A Novel Binary Slime Mould Algorithm with AU Strategy for Cognitive Radio Spectrum Allocation

Spectrum has now become a scarce resource due to the continuous development of wireless communication technology. Cognitive radio technology is considered to be a new method to solve the shortage of spectrum resources. The spectrum allocation model of cognitive radio can effectively avoid the waste of spectrum resources. A novel binary version of slime mould algorithm is proposed for the spectrum allocation model to solve the spectrum allocation scheme. In addition, adding unselected factors strategy can make the approach find a better solution. Compared with other algorithms, the novel binary slime mould algorithm and the strategy of adding unselected factors proposed in this paper have a good performance in spectrum allocation. The resulting spectrum allocation scheme can achieve efficient use of network resources.

Survey of psychiatric impairment among residents exposed to environmental pollution from a petrochemical complex

PURPOSE

This study first assessed the occurrence of major depressive disorder (MDD), post-traumatic stress disorder (PTSD), symptoms of poor sleep quality and high levels of distress among residents, caused by reported long-term stress from environmental pollution emitted from the biggest petroleum chemistry factory (PCF) in the world.

METHODS

A total of 328 long-term residents (Mean age = 57.5, SD = 16.5 years, ranging from 22 to 95) were recruited randomly from a total population of 26,632 in Mailiao township in Taiwan next to the PCF. Trained assistants used the Disaster-Related Psychological Screening test, the Perception of Life Threats Caused by the SCNP questionnaire and the Sleep Quality Scale to interview the participants.

RESULTS

The results support our hypotheses that most of the residents (71%) would report life threats caused by the PCF. The residents displayed higher rates of major depressive episodes (24.1%), PTSD (24.5%) and symptoms of poor sleep quality. The more they felt threat from the PCF, the stronger the connection with MDD and PTSD symptoms.

CONCLUSION

The results indicate an increased prevalence of MDD, PTSD and symptoms of poor sleep quality in those exposed to environmental pollution from the PCF, highlighting the need for prompt prevention, diagnostic and therapeutic attention.

[Cloning and expression analysis of two pro-inflammatory cytokines, IL-1β and its receptor, IL-1R2, in the Asian swamp eel Monopterus albus]

Interleukin-1β (IL-1β) is the prototypic pro-inflammatory cytokine, whose functions are mediated through interaction with its receptors (IL-1R1 and IL-1R2). Herein, we cloned the full-length cDNA and genomic DNA of IL-1β and IL-1R2 in the Asian swamp eel (Monopterus albus). The eel IL-1β cDNA encodes a putative polypeptide of 246 amino acids. The protein sequence includes a typical IL-1 family signature, but lacked an interleukin-converting enzyme cleavage site. The genomic DNA of eel IL-1β was 2520 bp and comprised five exons and four introns. The eel IL-1R2 cDNA encoded a putative propeptide of 423 amino acid residues, comprising a signal peptide, a transmembrane region and two Ig-like domains in the extracellular region. Similar to other vertebrates, the genomic DNA of the eel IL-1R2 has nine exons and eight introns. Real-time PCR analysis indicated that IL-1β and IL-1R2 were constitutively expressed in all tissues, especially in the liver and immune-related organs. After infection with Aeromonas hydrophila, the transcript levels of IL-1β and IL-1R2 were induced in the head kidney and spleen, reaching their highest levels at 6 h post injection. In vitro, IL-1β and IL-1R2 mRNA levels were also upregulated rapidly at 1h post infection with A. hydrophila. Furthermore, acanthocephalan Pallisentis (Neosentis) celatus could induce the expression of both genes in the head kidney and intestine. In infected intestines, the transcript levels of IL-1β and IL-1R2 were increased by 21.4-fold and 20.8-fold, respectively, relative to the control. The present study indicated that IL-1β and IL-1R2 play an important role in inflammation and host defense, especially in the antiacanthocephalan response.

A dose reduction x-ray beam positioning system for high-speed multislice CT scanners

The introduction of multislice CT scanners and the associated dose increase compared to single and dual slice scanners has concerned many radiologists, health and medical physicists, as well as members of the regulatory community. Since multislice CT scanners are inherently post-patient collimated, they are less dose efficient than single slice CT scanners, which use prepatient collimation. The x-ray beam must be wide enough in the Z axis so that the beam remains on the detector in spite of typical movements due to thermal and mechanical flexing. We describe the x-ray beam tracking system that is employed on a GE LightSpeed QX/i scanner to substantially reduce the multislice dose. The tracking system stabilizes the beam on the detector allowing a narrower x-ray exposure profile compared to the x-ray exposure profile without tracking. The tracking system measures the position of the beam every few milliseconds and continually repositions a source aperture to hold a narrow beam fixed on the detector. Using a standard LightSpeed QX/i source collimator and segmented detector, dose reductions of up to 40% were measured when tracking was employed. We also show that tracking has the potential to provide a dose efficiency approaching single slice scanners.

Attenuation compensation in 99mTc SPECT brain imaging: a comparison of the use of attenuation maps derived from transmission versus emission data in normal scans

Brain SPECT imaging using 99mTc lipophilic tracers such as hexamethyl propyleneamine oxime (HMPAO) attempts to estimate cerebral, cerebellar and subcortical perfusion by assessing the relative amount of tracer uptake among these regions. Most commonly, comparison is made with cerebellar activity. Because the assessment of relative tracer uptake may be rendered inaccurate by photon attenuation by the nonuniform attenuation properties of the head, brain SPECT reconstructions have been compared using attenuation correction (AC) with various methods for estimating the attenuation map.

METHODS

Patients underwent 99mTc-HMPAO brain SPECT with transmission line source AC hardware. In addition to the emission dataset, emission downscatter and transmission datasets were acquired. Iterative reconstructions using three different attenuation maps were investigated. These included: (a) that obtained from transmission imaging, (b) that obtained from segmentation of a reconstruction from a lower energy Compton scatter window and (c) a slice-independent, uniform, elliptical attenuation map. No AC was also compared.

RESULTS

Count profiles in patients having brain perfusion SPECT scans showed a significant difference in region count estimates in the brain depending on whether AC is used as well as on the attenuation map used. Scatter-based AC is able to provide external contour detection and attenuation compensation based on that contour, whereas transmission-based AC provides external contour detection as well as internal, nonuniform attenuation estimation and AC. If one considers transmission AC to be the clinical "gold standard," non-attenuation-corrected as well as fixed-ellipsoid, uniform attenuation-corrected studies provided unreliable regional estimates of tracer activity.

CONCLUSION

This study shows the significant difference in clinical brain SPECT count profiles depending on how and whether there is compensation for attenuation. Based on prior studies validating the improved quantitative accuracy of SPECT using transmission-based AC, this study suggests that clinical 99mTc brain perfusion SPECT would benefit from and, in situations demanding rigorous quantitative assessment, requires transmission-based AC. Estimating attenuation maps with scatter-based methods was the next most accurate (clinical) method tested and can be used if and when transmission imaging cannot be used.

Comparison of frequency-distance relationship and Gaussian-diffusion-based methods of compensation for distance-dependent spatial resolution in SPECT imaging

The goal of this investigation was to compare resolution recovery versus noise level of two methods for compensation of distance-dependent resolution (DDR) in SPECT imaging. The two methods of compensation were restoration filtering based on the frequency-distance relationship (FDR) prior to iterative reconstruction, and modelling DDR in the projector/backprojector pair employed in iterative reconstruction. FDR restoration filtering was computationally faster than modelling the detector response in iterative reconstruction. Using Gaussian diffusion to model the detector response in iterative reconstruction sped up the process by a factor of 2.5 over frequency domain filtering in the projector/backprojector pair. Gaussian diffusion modelling resulted in a better resolution versus noise tradeoff than either FDR restoration filtering or solely modelling attenuation in the projector/backprojector pair of iterative reconstruction. For the pixel size investigated herein (0.317 cm), accounting for DDR in the projector/backprojector pair by Gaussian diffusion, or by applying a blurring function based on the distance from the face of the collimator at each distance, resulted in very similar resolution recovery and slice noise level.

Reducing the influence of the partial volume effect on SPECT activity quantitation with 3D modelling of spatial resolution in iterative reconstruction

Quantitative parameters such as the maximum and total counts in a volume are influenced by the partial volume effect. The magnitude of this effect varies with the non-stationary and anisotropic spatial resolution in SPECT slices. The objective of this investigation was to determine whether iterative reconstruction which includes modelling of the three-dimensional (3D) spatial resolution of SPECT imaging can reduce the impact of the partial volume effect on the quantitation of activity compared with filtered backprojection (FBP) techniques which include low-pass, and linear restoration filtering using the frequency distance relationship (FDR). The iterative reconstruction algorithms investigated were maximum-likelihood expectation-maximization (MLEM), MLEM with ordered subset acceleration (ML-OS), and MLEM with acceleration by the rescaled-block-iterative technique (ML-RBI). The SIMIND Monte Carlo code was used to simulate small hot spherical objects in an elliptical cylinder with and without uniform background activity as imaged by a low-energy ultra-high-resolution (LEUHR) collimator. Centre count ratios (CCRs) and total count ratios (TCRs) were determined as the observed counts over true counts. CCRs were unstable while TCRs had a bias of approximately 10% for all iterative techniques. The variance in the TCRs for ML-OS and ML-RBI was clearly elevated over that of MLEM, with ML-RBI having the smaller elevation. TCRs obtained with FDR-Wiener filtering had a larger bias (approximately 30%) than any of the iterative reconstruction methods but near stationarity is also reached. Butterworth filtered results varied by 9.7% from the centre to the edge. The addition of background has an influence on the convergence rate and noise properties of iterative techniques.

Influence of OSEM, elliptical orbits and background activity on SPECT 3D resolution recovery

In maximum-likelihood expectation-maximization (MLEM) reconstruction of SPECT images, if both attenuation correction (AC) and detector response correction (DRC) are included, the reconstruction can be too time consuming to be clinically useful. With use of the ordered-subset expectation-maximization (OSEM) reconstruction, it has been reported that the reconstruction time can be substantially reduced. We investigated the reconstruction of point sources in a non-uniform attenuation medium in terms of the normalized FWHM of these sources. We compared MLEM versus OSEM reconstructions; circular versus elliptical orbits; and the presence versus the absence of background activity in the object. We found: (i) that OSEM does speed up the reconstruction by a factor of 10 over MLEM; (ii) that the resolution recovery does not depend on the type of orbit if both AC and DRC are included in the reconstruction; however, when there is background activity, a significant number of iterations are required to alleviate the effect of orbit; (iii) that background activity significantly slows down the resolution recovery of the point sources; and (iv) that if reconstruction only includes AC, and not DRC, changing orbit can change isotropy of recovered resolution, whereas introducing background activity may degrade the recovered resolution and also changes the isotropy.

Evaluation of right and left ventricular volume and ejection fraction using a mathematical cardiac torso phantom

The availability of gated SPECT has increased the interest in the determination of volume and ejection fraction of the left ventricle (LV) for clinical diagnosis. However, the same indices for the right ventricle (RV) have been neglected. The objective of this investigation was to use a mathematical model of the anatomical distribution of activity in gated blood-pool imaging to evaluate the accuracy of two ventricular volume and ejection fraction determination methods. In this investigation, measurements from the RV were emphasized.

METHODS

The mathematical cardiac torso phantom, developed to study LV myocardium perfusion, was modified to simulate the radioactivity distribution of a 99mTc-gated blood-pool study. Twenty mathematical cardiac torso phantom models of the normal heart with different LV volumes (122.3 +/- 11.0 ml), RV volumes (174.6 +/- 22.3 ml) and stroke volumes (75.7 +/- 3.3 ml) were randomly generated to simulate variations among patients. An analytical three-dimensional projector with attenuation and system response was used to generate SPECT projection sets, after which noise was added. The projections were simulated for 128 equidistant views in a 360 degrees rotation mode.

RESULTS

The radius of rotation was varied between 24 and 28 cm to mimic such variation in patient acquisitions. The 180 degrees and 360 degrees projection sets were reconstructed using the filtered backprojection reconstruction algorithm with Butter-worth filtering. Comparison was made with and without application of the iterative Chang attenuation correction algorithm. Volumes were calculated using a modified threshold and edge detection method (hybrid threshold), as well as a count-based method. A simple background correction procedure was used with both methods.

CONCLUSION

Results indicate that cardiac functional parameters can be measured with reasonable accuracy using both methods. However, the count-based method had a larger bias than the hybrid threshold method when RV parameters were determined for 180 degrees reconstruction without attenuation correction. This bias improved after attenuation correction. The count-based method also tended to overestimate the end systolic volume slightly. An improved background correction could possibly alleviate this bias.

Choice of initial conditions in the ML reconstruction of fan-beam transmission with truncated projection data

We investigate the effects of initial conditions in the iterative maximum-likelihood (ML) reconstruction of fan-beam transmission projection data with truncation. In an iterative ML reconstruction, the estimate of the transmission reconstructed image in the previous iteration is multiplied by some factors to obtain the current estimate. Normally, a flat initial condition (FIC) or an image with equal positive pixel values is used as initial condition for an ML reconstruction. Usage of FIC has also been perceived as a way of preventing any bias on the reconstruction which may have come from the initial condition. When projection data have truncation, we show that using an FIC in an ML iterative reconstruction can introduce a bias to the reconstruction inside the densely sampled region (DSR), whose projection data have no truncation at any angle. To reduce this bias, we propose to use the largest right singular vector (LRSV) of the system matrix as the initial condition, and demonstrate that the bias can be reduced with the LRSV. When data truncation is reduced, the LRSV approaches the FIC. This result does not contradict to the use of FIC when projection data are not truncated. We also demonstrate that the reconstructed transmission image using LRSV as initial condition provides a more accurate attenuation coefficient distribution than that using FIC. However, the improvement is mostly in the area outside the DSR.

Estimation of attenuation maps from scatter and photopeak window single photon-emission computed tomographic images of technetium 99m-labeled sestamibi

BACKGROUND

In single photon-emission computed tomographic imaging of the chest, nonuniform attenuation correction requires use of a patient-specific attenuation map. The aim of this study was to determine whether an estimate of the regions of the lungs and nonpulmonary tissues of the chest could be obtained by segmenting the photopeak and Compton scatter window images in a phantom and in patients to estimate patient-specific attenuation maps.

METHODS AND RESULTS

The photopeak and scatter window slices from 16 consecutive 99mTc-labeled sestamibi perfusion studies were segmented interactively. In these studies, visually reasonable regions could be obtained by estimating a "cold" lung region from scatter window data with additional anatomic information of the myocardium region, the backbone and sternum locations, the liver, and the rib cage from the photopeak window data. In an anthropomorphic torso phantom study and a patient study, comparison was made between the attenuation maps based on segmentation of the emission images and transmission imaging with a slant-hole collimator. It was determined that good agreement in the estimation of the body regions can be achieved with segmentation of the emission images in both the phantom and patient data. Attenuation correction using the maximum-likelihood expectation maximization method was performed on the phantom and the patient data. In both studies, attenuation correction with the segmented attenuation map improved uniformity of the inferior wall region in comparison with the other walls.

CONCLUSIONS

The estimation of patient-specific attenuation maps by segmenting the scatter and photopeak window slices of 99mTc-labeled sestamibi studies may be a way of reducing the loss of specificity due to attenuation artifacts. The potential limitations on the accuracy of correction inherent in the method due to the estimation of the regions and assignment of the attenuation coefficients need to be determined further, and the method needs to be further automated before it can be considered for routine clinical use.

Attenuation compensation for cardiac single-photon emission computed tomographic imaging: Part 2. Attenuation compensation algorithms

Attenuation is believed to be one of the major causes of false-positive cardiac single-photon emission computed tomographic perfusion images. This article provides an introduction to the approaches used to correct for nonuniform attenuation once a patient-specific attenuation map is available. Comparison is made of specific attenuation-correction algorithms from each of three major categories of compensation methods that are or will be available commercially. Examples of the use of the algorithms on simulated projections of a mathematic phantom modeling the anatomy of the upper torso are used to illustrate the ability of the methods to compensate for attenuation. The advantages and disadvantages of each approach are summarized, as well as areas that need further investigation.

A Monte Carlo investigation of artifacts caused by liver uptake in single-photon emission computed tomography perfusion imaging with technetium 99m-labeled agents

BACKGROUND

Significant hepatobiliary accumulation of technetium 99m-labeled cardiac perfusion agents has been shown to cause alterations in the apparent localization of the agents in the cardiac walls. A Monte Carlo study was conducted to investigate the hypothesis that the cardiac count changes are due to the inconsistencies in the projection data input to reconstruction, and that correction of the causes of these inconsistencies before reconstruction, or including knowledge of the physics underlying them in the reconstruction algorithm, would virtually eliminate these artifacts.

METHODS AND RESULTS

The SIMIND Monte Carlo package was used to simulate 64 x 64 pixel projection images at 128 angles of the three-dimensional mathematical cardiac-torso (MCAT) phantom. Simulations were made of (1) a point source in the liver, (2) cardiac activity only, and (3) hepatic activity only. The planar projections and reconstructed point spread functions (PSFs) of the point source in the liver were investigated to study the nature of the inconsistencies introduced into the projections by imaging, and how these affect the distribution of counts in the reconstructed slices. Bull's eye polar maps of the counts at the center of the left ventricular wall of filtered back-projection (FBP) and maximum-likelihood expectation-maximization (MLEM) reconstructions of projections with solely cardiac activity, and with cardiac activity plus hepatic activity scaled to have twice the cardiac concentration, were compared to determine the magnitude and location of apparent changes in cardiac activity when hepatic activity is present. Separate simulations were made to allow the investigation of stationary spatial resolution, distance-dependent spatial resolution, attenuation, and scatter. The point source projections showed significant inconsistencies as a function of projection angle with the largest effect being caused by attenuation. When consistent projections were simulated, no significant impact of hepatic activity on cardiac counts was noted with FBP, or 100 iterations of MLEM. With inconsistent projections, reconstruction of 180 degrees resulted in greater apparent cardiac count losses than did 360 degrees reconstruction for both FBP and MLEM. The incorporation of attenuation correction in MLEM reconstruction reduced the changes in cardiac counts to that seen in simulations in which attenuation was not included, but resulted in increased apparent localization of activity in the posterior wall of the left ventricle when scatter was present in the simulated images.

CONCLUSIONS

The apparent alterations in cardiac counts when significant hepatic localization is present is due to the inconsistency of the projections inherent in imaging. Prior correction of these, or accounting for them in the reconstruction algorithm, will virtually eliminate them as causes of artifactual changes in localization. Attenuation correction and scatter correction are both required to overcome the major sources of apparent count changes in the heart associated with hepatic uptake.

Segmentation of the body and lungs from Compton scatter and photopeak window data in SPECT: a Monte-Carlo investigation

In SPECT imaging of the chest, nonuniform attenuation correction requires use of a patient specific attenuation (mu) map. Such a map can be obtained by estimating the regions of (1) the lungs and (2) the soft tissues and bones, and then assigning an appropriate value of attenuation coefficient (mu) to each region. The authors proposed a method to segment such regions from the Compton scatter and photopeak window SPECT slices of Tc-99m Sestamibi studies. The Compton scatter slices are used to segment the body outline and to estimate the regions of the lungs. Locations of the back bone and sternum are estimated from the photopeak window slices to assist in the segmentation. To investigate the accuracy of using Compton scatter slices in estimating the regions of the body and the lungs, a Monte-Carlo SPECT simulation of an anthropomorphic phantom with an activity distribution and noise characteristics similar to patient data was conducted. Energy windows of various widths were simulated for use in locating a suitable Compton scatter window for imaging, The effects of attenuation correction using a mu map based on segmentation were also studied. The results demonstrated for the activity and mu maps studied herein that: (1) reasonable contrast could be obtained from Compton scatter data for the segmentation of the lung regions, (2) true positive rates of 99% and 89% for determining the body and lung regions, respectively, with total error rates of 4% and 29%, could be achieved, (3) usage of a mu map based on segmentation for attenuation correction improved relative quantification over filtered backprojection, (4) variations in the assigned mu value of 40% smaller or 40% larger in the lung regions had an insignificant impact on the results of relative quantification, (5) a wide energy window away from the photopeak window for recording scattered events could benefit both the segmentation of the lung regions and the attenuation correction of the activity in the myocardium region, and (6) usage of a smaller than true mu value in the lung regions of an assigned mu map might benefit attenuation correction for absolute quantification.

Attenuation compensation for cardiac single-photon emission computed tomographic imaging: Part 1. Impact of attenuation and methods of estimating attenuation maps

Attenuation is believed to be one of the major causes of false-positive cardiac single-photon emission computed tomographic (SPECT) perfusion images. This article reviews the physics of attenuation, the artifacts produced by attenuation, and the need for scatter correction in combination with attenuation correction. The review continues with a comparison of the various configurations for transmission imaging that could be used to estimate patient specific attenuation maps, and an overview of how these are being developed for use on multiheaded SPECT systems, including discussions of truncation, noise, and spatial resolution of the estimated attenuation maps. Ways of estimating patient specific attenuation maps besides transmission imaging are also discussed.

An analytical approach for compensation of non-uniform attenuation in cardiac SPECT imaging

Photon attenuation can reduce the diagnostic accuracy of cardiac SPECT imaging. Bellini et al have previously derived a mathematically exact method to compensate for attenuation in a uniform attenuator. Since the human thorax contains structures with differing attenuation properties, non-uniform attenuation compensation is required in cardiac SPECT. Given an estimate of the patient attenuation map, we show that the Bellini attenuation compensation method can be used in cardiac SPECT to provide a quantitatively accurate reconstruction of a central region in the image which includes the heart and surrounding soft tissue. Simulations using a mathematical cardiac-torso phantom were conducted to evaluate the Bellini method and to compare its performance to the ML-EM iterative algorithm, and to 180 degrees and 360 degrees filtered backprojection (FBP) with no attenuation compensation. 'Bulls-eye' polar maps and circumferential profiles showed that both the Bellini method and the ML-EM algorithm provided quantitatively accurate reconstructions of the myocardium, with a substantial reduction in attenuation-induced artifacts that were observed in the FBP images. The computational load required to implement the Bellini method is approximately equivalent to that required for one iteration of the ML-EM algorithm, thus it is suitable for routine clinical use.

Preconditioning methods for improved convergence rates in iterative reconstructions

Because of the characteristics of the tomographic inversion problem, iterative reconstruction techniques often suffer from poor convergence rates-especially at high spatial frequencies. By using preconditioning methods, the convergence properties of most iterative methods can be greatly enhanced without changing their ultimate solution. To increase reconstruction speed, spatially invariant preconditioning filters that can be designed using the tomographic system response and implemented using 2-D frequency-domain filtering techniques have been applied. In a sample application, reconstructions from noiseless, simulated projection data, were performed using preconditioned and conventional steepest-descent algorithms. The preconditioned methods demonstrated residuals that were up to a factor of 30 lower than the assisted algorithms at the same iteration. Applications of these methods to regularized reconstructions from projection data containing Poisson noise showed similar, although not as dramatic, behavior.

Acceleration and filtering in the generalized Landweber iteration using a variable shaping matrix

The generalized Landweber iteration with a variable shaping matrix is used to solve the large linear system of equations arising in the image reconstruction problem of emission tomography. The method is based on the property that once a spatial frequency image component is almost recovered within in in the generalized Landweber iteration, this component will still stay within in during subsequent iterations with a different shaping matrix, as long as this shaping matrix satisfies the convergence criterion for the component. Two different shaping matrices are used: the first recovers low-frequency image components; and the second may be used either to accelerate the reconstruction of high-frequency image components, or to attenuate these components to filter the image. The variable shaping matrix gives results similar to truncated inverse filtering, but requires much less computation and memory, since it does not rely on the singular value decomposition.

Acceleration of Landweber-type algorithms by suppression of projection on the maximum singular vector

A procedure that speeds up convergence during the initial stage (the first 100 forward and backward projections) of Landweber-type algorithms, for iterative image reconstruction for positron emission tomography (PET), which include the Landweber, generalized Landweber, and steepest descent algorithms, is discussed. The procedure first identifies the singular vector associated with the maximum singular value of the PET system matrix, and then suppresses projection of the data on this singular vector after a single Landweber iteration. It is shown that typical PET system matrices have a significant gap between their two largest singular values; hence, this suppression allows larger gains in subsequent iterations, speeding up convergence by roughly a factor of three.

Numerical study of multigrid implementations of some iterative image reconstruction algorithms

The numerical behavior of multigrid implementations of the Landweber, generalized Landweber, ART, and MLEM iterative image reconstruction algorithms is investigated. Comparisons between these algorithms, and with their single-grid implementations, are made on two small-scale synthetic PET systems, for phantom objects exhibiting different characteristics, and on one full-scale synthetic system, for a Shepp-Logan phantom. The authors also show analytically the effects of noise and initial condition on the generalized Landweber iteration, and note how to choose the shaping operator to filter out noise in the data, or to enhance features of interest in the reconstructed image. Original contributions include (1) numerical studies of the convergence rates of single-grid and multigrid implementations of the Landweber, generalized Landweber, ART, and MLEM iterations and (2) effects of noise and initial condition on the generalized Landweber iteration, with procedures for filtering out noise or enhancing image features.