Study of noise propagation and the effects of insufficient numbers of projection angles and detector samplings for iterative reconstruction using planar-integral data

A rotating slat collimator can be used to acquire planar-integral data. It achieves higher geometric efficiency than a parallel-hole collimator by accepting more photons, but the planar-integral data contain less tomographic information that may result in larger noise amplification in the reconstruction. Lodge evaluated the rotating slat system and the parallel-hole system based on noise behavior for an FBP reconstruction. Here, we evaluate the noise propagation properties of the two collimation systems for iterative reconstruction. We extend Huesman's noise propagation analysis of the line-integral system to the planar-integral case, and show that approximately 2.0(D/dp) SPECT angles, 2.5(D/dp) self-spinning angles at each detector position, and a 0.5dp detector sampling interval are required in order for the planar-integral data to be efficiently utilized. Here, D is the diameter of the object and dp is the linear dimension of the voxels that subdivide the object. The noise propagation behaviors of the two systems are then compared based on a least-square reconstruction using the ratio of the SNR in the image reconstructed using a planar-integral system to that reconstructed using a line-integral system. The ratio is found to be proportional to the square root of F/D, where F is a geometric efficiency factor. This result has been verified by computer simulations. It confirms that for an iterative reconstruction, the noise tradeoff of the two systems is not only dependent on the increase of the geometric efficiency afforded by the planar projection method, but also dependent on the size of the object. The planar-integral system works better for small objects, while the line-integral system performs better for large ones. This result is consistent with Lodge's results based on the FBP method.     

An iterative three-dimensional electron density imaging algorithm using uncollimated compton scattered x rays from a polyenergetic primary pencil beam

X-ray film-screen mammography is currently the gold standard for detecting breast cancer. However, one disadvantage is that it projects a three-dimensional (3D) object onto a two-dimensional (2D) image, reducing contrast between small lesions and layers of normal tissue. Another limitation is its reduced sensitivity in women with mammographically dense breasts. Computed tomography (CT) produces a 3D image yet has had a limited role in mammography due to its relatively high dose, low resolution, and low contrast. As a first step towards implementing quantitative 3D mammography, which may improve the ability to detect and specify breast tumors, we have developed an analytical technique that can use Compton scatter to obtain 3D information of an object from a single projection. Imaging material with a pencil beam of polychromatic x rays produces a characteristic scattered photon spectrum at each point on the detector plane. A comparable distribution may be calculated using a known incident x-ray energy spectrum, beam shape, and an initial estimate of the object's 3D mass attenuation and electron density. Our iterative minimization algorithm changes the initially arbitrary electron density voxel matrix to reduce regular differences between the analytically predicted and experimentally measured spectra at each point on the detector plane. The simulated electron density converges to that of the object as the differences are minimized. The reconstruction algorithm has been validated using simulated data produced by the EGSnrc Monte Carlo code system. We applied the imaging algorithm to a cylindrically symmetric breast tissue phantom containing multiple inhomogeneities. A preliminary ROC analysis scores greater than 0.96, which indicate that under the described simplifying conditions, this approach shows promise in identifying and localizing inhomogeneities which simulate 0.5 mm calcifications with an image voxel resolution of 0.25 cm and at a dose comparable to mammography.     

Comparing planar image quality of rotating slat and parallel hole collimation: influence of system modeling

The main remaining challenge for a gamma camera is to overcome the existing trade-off between collimator spatial resolution and system sensitivity. This problem, strongly limiting the performance of parallel hole collimated gamma cameras, can be overcome by applying new collimator designs such as rotating slat (RS) collimators which have a much higher photon collection efficiency. The drawback of a RS collimated gamma camera is that, even for obtaining planar images, image reconstruction is needed, resulting in noise accumulation. However, nowadays iterative reconstruction techniques with accurate system modeling can provide better image quality. Because the impact of this modeling on image quality differs from one system to another, an objective assessment of the image quality obtained with a RS collimator is needed in comparison to classical projection images obtained using a parallel hole (PH) collimator. In this paper, a comparative study of image quality, achieved with system modeling, is presented. RS data are reconstructed to planar images using maximum likelihood expectation maximization (MLEM) with an accurate Monte Carlo derived system matrix while PH projections are deconvolved using a Monte Carlo derived point-spread function. Contrast-to-noise characteristics are used to show image quality for cold and hot spots of varying size. Influence of the object size and contrast is investigated using the optimal contrast-to-noise ratio (CNR(o)). For a typical phantom setup, results show that cold spot imaging is slightly better for a PH collimator. For hot spot imaging, the CNR(o) of the RS images is found to increase with increasing lesion diameter and lesion contrast while it decreases when background dimensions become larger. Only for very large background dimensions in combination with low contrast lesions, the use of a PH collimator could be beneficial for hot spot imaging. In all other cases, the RS collimator scores better. Finally, the simulation of a planar bone scan on a RS collimator revealed a hot spot contrast improvement up to 54% compared to a classical PH bone scan.     

Image reconstruction algorithm for a rotating slat collimator

A slat collimator in single photon emission computed tomography consists of a set of parallel slats. As the collimator spins, the detector measures a one-dimensional projection data set. A complete data set can be obtained by rotating the detector/collimator assembly around the object (patient) while the collimator spins continuously. The measured projection data are assumed to be weighted planar integrals of the object. This paper describes the development of an approximate three-dimensional image reconstruction algorithm for a rotating/spinning slat collimator. This algorithm is in filtered backprojection form. Computer simulations were performed to verify the effectiveness of the algorithm.     

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.     

Image reconstruction algorithm for a spinning strip CZT SPECT camera with a parallel slat collimator and small pixels

This paper discusses the use of small pixels in a spinning CdZnTe single photon emission computed tomography (SPECT) camera that is mounted with a parallel slat collimator. In a conventional slat collimation configuration, there is a detector pixel between two adjacent collimator slats. In our design, the pixel size is halved. That is, there are two smaller pixels to replace a regular pixel between two adjacent slats while the collimator remains unchanged. It has an advantage over our older design that uses tilted slats. In order to acquire a complete data set the tilted-slat collimator must spin 360 degrees at each SPECT view while the proposed design requires only 180 degrees at each SPECT view. Computer simulations and phantom experiments have been carried out to investigate the performance of the small-pixel configuration. It is observed that this design has the potential to increase the spatial resolution of the detector while keeping photon counts the same.     

Joint optimization of collimator and reconstruction parameters in SPECT imaging for lesion quantification

Obtaining the best possible task performance using reconstructed SPECT images requires optimization of both the collimator and reconstruction parameters. The goal of this study is to determine how to perform this optimization, namely whether the collimator parameters can be optimized solely from projection data, or whether reconstruction parameters should also be considered. In order to answer this question, and to determine the optimal collimation, a digital phantom representing a human torso with 16 mm diameter hot lesions (activity ratio 8:1) was generated and used to simulate clinical SPECT studies with parallel-hole collimation. Two approaches to optimizing the SPECT system were then compared in a lesion quantification task: sequential optimization, where collimation was optimized on projection data using the Cramer–Rao bound, and joint optimization, which simultaneously optimized collimator and reconstruction parameters. For every condition, quantification performance in reconstructed images was evaluated using the root-mean-squared-error of 400 estimates of lesion activity. Compared to the joint-optimization approach, the sequential-optimization approach favoured a poorer resolution collimator, which, under some conditions, resulted in sub-optimal estimation performance. This implies that inclusion of the reconstruction parameters in the optimization procedure is important in obtaining the best possible task performance; in this study, this was achieved with a collimator resolution similar to that of a general-purpose (LEGP) collimator. This collimator was found to outperform the more commonly used high-resolution (LEHR) collimator, in agreement with other task-based studies, using both quantification and detection tasks.     

OSEM重建算法中几个关键问题的研究

目的：改进平行孔准直器SPECT系统的成像方法，快速、精确地实现有序子集期望值最大化（OSEM）重建算法。方法：采用理想平行孔和张角效应平行孔准直器两种模型，将准直器的空间响应融入系统传输矩阵，利用改进的射线跟踪算法进行衰减校正。结果：随着准直器张角的增加，Jaszczak模型的重建图像在边界出现明显的亮环；利用考虑准直器空间响应的系统矩阵进行图像重建．能较好的抑制边界伪影。结论：融入准直器空间响应函数的系统矩阵更为精确、贴近真实情况，能较好的抑制边界伪影，提高了重建图像的对比度和信噪比。     

Quantitative reconstruction for myocardial perfusion SPECT: an efficient approach by depth-dependent deconvolution and matrix rotation

An efficient reconstruction method for myocardial perfusion single-photon emission computed tomography (SPECT) has been developed which compensates simultaneously for attenuation, scatter, and resolution variation. The scattered photons in the primary-energy-window measurements are approximately removed by subtracting the weighted scatter-energy-window samples. The resolution variation is corrected by deconvolving the subtracted data with the detector-response kernel in frequency space using the depth-dependent frequency relation. The attenuated photons are compensated by recursively tracing the attenuation factors through the object-specific attenuation map. An experimental chest phantom with defects inside myocardium was used to test the method. The attenuation map of the phantom was reconstructed from transmission scans using a flat external source and a high-resolution parallel-hole collimator of a single-detector system. The detector-response kernel was approximated from measurements of a point source in air at several depths from the collimator surface. The emission data were acquired by the same detector setting. A computer simulation using similar protocols as in the experiment was performed. Both the simulation and experiment showed significant improvement in quantification with the proposed method, as compared to the conventional filtered-backprojection technique. The quantitative gain by the additional deconvolution was demonstrated. The computation time was less than 20 min on a HP/730 desktop computer for reconstruction of a 1282 x 64 array from 128 projections of 128 x 64 samples.     

System characteristics of SPECT with a slat collimated strip detector

In classical SPECT with parallel hole collimation, the sensitivity is constant over the field of view (FOV). This is no longer the case if a rotating slat collimator with planar photon collection is used: there will be a significant variation of the sensitivity within the FOV. Since not compensating for this inhomogeneous sensitivity distribution would result in non-quantitative images, an accurate knowledge of the sensitivity is mandatory to account for it during reconstruction. On the other hand, the spatial resolution versus distance dependency remains unaltered compared to parallel hole collimation. For deriving the sensitivity, different factors have to be taken into account: a first factor concerns the intrinsic detector properties and will be incorporated into the calculations as a detection efficiency term depending on the incident angle. The calculations are based on a second and more pronounced factor: the collimator and detector geometry. Several assumptions will be made for the calculation of the sensitivity formulae and it will be proven that these calculations deliver a valid prediction of the sensitivity at points far enough from the collimator. To derive a close field model which also accounts for points close to the collimator surface, a modified calculation method is used. After calculating the sensitivity in one plane it is easy to obtain the tomographic sensitivity. This is done by rotating the sensitivity maps for spin and camera rotation. The results derived from the calculations are then compared to simulation results and both show good agreement after including the aforementioned detection efficiency term. The validity of the calculations is also proven by measuring the sensitivity in the FOV of a prototype rotating slat gamma camera. An expression for the resolution of these planar collimation systems is obtained. It is shown that for equal collimator dimensions the same resolution-distance relationship is obtained as for parallel hole collimators. Although, a better spatial resolution can be obtained with our prototype camera due to the smaller pitch of the slats. This can be achieved without a major drop in system sensitivity due to the fact that the slats consist of less collimator material compared to a parallel hole collimator. The accuracy of the calculated resolution is proven by comparison with Monte Carlo simulation and measurement resolution values.     

The cardiofocal collimator: a variable-focus collimator for cardiac SPECT

Investigators in nuclear medicine have long been in search of a practical method to increase the number of detected events in cardiac SPECT. A clinically practical method requires a simple data acquisition protocol, clinically acceptable reconstruction times, artifact levels near or below visual threshold, and the use of currently available cameras and computers. Towards this end, we have developed the Cardiofocal collimator, a variable-focus collimator for cardiac SPECT that increases the number of detected events from the heart by more than a factor of two compared to that of a parallel-hole collimator with equivalent resolution. In both the transverse and axial dimensions, the focusing is strongest at the centre of the collimator, and gradually relaxes to nearly parallel-hole collimation at the edge of the collimator. The variable-focus concept provides an increase in the number of counts from organs imaged near the centre of the collimator, where the heart will spend most of the time during a cardiac SPECT study, while adequately sampling enough of the background activity distribution to prevent truncation artifacts in the reconstructed images. Images are reconstructed in clinically acceptable times using a filtered backprojection reconstruction algorithm. The algorithm supports both full-scan (360 degrees) and short-scan (180 degrees plus the fan angle) acquisitions. The results of simulations and phantom studies are included to demonstrate the performance of the Cardiofocal collimator.     

A non-linear programming method for optimizing parallel-hole collimator design.

A new method for optimizing the design of multi-aperture parallel-hole collimators for the gamma scintillation camera is presented. The method takes into account the frequency spectrum of a plane source object distribution as well as the energy of the radiation. A frequency dependent statistical figure of merit is calculated and combined with a weighted object distribution frequency spectrum to obtain an objective function which, when maximized, yields the optimum collimator design according to the chosen criteria. The optimization is performed by means of a sequential pattern search technique. The results show a positive correlation between te objective function and an experimental performance index evaluated for existing collimators. The optimal designs obtained by maximizing the objective function, under the assumption of no scatter within the source, exhibit somewhat higher sensitivity and lower resolution than the commercial low energy collimators tested. It is concluded that much of the resolution capability of very high resolution collimators is unused because of the limitation imposed by the intrinsic resolution of the detector assembly.     

3D cone-beam CT reconstruction for circular trajectories

3D reconstruction from 2D projections obtained along a single circular source trajectory is most commonly done using an algorithm due to Feldkamp, Davis and Kress. In this paper we propose an alternative approach based on a cone-beam to parallel-beam rebinning step, a corresponding rebinning step into a rectangular virtual detector plane and a filtered backprojection. This approach yields an improved image quality reflected by a decreased low-intensity drop which is well known for 3D reconstruction from projection data obtained along circular trajectories. At the same time the computational complexity is lower than in Feldkamp's original approach. Based on this idea, a hybrid 3D cone-beam reconstruction method is formulated that enlarges the reconstruction volume in its dimension along the rotation axis of the cone-beam CT system. This enlargement is achieved by applying different reconstruction conditions for each voxel. An optimal ratio between the reconstructible and irradiated volume of the scanned object is achieved.     

Pinhole collimation for ultra-high-resolution, small-field-of-view SPECT

The objective of this investigation was to evaluate small-field-of-view, ultra-high-resolution pinhole collimation for a rotating-camera SPECT system that could be used to image small laboratory animals. Pinhole collimation offers distinct advantages over conventional parallel-hole collimation when used to image small objects. Since geometric sensitivity increases markedly for points close to the pinhole, small-diameter and high-magnification pinhole geometries may be useful for selected imaging tasks when used with large-field-of-view scintillation cameras. The use of large magnifications can minimize the loss of system resolution caused by the intrinsic resolution of the scintillation camera. A pinhole collimator has been designed and built that can be mounted on one of the scintillation cameras of a triple-head SPECT system. Three pinhole inserts with approximate aperture diameters of 0.6, 1.2 and 2.0 mm have been built and can be mounted individually on the collimator housing. When a ramp filter is used with a three-dimensional (3D) filtered backprojection (FBP) algorithm, the three apertures have in-plane SPECT spatial resolutions (FWHM) at 4 cm of 1.5, 1.9 and 2.8 mm, respectively. In-air point source sensitivities at 4 cm from the apertures are 0.9, 2.6 and 5.7 counts s(-1) microCi(-1) (24, 70 and 154 counts s(-1) MBq(-1)) for the 0.6, 1.2 and 2.0 mm apertures, respectively. In vitro image quality was evaluated with a micro-cold-rod phantom and a micro-Defrise phantom using both the 3D FBP algorithm and a 3D maximum likelihood-expectation maximization (ML-EM) algorithm. In vivo image quality was evaluated using two (315 and 325 g) rats. Ultra-high-resolution pinhole SPECT is an inexpensive and simple approach for imaging small animals that can be used with existing rotating-camera SPECT system.     

Measuring the imaged-object distance with a stationary high-spatial-resolution scintillation camera

A method to measure the detector-to-object distance from the images obtained with stationary high-spatial-resolution gamma-ray cameras for in vivo studies has been developed. It exploits the shift of the imaged object in the image plane, obtained at a certain tilt of the parallel-hole collimator. A linear dependence of the image displacement on the distance to the object has been measured using a high-spatial-resolution scintillation camera employing an yttrium-aluminium perovskite (YAP) scintillator. It is shown that the modified YAP camera can be used to obtain three-dimensional information without moving the camera or the object. The method could be applied in scintimammography and radioguided surgery, in lymphoscintigraphy, as well as in the analysis of the biodistribution of radiopharmaceuticals.     

Performance assessment of a slat gamma camera collimator for 511 keV imaging.

The physical performance of a prototype slat collimator is described for gamma camera planar imaging at 511 keV. Measurements were made of sensitivity, spatial resolution and a septal penetration index at 511 keV. These measurements were repeated with a commercial parallel hole collimator designed for 511 keV imaging. The slat collimator sensitivity was 22.9 times that of the parallel hole collimator with 10 cm tissue equivalent scatter material, and 16.8 times the parallel hole collimator sensitivity in air. Spatial resolution was also better for the slat collimator than the parallel hole collimator (FWHM at 10 cm in air 17.9 mm and 21.2 mm respectively). Septal penetration was compared by a single value for the counts at 120 mm from the point source profile peak, expressed as a percentage of the peak counts, showing less penetration for the slat collimator than the parallel hole collimator (1.9% versus 3.6% respectively). In conclusion, these results show that the slat collimator may have advantages over the parallel hole collimator for 511 keV imaging, though the greater complexity of operation of the slat collimator and potential sources of artefact in slat collimator imaging are recognized.     

Automatic estimation of detector radial position for contoured SPECT acquisition using CT images on a SPECT/CT system

An algorithm was developed to estimate noncircular orbit (NCO) single-photon emission computed tomography (SPECT) detector radius on a SPECT/CT imaging system using the CT images, for incorporation into collimator resolution modeling for iterative SPECT reconstruction. Simulated male abdominal (arms up), male head and neck (arms down) and female chest (arms down) anthropomorphic phantom, and ten patient, medium-energy SPECT/CT scans were acquired on a hybrid imaging system. The algorithm simulated inward SPECT detector radial motion and object contour detection at each projection angle, employing the calculated average CT image and a fixed Hounsfield unit (HU) threshold. Calculated radii were compared to the observed true radii, and optimal CT threshold values, corresponding to patient bed and clothing surfaces, were found to be between -970 and -950 HU. The algorithm was constrained by the 45 cm CT field-of-view (FOV), which limited the detected radii to < or = 22.5 cm and led to occasional radius underestimation in the case of object truncation by CT. Two methods incorporating the algorithm were implemented: physical model (PM) and best fit (BF). The PM method computed an offset that produced maximum overlap of calculated and true radii for the phantom scans, and applied that offset as a calculated-to-true radius transformation. For the BF method, the calculated-to-true radius transformation was based upon a linear regression between calculated and true radii. For the PM method, a fixed offset of +2.75 cm provided maximum calculated-to-true radius overlap for the phantom study, which accounted for the camera system's object contour detect sensor surface-to-detector face distance. For the BF method, a linear regression of true versus calculated radius from a reference patient scan was used as a calculated-to-true radius transform. Both methods were applied to ten patient scans. For -970 and -950 HU thresholds, the combined overall average root-mean-square (rms) error in radial position for eight patient scans without truncation were 3.37 cm (12.9%) for PM and 1.99 cm (8.6%) for BF, indicating BF is superior to PM in the absence of truncation. For two patient scans with truncation, the rms error was 3.24 cm (12.2%) for PM and 4.10 cm (18.2%) for BF. The slightly better performance of PM in the case of truncation is anomalous, due to FOV edge truncation artifacts in the CT reconstruction, and thus is suspect. The calculated NCO contour for a patient SPECT/CT scan was used with an iterative reconstruction algorithm that incorporated compensation for system resolution. The resulting image was qualitatively superior to the image obtained by reconstructing the data using the fixed radius stored by the scanner. The result was also superior to the image reconstructed using the iterative algorithm provided with the system, which does not incorporate resolution modeling. These results suggest that, under conditions of no or only mild lateral truncation of the CT scan, the algorithm is capable of providing radius estimates suitable for iterative SPECT reconstruction collimator geometric resolution modeling.     

Monte Carlo modelling of the performance of a rotating slit-collimator for improved planar gamma-camera imaging.

Planar imaging with a gamma camera is currently limited by the performance of the collimator. Spatial resolution and sensitivity trade off against each other; it is not possible with conventional parallel-hole collimation to have high geometric sensitivity and at the same time excellent spatial resolution unless field-of-view is sacrificed by using fan- or cone-beam collimators. We propose a rotating slit-collimator which collects one-dimensional projections from which the planar image may be reconstructed by the theory of computed tomography. The performance of such a collimator is modelled by Monte Carlo methods and images are reconstructed by a convolution and backprojection technique. The performance is compared with that of a conventional parallel-hole collimator and it is shown that higher spatial resolution with increased sensitivity is possible with the slit-collimator. For a point source a spatial resolution of some 6 mm at a distance of 100 mm from the collimator with a x7 sensitivity compared with a parallel-hole collimator was achieved. Applications to bone scintigraphy are modelled and an improved performance in hot-spot imaging is demonstrated. The expected performance in cold-spot imaging is analytically investigated. The slit-collimator is not expected to improve cold-spot imaging. Practical design considerations are discussed.     

Design and simulation of a high-resolution stationary SPECT system for small animals

Exciting new SPECT systems can be created by combining pinhole imaging with compact high-resolution gamma cameras. These new systems are able to solve the problem of the limited sensitivity-resolution trade-off that hampers contemporary small animal SPECT. The design presented here (U-SPECT-III) uses a set of detectors placed in a polygonal configuration and a cylindrical collimator that contains 135 pinholes arranged in nine rings. Each ring contains 15 gold pinhole apertures that focus on the centre of the cylinder. A non-overlapping projection is acquired via each pinhole. Consequently, when a mouse brain is placed in the central field-of-view, each voxel in the cerebrum can be observed via 130 to 135 different pinholes simultaneously. A method for high-resolution scintillation detection is described that eliminates the depth-of-interaction problem encountered with pinhole cameras, and is expected to provide intrinsic detector resolutions better than 150 microm. By means of simulations U-SPECT-III is compared to a simulated dual pinhole SPECT (DP-SPECT) system with a pixelated array consisting of 2.0 x 2.0 mm NaI crystals. Analytic calculations indicate that the proposed U-SPECT-III system yields an almost four times higher linear and about sixty times higher volumetric system resolution than DP-SPECT, when the systems are compared at matching system sensitivity. In addition, it should be possible to achieve a 15 up to 30 times higher sensitivity with U-SPECT-III when the systems are compared at equal resolution. Simulated images of a digital mouse-brain phantom show much more detail with U-SPECT-III than with DP-SPECT. In a resolution phantom, 0.3 mm diameter cold rods are clearly visible with U-SPECT-III, whereas with DP-SPECT the smallest visible rods are about 0.6-0.8 mm. Furthermore, with U-SPECT-III, the image deformations outside the central plane of reconstruction that hamper conventional pinhole SPECT are strongly suppressed. Simulation results indicate that future pinhole SPECT systems are likely to bring about significant improvements in radio-molecular imaging of small animals.     

Compensation of spatial system response in SPECT with conjugate gradient reconstruction technique

A procedure for the determination of the system matrix in single photon emission tomography (SPECT) is described which uses the conjugate gradient reconstruction technique in order to take into account the variable system resolution of a camera equipped with parallel-hole collimators. The procedure involves the acquisition of the system line spread functions (LSF) in the region occupied by the object to be studied. Those data are used to generate a set of weighting factors based on the assumption that the LSFs of the collimated camera are of Gaussian shape with the full width at half maximum (FWHM) linearly dependent on the source depth in the span of image space. The factors are stored on a disc file for subsequent use in the reconstruction process. Afterwards the reconstruction is performed using the conjugate gradient method with the system matrix modified by the incorporation of these precalculated factors in order to take into account the variable geometrical system response. The set of weighting factors is regenerated whenever the acquisition conditions are changed (collimator, radius of rotation). In the case of an ultra high resolution (UHR) collimator 2000 weighting factors need to be calculated. The modification of the system matrix for the geometrical response allows the number of iterations to increase, considerably improving image definition without the appearance of noise artifacts. Moreover, phantom studies show that the number of iterations is less critical because of improved stability in the convergence to the solution. For brain studies of patients 10-15 iterations are usually performed. Studies with a single line source give a value between 7 and 8 mm for the FWHM of the point spread function (PSF) when the conjugate gradient method with modified system matrix is used on data acquired with a UHR collimator, whereas without the modification of the system matrix the result is 9 mm FWHM, if filtered backprojection (FBP) is used with the same filter as in the clinical studies the result is 15 mm FWHM. The results of this work show that proper definition of the system matrix using conjugate gradients influences the quality of the reconstruction remarkably. Nevertheless, further work has to be done in order to assess to what extent the system matrix is ill-conditioned and, eventually, to define a suitable regularization technique.