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Radon transform. Maps f on the (x, y)-domain to Rf on the (α, s)-domain.. In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line.
In theory, the inverse Radon transformation would yield the original image. The projection-slice theorem tells us that if we had an infinite number of one-dimensional projections of an object taken at an infinite number of angles, we could perfectly reconstruct the original object, f ( x , y ) {\displaystyle f(x,y)} .
Radon compounds are chemical compounds formed by the element radon (Rn). Radon is a noble gas, i.e. a zero-valence element, and is chemically not very reactive. The 3.8-day half-life of radon-222 makes it useful in physical sciences as a natural tracer. Because radon is a gas under normal circumstances, and its decay-chain parents are not, it ...
The fourth is a modified wave-field transform base on frequency decomposition and slant stacking, performed by Xia et al. (2007). [9] The fifth is a high-resolution Linear Radon transformation performed by Luo et al. (2008). [10] In performing a wave-field transformation, a slant stack is done, followed by a Fourier transform. The way in which ...
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field.
The pressure on a pressure-temperature diagram (such as the water phase diagram shown above) is the partial pressure of the substance in question. A phase diagram in physical chemistry , engineering , mineralogy , and materials science is a type of chart used to show conditions (pressure, temperature, etc.) at which thermodynamically distinct ...
Natural radon concentrations in the Earth's atmosphere are so low that radon-rich water in contact with the atmosphere will continually lose radon by volatilization. Hence, ground water has a higher concentration of 222 Rn than surface water, because radon is continuously produced by radioactive decay of 226 Ra present in rocks.
The discontinuity in , and other properties, e.g. internal energy, , and entropy,, of the substance, is called a first order phase transition. [12] [13] In order to specify the unique experimentally observed pressure, (), at which it occurs another thermodynamic condition is required, for from Fig.1 it could clearly occur for any pressure in the range .