Using fractal downscaling of satellite precipitation products for hydrometeorological applications

The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L»l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (~25-km grid spacing) to the same resolution as the NCEP stage IV products (~4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied. © 2010 American Meteorological Society.

Harmonic source wavefront aberration correction for ultrasound imaging.

A method is proposed which uses a lower-frequency transmit to create a known harmonic acoustical source in tissue suitable for wavefront correction without a priori assumptions of the target or requiring a transponder. The measurement and imaging steps of this method were implemented on the Duke phased array system with a two-dimensional (2-D) array. The method was tested with multiple electronic aberrators [0.39π to 1.16π radians root-mean-square (rms) at 4.17 MHz] and with a physical aberrator 0.17π radians rms at 4.17 MHz) in a variety of imaging situations. Corrections were quantified in terms of peak beam amplitude compared to the unaberrated case, with restoration between 0.6 and 36.6 dB of peak amplitude with a single correction. Standard phantom images before and after correction were obtained and showed both visible improvement and 14 dB contrast improvement after correction. This method, when combined with previous phase correction methods, may be an important step that leads to improved clinical images.

Calibrating single-ended fiber-optic Raman spectra distributed temperature sensing data.

Hydrologic research is a very demanding application of fiber-optic distributed temperature sensing (DTS) in terms of precision, accuracy and calibration. The physics behind the most frequently used DTS instruments are considered as they apply to four calibration methods for single-ended DTS installations. The new methods presented are more accurate than the instrument-calibrated data, achieving accuracies on the order of tenths of a degree root mean square error (RMSE) and mean bias. Effects of localized non-uniformities that violate the assumptions of single-ended calibration data are explored and quantified. Experimental design considerations such as selection of integration times or selection of the length of the reference sections are discussed, and the impacts of these considerations on calibrated temperatures are explored in two case studies.

On-board Robotic Multi-pinhole SPECT System for Region-of-interest (ROI) Imaging

On-board image guidance, such as cone-beam CT (CBCT) and kV/MV 2D imaging, is essential in many radiation therapy procedures, such as intensity modulated radiotherapy (IMRT) and stereotactic body radiation therapy (SBRT). These imaging techniques provide predominantly anatomical information for treatment planning and target localization. Recently, studies have shown that treatment planning based on functional and molecular information about the tumor and surrounding tissue could potentially improve the effectiveness of radiation therapy. However, current on-board imaging systems are limited in their functional and molecular imaging capability. Single Photon Emission Computed Tomography (SPECT) is a candidate to achieve on-board functional and molecular imaging. Traditional SPECT systems typically take 20 minutes or more for a scan, which is too long for on-board imaging. A robotic multi-pinhole SPECT system was proposed in this dissertation to provide shorter imaging time by using a robotic arm to maneuver the multi-pinhole SPECT system around the patient in position for radiation therapy.

A 49-pinhole collimated SPECT detector and its shielding were designed and simulated in this work using the computer-aided design (CAD) software. The trajectories of robotic arm about the patient, treatment table and gantry in the radiation therapy room and several detector assemblies such as parallel holes, single pinhole and 49 pinholes collimated detector were investigated. The rail mounted system was designed to enable a full range of detector positions and orientations to various crucial treatment sites including head and torso, while avoiding collision with linear accelerator (LINAC), patient table and patient.

An alignment method was developed in this work to calibrate the on-board robotic SPECT to the LINAC coordinate frame and to the coordinate frames of other on-board imaging systems such as CBCT. This alignment method utilizes line sources and one pinhole projection of these line sources. The model consists of multiple alignment parameters which maps line sources in 3-dimensional (3D) space to their 2-dimensional (2D) projections on the SPECT detector. Computer-simulation studies and experimental evaluations were performed as a function of number of line sources, Radon transform accuracy, finite line-source width, intrinsic camera resolution, Poisson noise and acquisition geometry. In computer-simulation studies, when there was no error in determining angles (α) and offsets (ρ) of the measured projections, the six alignment parameters (3 translational and 3 rotational) were estimated perfectly using three line sources. When angles (α) and offsets (ρ) were provided by Radon transform, the estimation accuracy was reduced. The estimation error was associated with rounding errors of Radon transform, finite line-source width, Poisson noise, number of line sources, intrinsic camera resolution and detector acquisition geometry. The estimation accuracy was significantly improved by using 4 line sources rather than 3 and also by using thinner line-source projections (obtained by better intrinsic detector resolution). With 5 line sources, median errors were 0.2 mm for the detector translations, 0.7 mm for the detector radius of rotation, and less than 0.5° for detector rotation, tilt and twist. In experimental evaluations, average errors relative to a different, independent registration technique were about 1.8 mm for detector translations, 1.1 mm for the detector radius of rotation (ROR), 0.5° and 0.4° for detector rotation and tilt, respectively, and 1.2° for detector twist.

Simulation studies were performed to investigate the improvement of imaging sensitivity and accuracy of hot sphere localization for breast imaging of patients in prone position. A 3D XCAT phantom was simulated in the prone position with nine hot spheres of 10 mm diameter added in the left breast. A no-treatment-table case and two commercial prone breast boards, 7 and 24 cm thick, were simulated. Different pinhole focal lengths were assessed for root-mean-square-error (RMSE). The pinhole focal lengths resulting in the lowest RMSE values were 12 cm, 18 cm and 21 cm for no table, thin board, and thick board, respectively. In both no table and thin board cases, all 9 hot spheres were easily visualized above background with 4-minute scans utilizing the 49-pinhole SPECT system while seven of nine hot spheres were visible with the thick board. In comparison with parallel-hole system, our 49-pinhole system shows reduction in noise and bias under these simulation cases. These results correspond to smaller radii of rotation for no-table case and thinner prone board. Similarly, localization accuracy with the 49-pinhole system was significantly better than with the parallel-hole system for both the thin and thick prone boards. Median localization errors for the 49-pinhole system with the thin board were less than 3 mm for 5 of 9 hot spheres, and less than 6 mm for the other 4 hot spheres. Median localization errors of 49-pinhole system with the thick board were less than 4 mm for 5 of 9 hot spheres, and less than 8 mm for the other 4 hot spheres.

Besides prone breast imaging, respiratory-gated region-of-interest (ROI) imaging of lung tumor was also investigated. A simulation study was conducted on the potential of multi-pinhole, region-of-interest (ROI) SPECT to alleviate noise effects associated with respiratory-gated SPECT imaging of the thorax. Two 4D XCAT digital phantoms were constructed, with either a 10 mm or 20 mm diameter tumor added in the right lung. The maximum diaphragm motion was 2 cm (for 10 mm tumor) or 4 cm (for 20 mm tumor) in superior-inferior direction and 1.2 cm in anterior-posterior direction. Projections were simulated with a 4-minute acquisition time (40 seconds per each of 6 gates) using either the ROI SPECT system (49-pinhole) or reference single and dual conventional broad cross-section, parallel-hole collimated SPECT. The SPECT images were reconstructed using OSEM with up to 6 iterations. Images were evaluated as a function of gate by profiles, noise versus bias curves, and a numerical observer performing a forced-choice localization task. Even for the 20 mm tumor, the 49-pinhole imaging ROI was found sufficient to encompass fully usual clinical ranges of diaphragm motion. Averaged over the 6 gates, noise at iteration 6 of 49-pinhole ROI imaging (10.9 µCi/ml) was approximately comparable to noise at iteration 2 of the two dual and single parallel-hole, broad cross-section systems (12.4 µCi/ml and 13.8 µCi/ml, respectively). Corresponding biases were much lower for the 49-pinhole ROI system (3.8 µCi/ml), versus 6.2 µCi/ml and 6.5 µCi/ml for the dual and single parallel-hole systems, respectively. Median localization errors averaged over 6 gates, for the 10 mm and 20 mm tumors respectively, were 1.6 mm and 0.5 mm using the ROI imaging system and 6.6 mm and 2.3 mm using the dual parallel-hole, broad cross-section system. The results demonstrate substantially improved imaging via ROI methods. One important application may be gated imaging of patients in position for radiation therapy.

A robotic SPECT imaging system was constructed utilizing a gamma camera detector (Digirad 2020tc) and a robot (KUKA KR150-L110 robot). An imaging study was performed with a phantom (PET CT PhantomTM), which includes 5 spheres of 10, 13, 17, 22 and 28 mm in diameter. The phantom was placed on a flat-top couch. SPECT projections were acquired with a parallel-hole collimator and a single-pinhole collimator both without background in the phantom, and with background at 1/10th the sphere activity concentration. The imaging trajectories of parallel-hole and pinhole collimated detectors spanned 180 degrees and 228 degrees respectively. The pinhole detector viewed a 14.7 cm-diameter common volume which encompassed the 28 mm and 22 mm spheres. The common volume for parallel-hole was a 20.8-cm-diameter cylinder which encompassed all five spheres in the phantom. The maneuverability of the robotic system was tested by navigating the detector to trace the flat-top table while avoiding collision with the table and maintaining the closest possible proximity to the common volume. For image reconstruction, detector trajectories were described by radius-of-rotation and detector rotation angle θ. These reconstruction parameters were obtained from the robot base and tool coordinates. The robotic SPECT system was able to maneuver the parallel-hole and pinhole collimated SPECT detectors in close proximity to the phantom, minimizing impact of the flat-top couch on detector to center-of-rotation (COR) distance. In no background case, all five spheres were visible in the reconstructed parallel-hole and pinhole images. In with background case, three spheres of 17, 22 and 28 mm diameter were readily observed with the parallel-hole imaging, and the targeted spheres (22 and 28 mm diameter) were readily observed in the pinhole ROI imaging.

In conclusion, the proposed on-board robotic SPECT can be aligned to LINAC/CBCT with a single pinhole projection of the line-source phantom. Alignment parameters can be estimated using one pinhole projection of line sources. This alignment method may be important for multi-pinhole SPECT, where relative pinhole alignment may vary during rotation. For single pinhole and multi-pinhole SPECT imaging onboard radiation therapy machines, the method could provide alignment of SPECT coordinates with those of CBCT and the LINAC. In simulation studies of prone breast imaging and respiratory-gated lung imaging, the 49-pinhole detector showed better tumor contrast recovery and localization in a 4-minute scan compared to parallel-hole detector. On-board SPECT could be achieved by a robot maneuvering a SPECT detector about patients in position for radiation therapy on a flat-top couch. The robot inherent coordinate frames could be an effective means to estimate detector pose for use in SPECT image reconstruction.

Numerical Simulations for the Design of Novel Integrated Parallel Reception, Excitation, and Shimming (iPRES) Coil Arrays

Magnetic field inhomogeneity results in image artifacts including signal loss, image blurring and distortions, leading to decreased diagnostic accuracy. Conventional multi-coil (MC) shimming method employs both RF coils and shimming coils, whose mutual interference induces a tradeoff between RF signal-to-noise (SNR) ratio and shimming performance. To address this issue, RF coils were integrated with direct-current (DC) shim coils to shim field inhomogeneity while concurrently emitting and receiving RF signal without being blocked by the shim coils. The currents applied to the new coils, termed iPRES (integrated parallel reception, excitation and shimming), were optimized in the numerical simulation to improve the shimming performance. The objectives of this work is to offer a guideline for designing the optimal iPRES coil arrays to shim the abdomen.

In this thesis work, the main field () inhomogeneity was evaluated by root mean square error (RMSE). To investigate the shimming abilities of iPRES coil arrays, a set of the human abdomen MRI data was collected for the numerical simulations. Thereafter, different simplified iPRES(N) coil arrays were numerically modeled, including a 1-channel iPRES coil and 8-channel iPRES coil arrays. For 8-channel iPRES coil arrays, each RF coil was split into smaller DC loops in the x, y and z direction to provide extra shimming freedom. Additionally, the number of DC loops in a RF coil was increased from 1 to 5 to find the optimal divisions in z direction. Furthermore, switches were numerically implemented into iPRES coils to reduce the number of power supplies while still providing similar shimming performance with equivalent iPRES coil arrays.

The optimizations demonstrate that the shimming ability of an iPRES coil array increases with number of DC loops per RF coil. Furthermore, the z direction divisions tend to be more effective in reducing field inhomogeneity than the x and y divisions. Moreover, the shimming performance of an iPRES coil array gradually reach to a saturation level when the number of DC loops per RF coil is large enough. Finally, when switches were numerically implemented in the iPRES(4) coil array, the number of power supplies can be reduced from 32 to 8 while keeping the shimming performance similar to iPRES(3) and better than iPRES(1). This thesis work offers a guidance for the designs of iPRES coil arrays.