Point Response Function Research Articles

A slice-by-slice blurring model and kernel evaluation using theKlein-Nishina formula for 3D scatter compensation in parallel and convergingbeam SPECT

Converging collimation increases the geometric efficiency for imaging smallorgans, such as the heart, but also increases the difficulty of correcting forthe physical effects of attenuation, geometric response and scatter in SPECT. Inthis paper, 3D first-order Compton scatter in non-uniform scattering media ismodelled by using an efficient slice-by-slice incremental blurring technique inboth parallel and converging beam SPECT. The scatter projections are generatedby first forming an effective scatter source image (ESSI), thenforward-projecting the ESSI. The Compton scatter cross section described by theKlein-Nishina formula is used to obtain spatial scatter response functions(SSRFs) of scattering slices which are parallel to the detector surface. TwoSSRFs of neighbouring scattering slices are used to compute two small orthogonal1D blurring kernels used for the incremental blurring from the slice which isfurther from the detector surface to the slice which is closer to the detectorsurface. First-order Compton scatter point response functions (SPRFs) obtainedusing the proposed model agree well with those of Monte Carlo (MC) simulationsfor both parallel and fan beam SPECT. Image reconstruction in fan beam SPECT MCsimulation studies shows increased left ventricle myocardium-to-chamber contrast(LV contrast) and slightly improved image resolution when performing scattercompensation using the proposed model. Physical torso phantom fan beam SPECTexperiments show increased myocardial uniformity and image resolution as well asincreased LV contrast. The proposed method efficiently models the 3D first-orderCompton scatter effect in parallel and converging beam SPECT.

Multiple CCD detector for macromolecular X-ray crystallography

A charge-coupled device (CCD)-based detector designed for macromolecular crystallography is described. The detector has an area of 200 × 200 mm, a readout time of 1.6 s, and total noise equivalent to approximately three 12 keV X-ray photons per pixel. The detector is constructed from a 2 × 2 array of four identical units, each unit consisting of a 4.1:1 demagnifying fiber-optic taper bonded to a 1 k × 1 k, 24 µm pixel, CCD sensor. Each CCD is read out in parallel though four channels and digitized to 16 bits. A Gd2O2S phosphor X-ray-to-light converter bonded to an aluminized-plastic film is held in contact with the input surfaces of the fiber-optic tapers with an air pillow. The full width at half-maximum (FWHM) of the point response function is 120 µm, the response is linear to better than 1% over the entire range of intensity from background to nearly full well, the gain is 3.4 e per 8 keV incident X-ray photon, the noise is 12.6 e per pixel for a 10 s integration time, the modulation transfer function (MTF) is 0.35 at 5 line pairs (lp) mm−1(the Nyquest frequency), and the measured detective quantum efficiency (DQE) is 0.74 for relatively strong Bragg peaks. Data collected from crystallographic studies with synchrotron radiation are presented. In an anomalous difference Patterson map for a data set collected in 40 min on a monoclinic myoglobin crystal, the magnitude of the Fe–Fe peaks is 18 times the standard uncertainty of the map.

A transformation cross-talk technique for simultaneous dual radionuclide imaging: a myocardial perfusion 201Tl/99Tcm sestamibi dog SPECT study.

We have developed a novel transformation method for the correction of cross-talk in simultaneous dual radionuclide single photon emission CT (SPECT) imaging. It is based on the assumption that the transformations, which transform the primary energy window images into the scatter images as viewed in the other energy windows, are known. The method was tested on a dog model. These transformations were found by measuring the point response functions (prf) in different energy windows for both radionuclides in water. The dual radionuclide correction method described takes into account the different spatial distributions of the primary and scatter cross-talk photons in different energy windows. This method also includes the sequential application of restoration filters to the resulting cross-talk corrected images. We used a dog model in three separate studies: two single radionuclide studies used as references and one dual radionuclide study. Contrast between the left ventricular cavity (LVC) and the myocardium was used in horizontal long axis (HLA) slices as a parameter to evaluate the results of the dual radionuclide correction method with restoration. The increase of the contrast in the dual radionuclide corrected images in both energy windows, i.e. 201Tl primary window (70 keV) and 99Tcm primary window (140 keV), was significant. The cross-talk corrected 70 keV dual radionuclide HLA slice had a contrast of 0.62 compared with 0.35, which was the value in the non-corrected dual radionuclide HLA slice. Restoration improved the contrast to 0.68. In the single radionuclide 201Tl image, the same contrast was 0.59, improving to 0.70 after restoration. For the dual radionuclide 140 keV HLA slice, the contrast increased from 0.69 to 0.76 after cross-talk correction. Additional increase of the contrast to 0.83 resulted from restoration filtering. In the single radionuclide 99Tcm sestamibi 140 keV HLA slice the improvement of contrast was from 0.63 to 0.86 as a result of the restoration. The transformation three-window, dual radionuclide correction method with restoration improves the quality of the simultaneous rest 201Tl/stress 99Tcm sestamibi SPECT imaging.

Time-reversal mirrors and rough surfaces: Experiment

A novel acoustic time-reversal technique has been tested for determining the surface-height autocorrelation function and rms height of rough surfaces. A time-reversal mirror (TRM) was used to insonify periodically and “randomly” rough surfaces of otherwise flat samples immersed in water. The standard use of the TRM is as follows: transmit an initial planar pulse, record the signals at each array element, digitally time reverse each signal, and then retransmit the time-reversed signal. As expected from time-reversal symmetry, one approximately recovers the incident planar pulse after the reflection of the retransmitted wave. The new technique is a simple modification of this procedure. Namely, as before, we record and time reverse the initial reflection. However, we next translate the transducer a fixed distance parallel to the surface before retransmitting. For very small displacements, little change is observed in the TRM’s signal. For larger and larger translations, the TRM’s signal decorrelates, i.e., it less and less resembles the incident pulse. The signal’s decorrelation as a function of displacement is directly related to the autocorrelation function of the rough surface—within the limits set by the system’s point response function. The TRM was used both in reflection mode and in transmission mode. Samples consisted of “randomly” rough surfaces of metal and plastic plates, as well as metal plates machined to have periodically rough surfaces. Evidence is provided that the time-reversal mirror is sensitive to the surface-height autocorrelation and, in favorable cases, determines the autocorrelation function and rms height.

Study of Fiber-Optic Probes for in vivo Medical Raman Spectroscopy

Recent reports indicate that useful diagnostic information can be obtained from ex vivo tissue by using near-infrared Raman spectroscopy. A fiber-optic-based Raman system has been constructed that can obtain spectra in vivo from tissue, typically in less than 30 s. The spectral details are limited by the fluorescence and Raman signal generated in the silica delivery and collection fibers. In this study, fiber-optic probes that are designed to suppress these confounding signals have been characterized and compared with a probe constructed of unfiltered silica fiber. These suppressing probes used a novel design with “in-the-tip” filters, which also had optimized light collection efficiency. The spatial point response functions of the fibers were measured in air, water, and a tissue-simulating, optically turbid medium. Spectra from rabbit tissues were also collected with these probes to demonstrate their performance.

Motion compensated high-frequency synthetic aperture sonar

The Coastal Systems Station has recently completed a set of sea tests using a high-frequency synthetic aperture sonar (HFSAS) mounted on a towed underwater vehicle. The processed results from these tests demonstrate that 2.5-cm resolution can be achieved in shallow water from a small physical array. This system had a Doppler unit to control the ping rate, but had no inertial navigation system and depended entirely upon acoustic backscatter from the seabed to correct for vehicle deviations in the line of sight. In these sea tests the dual overlapped phase center technique [Sheriff, Symposium on Autonomous Underwater Vehicle Technology, pp. 236–245, 1992] was used as the motion compensation algorithm. The tests were conducted over a target field in the Gulf of Mexico that contained a variety of targets, both small sphere and minelike targets. This paper will present results from the HFSAS in the form of a point response function and an acoustic image. The HFSAS achieved between 2.5- and 3-cm resolution on the smallest sphere and produced excellent images of the remaining targets out to a range of approximately 70 m. [Work supported by ONR.]

Optimal design of planar-concave collimators for SPECT - an analytical approach

In this paper we present an analytical tool for the design and optimization of planar-concave collimators for SPECT. We conclude that a single general planar-concave collimator that eliminates the non-isotropic blurring for all SPECT applications does not exist. On the other hand, it is possible to achieve pseudo-optimal collimators for different clinical applications by a careful choice of the design parameters. By classifying the clinical applications into two groups, for instance body and brain studies, the non-isotropic blurring for most SPECT situations may be dramatically reduced by means of planar-concave collimators. The results based on Monte Carlo simulations show that the shape of the point source response function of the reconstructed image obtained from the planar-concave collimator is more isotropic than that obtained from a conventional parallel-hole collimator. Specifically, the ratio of the FWHM of the reconstructed point response function in the radial and tangential direction is increased from 0.5 for the parallel-hole to 0.85 for the planar-concave collimator for sources 200 mm away from the centre of rotation.

Astronomy on the Midcourse Space Experiment

The Midcourse Space Experiment (MSX) carries a varied suite of sensors for imaging in the ultraviolet to the mid-infrared, hyperspectral imaging in the ultraviolet through visible and infrared spectroscopy with a Michelson interferometer. At comparable sensitivity to the Infrared Astronomical Satellite (IRAS) but with a 40 times smaller point response function, the MSX infrared radiometer is ideal for surveying specific large areas such as those in which IRAS was degraded by confusion or not covered at all. This experiment obtains simultaneous observations over a very wide spectral range, from 0.11 to 25 μm, thus providing unique information on the energetics of such diverse objects as comets and H II regions. Initial observations indicate that the astronomy objectives on this experiment will be achieved.

Quantitative characterization of the x-ray imaging capability of rotating modulation collimators with laser light

We developed a method for making quantitative characterizations of bi-grid rotating modulation collimators (RMC's) that are used in a Fourier transform x-ray imager. With appropriate choices of the collimator spacings, this technique can be implemented with a beam-expanded He-Ne laser to simulate the plane wave produced by a point source at infinity even though the RMC's are diffraction limited at the He-Ne wavelength of 632.8 nm. The expanded beam passes through the grid pairs at a small angle with respect to their axis of rotation, and the modulated transmission through the grids as the RMC's rotate is detected with a photomultiplier tube. In addition to providing a quantitative characterization of the RMC's, the method also produces a measured point response function and provides an end-to-end check of the imaging system. We applied our method to the RMC's on the high-energy imaging device (HEIDI) balloon payload in its preflight configuration. We computed the harmonic ratios of the modulation time profile from the laser measurements and compared them with theoretical calculations, including the diffraction effects on irregular grids. Our results indicate the 25-in. (64-cm) x-ray imaging optics on HEIDI are capable of achieving images near the theoretical limit and are not seriously compromised by imperfections in the grids.

Monte Carlo modeling of penetration effect for iodine-131 pinhole imaging

In our Monte Carlo simulation, we employed the variance reduction technique, forced detection, to improve simulation efficiency. For the forced detection, the minimal cone that covers the knife-edge region of a pinhole aperture was used to confine the direction of a photon emission with the vertex located at the emission point. A lead pinhole insert was used to validate our Monte Carlo model. For the validation, the responses of a point source at six different locations along the central ray of the pinhole aperture were measured to compare with simulated responses. The range of distances for the source locations was 3-18 cm from the aperture with the inter-location distance equal to 3 cm. The comparison demonstrated the accuracy of our Monte Carlo model. With the validated Monte Carlo program, we simulated point response functions for pinhole aperture with various aperture span angle, hole size, and materials. The point responses were parameterized using radially circularly symmetric two-dimensional exponential functions. The parameter describing the roll-off rate of an exponential function was expressed in terms of the span angle of the pinhole knife-edge opening and the material used to make the pinhole aperture. The parameterized penetration model can he incorporated into image reconstruction algorithms that compensate for the penetration effect.

Point spread function and coherent line response in optical systems with non-uniform transmission pupils: application to photolithography

The three-dimensional (3D) coherent line and the 3D point response functions of optical systems with non-uniform pupils are discussed for possible applications of these filters in photolithography. In this case, filters that are hyper-resolving in the transverse direction and apodizing in the axial direction are of special interest. For both line- and point-like objects, we analyse the resulting image intensities and show that the resolution, the heights of the side lobes (pseudostructures) and the depth of focus differ in dependence on the pupil filter.

Intraoperative tumor detection: relative performance of single-element, dual-element, and imaging probes with various collimators

Accurate tumor staging depends on finding all tumor sites, and curative surgery requires the removal of ail cancerous tissue from those sites. One technique for locating tumors is to inject patients before surgery with a radiotracer that is preferentially taken up by cancerous tissue. Then, an intraoperative gamma-sensitive probe is used to locate the tumors. Small (<1-cm diameter) tumors, often undetectable by external imaging and by the standard surgical inspection with sight and touch, can be found with probes, Simple calculations and measurements with radioactive tumor models show that small tumors should be detected by single-element probes, but often such probes fail to detect these small tumors in practice. This discrepancy is often caused by the use of a uniform background to predict probe performance, Real backgrounds are nonuniform and can decrease probe performance dramatically. Dual-element, coincidence, or imaging probes may solve the background problem. The authors devised a method to predict probe performance in a realistic background which includes variations in normal organ uptakes. They predict the relative performance of both existing probes and those in the design stage so that optimal detector and collimator configurations can be determined. The procedure includes a Monte-Carlo-calculated point-response function, a numerical torso phantom, and measured biodistributions of a monoclonal antibody. The Hotelling Trace Value, a measure of tumor-detection performance, is computed from the probe responses in simulated studies.

Fourier correction for spatially variant collimator blurring in SPECT

In single-photon emission computed tomography (SPECT), projection data are acquired by rotating the photon detector around a patient, either in a circular orbit or in a noncircular orbit. The projection data of the desired spatial distribution of emission activity is blurred by the point-response function of the collimator that is used to define the range of directions of gamma-ray photons reaching the detector. The point-response function of the collimator is not spatially stationary, but depends on the distance from the collimator to the point. Conventional methods for deblurring collimator projection data are based on approximating the actual distance-dependent point-response function by a spatially invariant blurring function, so that deconvolution methods can be applied independently to the data at each angle of view. A method is described here for distance-dependent preprocessing of SPECT projection data prior to image reconstruction. Based on the special distance-dependent characteristics of the Fourier coefficients of the sinogram, a spatially variant inverse filter can be developed to process the projection data in all views simultaneously. The algorithm is first derived from Fourier analysis of the projection data from the circular orbit geometry. For circular orbit projection data, experimental results from both simulated data and real phantom data indicate the potential of this method. It is shown that the spatial filtering method can be extended to the projection data from the noncircular orbit geometry. Experiments on simulated projection data from an elliptical orbit demonstrate correction of the spatially variant blurring and distortion in the reconstructed image caused by the noncircular orbit geometry.

A rotating and warping projector/backprojector for fan-beam and cone-beam iterative algorithm

A rotating-and-warping projector/backprojector is proposed for iterative algorithms used to reconstruct fan-beam and cone-beam single photon emission computed tomography (SPECT) data. The development of a new projector/backprojector for implementing attenuation, geometric point response, and scatter models is motivated by the need to reduce the computation time yet to preserve the fidelity of the corrected reconstruction. At each projection angle, the projector/backprojector first rotates the image volume so that the pixelized cube remains parallel to the detector, and then warps the image volume so that the fan-beam and cone-beam rays are converted into parallel rays. In the authors' implementation, these two steps are combined so that the interpolation of voxel values are performed only once. The projection operation is achieved by a simple weighted summation, and the backprojection operation is achieved by copying weighted projection array values to the image volume. An advantage of this projector/backprojector is that the system point response function can be deconvolved via the Fast Fourier Transform using the shift-invariant property of the point response when the voxel-to-detector distance is constant. The fan-beam and cone-beam rotating-and-warping projector/backprojector is applied to SPECT data showing improved resolution. >

A new dual-isotope convolution cross-talk correction method: a Tl-201/Tc-99m SPECT cardiac phantom study.

Simultaneous dual-isotope SPECT imaging provides a clear advantage in situations where two concurrent metabolic, anatomic, or background measurements are desired. It obviates the need for two separate imaging sessions, reduces patient motion problems, and provides exact image registration between images. However, a potential limitation of dual-isotope SPECT imaging is contribution of scattered and primary photons from one radionuclide into the second radionuclide's photopeak energy window, referred to here as cross-talk. Cross-talk in both photopeak energy windows can significantly degrade image quality, resolution, and quantitation to an unacceptable level. Simple cross-talk correction method used in dual-radionuclide in vitro counting, even applied on a pixel-by-pixel basis, does not account for the differences in spatial distribution of the photopeak and cross-talk photons. Here a new convolution cross-talk correction method is presented. The convolution filters are derived from point response functions (PRFs) for Tc-99m and Tl-201 point sources. Three separate acquisitions were performed, each with two 20% wide energy windows, one centered at 140 keV and another at 70 keV. The first acquisition was done with Tc-99m solution only, the second with Tl-201 solution only, and the third with a mixture of Tc-99m and Tl-201. The nonuniform RH-2 thorax-heart phantom was used to test a new correction technique. The main difficulty and limitation of the convolution correction approach is caused by the variation in PRF as a function of depth. Thus, average PRF should be used in the creation of an approximative filter.(ABSTRACT TRUNCATED AT 250 WORDS)

Characterization and data collection on a direct-coupled CCD X-ray detector

A large-area, multi-module, CCD-based detector without intensification stages is being developed by our group for X-ray diffraction applications. Each module consists of a fiberoptic taper with a phosphor deposited on the large end and a large-format, scientific CCD bonded to the small end. A single module has been constructed to evaluate the performance of this type of detector. This module has an active area of 43 × 43 mm 2, a point response function FWHM = 80 μm, a dynamic range of > 20 000:1, and a high DQE. Using four parallel readout circuits, the CCD can be read out in 1.8 s. Crystallographic data collected using a rotating-anode source demonstrate the capability of this type of detector.

A filtering technique to compensate for detector response in converging-beam SPECT reconstruction

A nonstationary filtering technique was developed to compensate for spatially variant detector response in fan- and cone-beam SPECT. First the frequency-distance relation for fan- and cone-beam geometries was derived from their parallel-beam counterpart, and then used to compute the Fourier transform of the detector response that was used as the MTF of a Metz filter. The filter was applied to the blurred data before reconstruction. The unique feature of the derived MTF is that it depends on source location, so the filtering is spatially variant. Results of evaluation studies demonstrate that the ratio between the tangential and radial FWHMS of the reconstructed point response function obtained from the authors' filtering technique is closer to one and varies less with source location as compared to the ratio obtained without compensation or using Metz filtering with a stationary detector response. This improvement is mainly because the tangential FWHM is increased to match the radial FWHM better. With a higher order of Metz filter, both tangential and radial FWHMS are slightly smaller but their ratio deviates more from one compared to those of lower orders. In conclusion, the authors' filtering technique provides an effective means to compensate for detector response mainly in terms of reducing anisotropy of the point response function.

Gradients in giant branch morphology in the core of 47 Tucanae

I describe an algorithm which uses the high spatial resolution of the Hubble Space Telescope to complement the high spatial-to-noise, approximately symmetric point response function, relatively large spatial coverage, and standard filters available from ground based images of crowded fields. Applying this technique to the central regions of the globular cluster 47 Tucanae, I find that the morphology of the giant branch in the core is significantly different from that in more distant regions (r approximately equals 5 to 10 core radii) of the cluster. In particular, there appear to be fewer bright giants in the core, along with an enhanced `asymptotic giant branch' (AGB) sequence. Depletion of giants has been observed in the cores of other dense clusters, and may be due to `stripping' of large stars by stellar encounters and/or mass transfer in binary systems. Central concentrations of true asymptotic giant branch stars are not expected to result from dynamical processes; possibly some of these stars may be evolved blue stragglers.

A CCD-based area detector for X-ray crystallography using synchrotron and laboratory sources

The design and characteristics of a CCD-based area detector suitable for X-ray crystallographic studies using both synchrotron and laboratory sources are described. The active area is 75 mm in diameter, the FWHM of the point response function is 0.20 mm, and for Bragg peaks the dynamic range is 900 and the DQE ∼ 0.3. The 1320 × 1035-pixel Kodak CCD is read out into an 8 Mbyte memory system in 0.14 s and digitized to 12 bits. X-ray crystallographic data collected at the NSLS synchrotron from cubic insulin crystals are presented.

The convolution scatter subtraction hypothesis and its validity domain in radioisotope imaging

The additive degradation model assumes that the measured projection data is the sum of scatter and primary distributions. Within this framework, the scatter projection can be estimated by convolving the primary projection with a point or line response function normalized to primary. The convolution scatter-subtraction was formulated to overcome the fact that the primary projection is not available for such estimation. This hypothesis assumes that accurate scatter projection data can be obtained by convolving the measured projection (which is readily available) with scatter response function normalized to primary plus scattered events. The aims of this work are (i) to investigate the truth of this assumption and (ii) to delineate its validity domain. The authors have found that the assumption is valid if relatively large matrices are used to accommodate all the values of the scatter response functions. This requirement is particularly critical when imaging large objects using large discrimination windows. The validity of the assumption rapidly deteriorates as the measured projections change from smooth to diffuse distributions. At this point, the shapes of scatter response functions become important.