on a transverse circle. This distribution provides a strong focusing at the center of the detector like a cone-beam collimator, with a good sensitivity, and a weak transverse focusing at the periphery, to ensure acquisition of sufficient data, in order to prevent truncation artifacts. For a circular acquisition trajectory, each projection set of the multifocal geometry is equivalent to a virtual cone-beam projection set with a larger detector. Due to this equivalence, the authors derive a first solution for an analytical multifocal reconstruction algorithm: to rebin the projection set from multifocal to cone-beam geometry, then to use a 3D cone-beam reconstruction algorithm. The authors propose to use the Grangeat algorithm in order to deal with a large cone-beam aperture. Finally, they present results on simulated data for heart phantom, for a Defrise phantom and for a MTF study. The conclusion is that, from a multifocal projection set, objects are reconstructed without truncation artifacts, with a good precision at their center and with a loss of resolution at the periphery. In addition, the 3D cone-beam artifacts are reduced with the use of the Grangeat algorithm for the reconstruction step.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Implementation of Tuy's cone-beam inversion formula

Tuy's cone-beam inversion formula (see SIAM J. appl. math., vol.43, p.546-52, 1983) was modified to develop a cone-beam reconstruction algorithm. The algorithm was implemented for a cone-beam vertex orbit consisting of a circle and two orthogonal lines. This orbit geometry satisfies the cone-beam data sufficiency condition and is easy to implement on commercial single photon emission computed tomography (SPECT) systems. The algorithm, which consists of two derivative steps, one rebinning step, and one three-dimensional backprojection step, was verified by computer simulations and by reconstructing physical phantom data collected on a clinical SPECT system. The proposed algorithm gives equivalent results and is as efficient as other analytical cone-beam reconstruction algorithms.

Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry

A new analytical three-dimensional cone beam reconstruction algorithm is presented for truncated spherical detection geometry. The basic idea of the proposed algorithm is the formation of spatially invariant 3D blurred back-projected volumetric image by the use of the weighted backprojection of cone beam projection data and subsequent 3D filtering using an acceptance angle dependent rho filter. The backprojection weighting function is calculated on the basis of each given geometrical condition, i.e. detection geometry or degree of truncation, position of cone beam apex, and backprojection point. The proposed algorithm is derived analytically and is computationally efficient. Performance of the algorithm is evaluated by the reconstruction of 3D volumetric images using simulated data from arbitrarily truncated spherical detector geometries.

An analytical reconstruction algorithm for multifocal converging-beam SPECT

Multifocal converging-beam collimation has been suggested for cardiac SPECT imaging to increase sensitivity over the heart without truncation of the activity distribution in the chest. In this study, an analytical reconstruction algorithm is derived for multifocal fan-beam and multifocal cone-beam tomography. In the algorithm, the projection data are differently weighted and filtered, depending on the distance from the detector. For a given image point, the set of filtered data corresponding to the distance between this point and detector is backprojected to determine the pixel value of the point. Thus, the backprojection is done only once at each projection view. To evaluate the algorithm, simulation studies are performed using a 3D Defrise slab phantom without considering photon attenuation and scatter, detector response, and statistical noise. Reconstructed images demonstrate that reasonable quality can be achieved with a modest focal-length variation rate and with a small radius of rotation. A collimator with a focal length increasing quickly near its centre provides better quality in the image region distant from the central plane of the cone geometry, but produces more severe artifacts at the centre of the reconstructed image, compared to a collimator with an initially slowly varying focal length.