True Source Position Research Articles

Assessment of the axial resolution of a compact gamma camera with coded aperture collimator

PurposeHandheld gamma cameras with coded aperture collimators are under investigation for intraoperative imaging in nuclear medicine. Coded apertures are a promising collimation technique for applications such as lymph node localization due to their high sensitivity and the possibility of 3D imaging. We evaluated the axial resolution and computational performance of two reconstruction methods.MethodsAn experimental gamma camera was set up consisting of the pixelated semiconductor detector Timepix3 and MURA mask of rank 31 with round holes of 0.08 mm in diameter in a 0.11 mm thick Tungsten sheet. A set of measurements was taken where a point-like gamma source was placed centrally at 21 different positions within the range of 12–100 mm. For each source position, the detector image was reconstructed in 0.5 mm steps around the true source position, resulting in an image stack. The axial resolution was assessed by the full width at half maximum (FWHM) of the contrast-to-noise ratio (CNR) profile along the z-axis of the stack. Two reconstruction methods were compared: MURA Decoding and a 3D maximum likelihood expectation maximization algorithm (3D-MLEM).ResultsWhile taking 4400 times longer in computation, 3D-MLEM yielded a smaller axial FWHM and a higher CNR. The axial resolution degraded from 5.3 mm and 1.8 mm at 12 mm to 42.2 mm and 13.5 mm at 100 mm for MURA Decoding and 3D-MLEM respectively.ConclusionOur results show that the coded aperture enables the depth estimation of single point-like sources in the near field. Here, 3D-MLEM offered a better axial resolution but was computationally much slower than MURA Decoding, whose reconstruction time is compatible with real-time imaging.

Real-Time Gamma Radioactive Source Localization by Data Fusion of 3D-LiDAR Terrain Scan and Radiation Data from Semi-Autonomous UAV Flights.

Rapid and accurate reconnaissance in the event of radiological and nuclear (RN) incidents or attacks is vital to launch an appropriate response. This need is made stronger by the increasing threat of RN attacks on soft targets and critical infrastructure in densely populated areas. In such an event, even small radioactive sources can cause major disruption to the general population. In this work, we present a real-time radiological source localization method based on an optimization problem considering a background and radiation model. Supported by extensive real-world experiments, we show that an airborne system using this method is capable for reliably locating category 3-4 radioactive sources according to IAEA safety standards in real time from altitudes up to 150 m. A sensor bundle including a LiDAR sensor, a Gamma probe as well as a communication module was mounted on a UAV that served as a carrier platform. The method was evaluated on a comprehensive set of test flights, including 28 flight scenarios over 316 min using three different radiation sources. All additional gamma sources were correctly detected, multiple sources were detected if they were sufficiently separated from each other, with the distance between the true source position and the estimated source averaging 17.1 m. We also discuss the limitations of the system in terms of detection limit and source separation.

How are cosmic gravity fields seen by moving objects? can gravitons deny their origins?

We put the question, how gravitational fields are communicated to space, and how they are recognized in space by moving objects. The general answer given to this question in these days is that field quanta of the gravitational field, called gravitons, are responsible for the communication of such fields. This answer is taken serious here, and then consequently is put into serious doubts when studying several physically coherent consequences. We start by investigating the gravitational influence of cosmic mass associations on moving massive objects when hereby the effect of propagating gravity field quanta, i.e. the gravitons, communicating the position of gravity sources, is taken into account. It is shown that moving objects are affected by gravity sources from a relativistically displaced position, like stars are seen under an aberration angle compared to the true source position. The astonishing effect of that mislocation is that a moving object at its passage through the center of a centrally symmetric galactic mass association undergoes a permanent gravitational deceleration of its relative motion. Furtheron it is shown that under this new view the problem of a planetary object, orbiting a central mass like the sun, takes a non-Keplerian solution, because the orbiting planet permanently should lose orbital angular momentum, since it permanently experiences a gravitational force component antiparallel to its orbital motion. From that an orbital decay time can be derived which predicts that a terrestrial planet should have a spiralling-in period of only a few 104 years which, compared to the expected age of the Earth of about 4.5 Billion years, represents a big problem of understanding. In addition, in view of the presumed action of gravitons from an aberrated source position, this article studies the propagation of cosmic photons over the photospheric limbs of stars. We show that when the center of the gravity field acts from a relativistically displaced position, then no energy change of limb photons when again propagating to larger distances should occur - which does confirm Einstein‘s view - , but also no deflection from the original propagation direction of the photon should occur - which contradicts Einstein‘s derivations. In this article we do not yet offer a rational solution of these newly pinpointed problems, but we simply end with the recommendation to perhaps reinvestigate the theoretical concept of gravitons, thought as to be the quantum messengers of gravitational fields.

Implementation of marine seismic source wavefields in finite-difference methods using wavefield injection

We have developed a method for implementing source wavefields in finite-difference (FD) schemes for marine seismic modeling, migration, and inversion. By using the wavefield injection technique, it is possible to inject arbitrary source wavefields into an FD grid. We have assumed that the notional source signatures from each gun in an air-gun array and their positions are known. The source wavefield is extrapolated to a specified surface below the true source positions using analytical Green’s functions. On this surface, the pressure and its vertical derivative are inserted into the FD grid. The wavefield propagating from this surface will then propagate downward and appear as if it came from the true source position. The source positions do not need to coincide with the FD grid points, and the free-surface reflection coefficient for the source ghost can be specified; i.e., it can deviate from [Formula: see text], and it can be frequency dependent. These features are possible because of the analytical extrapolation step. The presented method allows modeling of any kind of marine seismic source as long as the notional source signature and radiation pattern from each individual source element is known. A simple full-waveform inversion example shows that it is important to honor the source geometry in forward modeling of seismic data.

Improved source path localisation in ring applicators and the clinical impact for gynecological brachytherapy.

PurposeThe path of subsequent dwell positions of an afterloader source being moved through a ring applicator for cervix cancer brachytherapy deviates from an ideal circle and the position of marker wires. This can lead to deviations of several millimetres between real and assumed dwell positions for treatment planning with simplified source path models. The aim of this study was to test video- and autoradiography-based methods for source path determination, and to study the influence of dwell position accuracy on dose-volume histogram (DVH)-parameters.Material and methodsVideos of the exact motion of the source wire through three different (r = 26, 30, 34 mm) computed tomography/magnetic resonance (CT/MR) compatible plastic ring applicators were recorded. Observed dwell positions covering the whole length of each applicators channel were used to adjust the circular source path model. The agreement of the true source positions derived from video analysis with those of the corrected circular source path was verified using autoradiography. The impact of an accurate source path definition on dose planning was analysed by simulating clinically relevant uncertainties in 10 clinical treatment plans.ResultsDepending on the ring size, source path diameters had to be increased by 0.5-1.0 mm in order to achieve acceptable maximum differences between observed and corrected dwell positions (1.3-2.0 mm). Autoradiography analysis showed a positional accuracy within ± 3 mm (extended standard deviation k = 2). For shifts of ± 2.5 mm for even all dwell positions, the systematic and random variation of the D2cm3 for bladder, rectum, and sigmoid was within 3%, while the impact on DVH uncertainties was much smaller for clinical target volume (CTV)HR and gross tumour volume (GTV).ConclusionsIt is strongly advised to verify the real source path for ring applicators during acceptance testing in order to assure accurate source path definition and dose planning. Autoradiography can be used for source path verification with acceptable accuracy for treatment planning and dose reporting.

BrachyView, A novel inbody imaging system for HDR prostate brachytherapy: Design and Monte Carlo feasibility study

High dose rate (HDR) brachytherapy is a form of radiation therapy for treating prostate cancer whereby a high activity radiation source is moved between predefined positions inside applicators inserted within the treatment volume. Accurate positioning of the source is essential in delivering the desired dose to the target area while avoiding radiation injury to the surrounding tissue. In this paper, HDR BrachyView, a novel inbody dosimetric imaging system for real time monitoring and verification of the radioactive seed position in HDR prostate brachytherapy treatment is introduced. The current prototype consists of a 15 × 60 mm(2) silicon pixel detector with a multipinhole tungsten collimator placed 6.5 mm above the detector. Seven identical pinholes allow full imaging coverage of the entire treatment volume. The combined pinhole and pixel sensor arrangement is geometrically designed to be able to resolve the three-dimensional location of the source. The probe may be rotated to keep the whole prostate within the transverse plane. The purpose of this paper is to demonstrate the efficacy of the design through computer simulation, and to estimate the accuracy in resolving the source position (in detector plane and in 3D space) as part of the feasibility study for the BrachyView project. Monte Carlo simulations were performed using the GEANT4 radiation transport model, with a (192)Ir source placed in different locations within a prostate phantom. A geometrically accurate model of the detector and collimator were constructed. Simulations were conducted with a single pinhole to evaluate the pinhole design and the signal to background ratio obtained. Second, a pair of adjacent pinholes were simulated to evaluate the error in calculated source location. Simulation results show that accurate determination of the true source position is easily obtainable within the typical one second source dwell time. The maximum error in the estimated projection position was found to be 0.95 mm in the imaging (detector) plane, resulting in a maximum source positioning estimation error of 1.48 mm. HDR BrachyView is a feasible design for real-time source tracking in HDR prostate brachytherapy. It is capable of resolving the source position within a subsecond dwell time. In combination with anatomical information obtained from transrectal ultrasound imaging, HDR BrachyView adds a significant quality assurance capability to HDR brachytherapy treatment systems.

Positions and sizes of X-ray solar flare sources

We investigate the positions and source sizes of X-ray solar flare sources taking into account Compton backscattering (albedo). Using a Monte Carlo simulation of X-ray photon transport including photo-electric absorption and Compton scattering, we calculate the apparent source sizes and positions of X-ray sources at the solar disk for various source sizes, spectral indices and directivities of the primary source. We show that the albedo effect will alter the true source positions and substantially increase the measured source sizes. The source positions are shifted up to $\sim 0.5"$ radially towards the disk centre and 5 arcsecond source sizes can be two times larger even for an isotropic source (minimum albedo effect) at 1 Mm above the photosphere. X-ray sources therefore should have minimum observed sizes, thus FWHM source size (2.35 times second-moment) will be as large as $\sim 7"$ in the 20-50 keV range for a disk-centered point source at a height of 1 Mm ($\sim 1.4"$) above the photosphere. The source size and position change is the largest for flatter primary X-ray spectra, stronger downward anisotropy, for sources closer to the solar disk centre, and between the energies of 30 and 50 keV. Albedo should be taken into account when X-ray footpoint positions, footpoint motions or source sizes from e.g. RHESSI or Yohkoh data are interpreted, and suggest that footpoint sources should be larger in X-rays than in optical or EUV ranges.

Locating volcano-seismic signals in the presence of rough topography: wave simulations on Arenal volcano, Costa Rica

SUMMARY Quantifying the scattering effects of pronounced volcano topography on the seismic wavefield is an important component in locating and interpreting volcano seismic sources. In this study, we perform seismic wave simulations to quantify the scattering generated by a 3-D digital elevation map and 1-D velocity model of Arenal volcano, Costa Rica. Full waveform synthetic seismograms were generated using a 3-D elastic lattice method including complex topography. Several different simulations were performed where the source location, source type and topographic models were varied. Synthetic seismograms were calculated for 35 seismic arrays each one comprising nine stations. At each array, the slowness vector of wave propagation is estimated from the time delays between the sensors obtained using the cross-spectral method. Results show that the backazimuth estimated for some arrays, in particular those close to the source, deviate from the true source position suggesting strong topographic effects in these regions. The maximum of the probability density function, obtained by crossing the backazimuths of the remaining arrays, coincides exactly with the true source location. We also compare our synthetic seismograms with array results from a physical field study. The true and calculated location misfit depends largely on the topography, but also on the number of antennas, the distance from the source and the spatial resolution of the antennas. The results show that this kind of study could be undertaken prior to the installation of seismic arrays to select the sites that minimize the topographic effects leading to improved source locations.

Evolutionary Optimization of Dynamics Models in Sequential Monte Carlo Target Tracking

This paper describes a new method for the online parameter optimization of various models used to represent the target dynamics in particle filters. The optimization is performed with an evolutionary strategy algorithm, by using the performance of the particle filter as a basis for the objective function. Two different approaches to forming the objective function are presented: the first assumes knowledge of the true source position during the optimization, and the second uses the position estimates from the particle filter to form an estimate of the current ground-truth data. The new algorithm has low computational complexity and is suitable for real-time implementation. A simple and intuitive real-world application of acoustic source localization and tracking is used to highlight the performance of the algorithm. Results show that the algorithm converges to an optimum tracker for any type of dynamics model that is capable of representing the target dynamics.

Sound Source Separation on ICE 3 High Speed Trains Based on Combined Sound Pressure and Sound Velocity Measurements

A measurement method is presented that allows a separation of sound sources based on pass-by measurements of trains. It combines a sound pressure microphone with two sound velocity transducers, all of which are positioned at one point. The velocity transducers are employed as directional microphones. The true source positions and their sound power are determined by solving an inverse problem: In a system of propagation equations the source positions are optimized until a best fit to the measured signals is achieved. Measurement results are shown for pass-by measurements of German ICE 3 high speed trains at speeds between 200 and 250 km/h. The extended pantographs are thereby identified as dominating sound sources in the upper part of the vehicles. The measurements yield reproducible results and are in accordance with data taken from literature. The method represents an alternative to the array measurement technique although with a considerably smaller measurement and data analysis effort. Information on the sound power of multiple sources is gathered with an accuracy comparable to array measurements. The localization of the sources is though less precise and the separation is limited to two sources at a time. Therefore the measurement concept can not be seen as a general replacement of the array measurement technique. Nevertheless there is a broad range of applications where a fine spacial resolution is not of major interest. In these cases the method is likely to represent an appropriate substitute.

Non‐double‐couple mechanism of moderate earthquakes near Zakynthos, Greece, April 2006; explanation in terms of complexity

ABSTRACTDeviation of earthquakes from the double‐couple mechanism is an important, but delicate tool to study their source processes. For assessing the double‐couple percentage, the paper suggests to complement the standard least‐square moment‐tensor retrieval with a hierarchic spatio‐temporal grid search, progressively closer to the true source position and time. It enables identification of the double‐couple percentage convergence, while its limit is the resulting double‐couple percentage value, or range. The so‐called double‐couple percentage (DC%) versus correlation plots are introduced and difficulties of the double‐couple percentage assessment are discussed. It is proved that even close to the true source position, where the strike‐dip‐rake angles are already stable (within a few degrees), the double‐couple percentage may still vary by dozens of per cent. Moreover, even at the optimum spatial position, the double‐couple percentage estimate is extremely sensitive (0 to 100%) to small variations of the subevent origin time. This behaviour is explained in terms of the source complexity, implying a time‐dependent moment tensor. Therefore, the double‐couple percentage of complex events depends on the studied frequency band and, in general, also on the station azimuth. This explains broad variations of the double‐couple percentage reports among seismic agencies. Three earthquakes of mutually close epicentres were investigated (Zakynthos, Western Greece, April 2006, magnitudes ∼5.5) and a strong non‐double‐couple component of one of them was identified (double‐couple percentage of about 20%). Two equivalent models of this earthquake were found: a single‐event non‐ double‐couple model, and a double‐event model consisting of two double‐couple sources with highly different mechanisms.

Ambiguity analysis of matched-field source localization under spatially correlated noise field

Matched-field processing (MFP) concerns estimation of source location by exploiting full-wave modeling of acoustic waveguide propagation. The ambiguity output in MFP relies on the correlation between the signal field at the true source position and the signal field at each scanning source position. This correlation often shows a multimodal structure due to the nonlinear parameter dependence: in addition to a mainlobe around the true source position, there are unpredictable prominent high sidelobes elsewhere. For a well-conditioned problem, in the absence of noise the peak output is guaranteed to occur at the true source position. In the presence of noise, we will probably have some peak outputs around the sidelobes, introducing a large localization error. Therefore, output ambiguity structure is a very important factor in the development of any matched-field algorithm operated in low-SNR scenarios. To analyze the ambiguity behavior, a quantitative approach for error analysis has previously been developed in the context of the maximum likelihood estimate (MLE) with spatially white noise. In this talk, generalization to including spatially correlated noise field introduced by discrete interferences and/or surface distribution sources is discussed.

Ray-theoretic localization of an impulsive source in a stratified ocean using two hydrophones

A method is presented for passive localization of impulsive acoustic sources in a stratified ocean by measuring relative times of direct and surface-reflected arrivals at two hydrophones. The proposed method is based on ray theory and takes into account the effects of refraction on the geometry of acoustic paths (ray bending) and travel times, generalizing previous approaches based on the homogeneous-ocean assumption (straight-line localization). If the hydrophone depths are known, then the source depth and distance from each hydrophone can be estimated from the three differential arrival times. If in addition the hydrophone separation is known, the bearing of the source can be estimated as well. Apart from the effects on ray geometry and travel times, stratification affects localization by introducing shadow zones and caustics. For source locations in the neighborhood of caustics, the localization problem accepts two solutions, one of which is the true source location and the other one which is an artifact (ghost solution). This ambiguity can be resolved in the case of tracking moving sources since as the source moves away from the caustic only the track corresponding to the true source position will be continued. The present method has been developed primarily for monitoring the dive behavior of sperm whales producing acoustic clicks, yet it is general and can be applied for the localization and tracking of any kind of impulsive acoustic source in the ocean.

A comparison of model-based and hyperbolic localization techniques as applied to marine mammal calls

A common technique for the passive acoustic localization of singing marine mammals is that of hyperbolic fixing. This technique assumes straight-line, constant wave speed acoustic propagation to associate travel time with range, but in some geometries, these assumptions can lead to localization errors. A new localization algorithm based on acoustic propagation models can account for waveguide and multipath effects, and it has successfully been tested against real acoustic data from three different environments (Hawaii, California, and Bahamas) and three different species (humpback, blue, and sperm whales). Accuracy of the model-based approach has been difficult to verify given the absence of concurrent visual and acoustic observations of the same animal. However, the model-based algorithm was recently exercised against a controlled source of known position broadcasting recorded whale sounds, and location estimates were then compared to hyperbolic techniques and true source position. In geometries where direct acoustic paths exist, both model-based and hyperbolic techniques perform equally well. However, in geometries where bathymetric and refractive effects are important, such as at long range, the model-based approach shows improved accuracy.

A deghosting algorithm using cross-correlation in triangulate positioning systems

By determining the direction of arrival (DOA) of the radio waves using multiple DOA sensors, the position of the radio wave source can be determined passively by calculating the intersection of the directional lines. When, however, more than one wave source exists and the multiple positions of the wave sources are determined simultaneously using DOA sensors that can measure the angles separately, ghosts may appear at the intersections of the directional lines, which cause ambiguity. In this study, DOA sensors using the MUSIC algorithm are assumed, and an algorithm is proposed, which can eliminate such ghosts and determine the true source positions by determining the match between the directional lines based on the cross-correlation coefficient among the multiple incident waves. The idea is to eliminate the ghosts and estimate the wave sources by estimating the match between the directional lines, utilizing the property that the cross-correlation coefficient does not depend much on the sensor position. Simulation results demonstrating the usefulness of the proposed deghosting algorithm are also presented. © 2000 Scripta Technica, Electron Comm Jpn Pt 1, 83(5): 37–46, 2000

Rapid estimation of dolphin whistle bearings using a sparse towed hydrophone array

Acoustic bearings were obtained from modulated dolphin whistles (3–20 kHz range) using a three-element towed array with a 9-m aperture. This system has performed reliably on animals whose range was known to be greater than 3 km away. It also has worked well under Beaufort five sea states. The algorithm presented here is unusual in that the signals are beamformed in the frequency domain, instead of being cross-correlated in the time domain. Beamforming on such a sparse array is feasible because the signals are broadband, allowing beams to be computed at multiple frequencies. The grating lobes, or false locations, shift their bearings with frequency, while the true source position remains fixed and can thus be identified. Frequency beamforming may complement temporal cross-correlation methods in situations when the signals are heavily contaminated with noise and multipaths, when multiple animal calls are received simultaneously, or when long time sequences need to be processed and compactly stored to memory. [Work funded by U.S. Dept. of Commerce.]

Sensor array processing performance evaluation via bootstrap resampling

This paper examines bootstrap resampling methods for evaluating the performance of source localization methods on real sensor array data without precise a priori knowledge of true source positions and the underlying data distribution. Bootstrap resampling methods are used here to measure the standard deviation of bearing estimates achieved by performing delay-and-sum, minimum variance, and MUSIC spatial spectral estimation on a real narrow-band towed-array data set. Some simple theoretical guidelines are given to indicate the sample size required to achieve accurate performance estimation. Results suggest that quantitative bearing estimation performance comparisons can be made within the observation time constraints imposed by source and field dynamics. Further, comparisons of bootstrap estimates to Monte Carlo and theoretical benchmarks provide a means of validating the parametric models assumed by these conventional analysis techniques.

Simulations of Matched-Field Processing in a Deep-Water Pacific Environment

Conventional bearing estimation procedures employ planewave steering vectors as replicas of the true field and seek to resolve in angle by maximizing a power function representing the agreement between actual and replica fields. For vertical arrays in oceanic waveguides the received field depends on range and depth, and it is natural to replace the look-direction ( \theta ) by a look-position ( r, z ). Thus an environmental model is constructed by specifying ocean depth, sound speed profile, bottom properties, etc., and a propagation model is employed to construct a replica of the field that would be received on the array for a particular source position. The usual estimators (e.g., Bartlett or maximum likelihood) are then used to gauge the agreement between actual and replica fields and the true source position is identified as that position where the agreement is best. The performance of this kind of matched-field processing is strongly affected by the environment. In particular, we demonstrate through simulations that for a deep-water Pacific environment dominated by waterborne paths, ambiguities or sidelobes are associated with convergence zones. In the absence of mismatch between replica and actual fields we find that a 16-element array performs extremely well in low-frequency regimes. Mismatch caused by uncertainties in phone positions, bottom parameters, ocean sound speed, surface and bottom roughness, etc., causes degradation in localization performance. The impact of some of these effects on conventional and maximum likelihood estimators is examined through simulation.

Simulations of matched‐field processing in a deep‐water Pacific environment

Matched‐field processing is a signal processing technique for arrays in which field vectors for assumed source positions (range and depth) are substituted for plane‐wave steering vectors in conventional linear and nonlinear beamformers. The field vectors are computed by standard acoustic field models (FFP, normal mode, etc.) which take into account propagation effects in an oceanic waveguide. The output is an ambiguity surface over possible source positions in which a peak is expected at the true source position. Accuracy of the computed fields is limited in large part by our knowledge of the environment. This environmental mismatch causes degradation in localization performance, sometimes leading to large errors in estimation of source position. In order to assess the significance of this effect, simulations were performed in which a measured field is synthesized using a slightly different environmental model from that used for the steering vectors. The differences were introduced to simulate expected er...

Correcting Low-Frequency Solar Radio Source Positions for Ionospheric Refraction

We describe a method for reducing displacements in radio source positions caused by ionospheric refraction. Our method is an improvement on that used by Wild et al. (1959), who assumed all frequencies in the 40-70 MHz band came from the same position above the Sun and applied an f-2 correction for ionospheric refraction. Our method retains the dispersion of source position with frequency, which is inherent in the radio source, but allows for the f-2 ionospheric effect. We also discuss ways of estimating the absolute source positions from a knowledge of ionospheric density gradients. A typical example of ionospheric variations on solar records is shown in Figure 1(a). Here we have plotted the observed source positions on an f-2 scale. The measurements refer to a solar storm continuum burst which occurred on 1981 May 9 following an importance 2B flare at 08°N., 38°E., heliographic coordinates. From previous observations of such events we think it highly likely that the true source positions are stationary and displaced with decreasing frequency outwards along a line close to the radial direction above the flare. Figure 1(a) shows that: (a) the 160, 80 and 43 MHz source displacements vary as f-2; (b) there is a systematic slow drift of the source positions towards the south and east which increases with increasing hour angle; (c) superimposed on this steady drift is a quasi-periodic variation in source position with a period ~20 min.