This dissertation considers a method for processing two-dimensional (2-D) signals (e.g. imagery) by transformation to a coordinate space where the 2-D operation separates into orthogonal 1-D operations. After processing, the 2-D output is reconstructed by a second coordinate transformation. This approach is based on the Radon transform, which maps a two-dimensional Cartesian representation of a signal into a series of one-dimensional signals by line-integral projection. The mathematical principles of this transformation are well-known as the basis for medical computed tomography. This approach can process signals more rapidly than conventional digital processing and more flexibly and precisely than optical techniques. A new formulation of the Radon transform is introduced that employs a new transformation--the central-slice transform--to symmetrize the operations between the Cartesian and Radon representations of the signal and to aid in analyzing operations that may be susceptible to solution in this manner. It is well-known that 2-D Fourier transforms and convolutions can be performed by 1-D operations after Radon transformation, as proven by the central-slice and filter theorems. Demonstrations of these operations via Radon transforms are described. An optical system has been constructed to derive the line-integral projections of 2-D transmissive or reflective input data. Fourier transforms of the projections are derived by a surface-acoustic-wave chirp Fourier transformer, and filtering is performed in a surface-acoustic-wave convolver. Reconstruction of the processed 2-D signal is performed optically. The system can process 2-D imagery at approximately 5 frames/second, though rates to 30 frames/second are achievable if a faster image rotator is added. Other signal processing operations in Radon space are demonstrated, including Labeyrie stellar speckle interferometry, the Hartley transform, and the joint coordinate-frequency representations such as the Wigner distribution function. Other operations worthy of further study include derivation of the 2-D cepstrum, and several spectrum estimation algorithms.

The project has been concerned with the study of radon and other natural radionuclides in the U-238 decay series in the environment. The contribution made by radon and its daughter radionuclides to population radiation dose both in the air and in water supplies has been investigated. The natural radioactivity of the river water, stream water, sediments and freshwater mussels have been measured using a thick source alpha counting technique and γ-spectrometry (water samples were preconcentrated by manganese dioxide precipitation method). The ^226Ra activity ranged from 10-20 Bq m^-3 in the river and 4-30 Bq m^-3 in stream water. The highest values were found close to the source of the river where the water flowed through an area of igneous rocks. Such granite type rocks are enriched in uranium and thorium. Concentrations of radon and its daughters were measured, indoors and outdoors, using a grab sample technique. Outdoor concentrations were 10-30 Bq m^-3 depending on underlying rocks, meteorological condition (pressure, temperature, snow, rain), while indoor values ranged between 20 and 600 Bq m^-3 depending on radon input rate (source strength, ventilation rate and pressure inside the building). The relationship between the indoor ^222Rn concentration and ventilation rate was investigated. The radiation dose and the consequent risk due to inhalation of radon and its daughters were estimated. The annual effective dose equivalent ranged from 0.12 to 11 mSv. The radon concentrations in well waters were measured and were found to range between 3 and 76 Bq ℓ-1. This variation can be associated with different bedrock. A model predicting average indoor increments due to this source is presented and supported by a series of measurements made in the houses which were supplied by well water. The maximum annual effective dose equivalent from inhalation and ingestion was found to be 0.27 and 0.054 mSv respectively.

Estudio breve sobre problemas mal condicionados y la Transformada de Radon. Obtención de la ecuación que gobierna la tomografía computarizada, estudio del mal condicionamiento del problema obtenido. Métodos para resolver este problema mal condicionado; modelo de Shepp - Logan, elaboración de algunos didacticos, elaboración de programas y resultados de la ejecución computacional. -- Palabras Claves: Tomografía computarizada, CT, Problemas inversos, Problemas mal condicionados transformada de radón. / -- A brief study of bad conditioned problems and the Radon Transform. We get the equation that model computerized tomography and study the bad conditioned of the obtained problem. Methods to solve this bad conditioned problem, Shepp-Logan model, elaboration of some didactical, elaboration of programs and results of the computacional execution. -- Key Words: Computarized tomography, CT, Inverse problems, Bad conditioned problems radon transform / Tesis

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Environmental Sciences." Includes bibliographical references (p. 117-119).

Carbon filled columns were built and tested as prototype radon filters. The length of time taken for a pulse of radon to travel from one end of the filter to the other was measured using nitrogen, and then air as the carrier gas. Its dependency on two variables were investigated: temperature of the tube and the flow-rate of carrier gas through the column. Using Height Equivalent to a Theoretical Stage (HETS) the carbon was found to have a adsorption constant (ka) of 9.7 ± 1.7 L/g at STP, and a binding energy value (Eb) of (30±1) kJ/mol. The radon concentration in the carrier gas was measured using a silicon detector housed in a metal chamber with a charged collector plate. Most filter tests measured Rn concentrations by measuring levels of the daughter atom 218Po. A computer simulation was created for aspects of both the working detector chamber and a prototype detector chamber. The charged fractions of 218Po and 214Po were calculated by comparing the Monte Carlo simulation to data obtained from the detectors. The positively charged fraction of 218Po was found to be (80 ± 9)% and 214Po was (110 ± 180)%. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2008-08-29 16:38:33.442

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Exploration for geothermal resources in Hawaii has required adaptation of conventional exploration techniques as well as the implementation of relatively new techniques because of the complexities introduced by the oceanic island environment / ill / maps

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (p. 47-51).