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A Box Spline Calculus for Computed Tomography

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Non-uniform discrete Fourier transform

In applied mathematics, the nonuniform discrete Fourier transform (NUDFT or NDFT) of a signal is a type of Fourier transform, related to a discrete Fourier transform or discrete-time Fourier transform, but in which the input signal is not sampled at equally spaced points or frequencies (or both). It is a generalization of the shifted DFT. It has important applications in signal processing, magnetic resonance imaging, and the numerical solution of partial differential equations.

Fourier analysis

In mathematics, Fourier analysis (ˈfʊrieɪ,_-iər) is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer. The subject of Fourier analysis encompasses a vast spectrum of mathematics.

Computed tomography angiography

Computed tomography angiography (also called CT angiography or CTA) is a computed tomography technique used for angiography—the visualization of arteries and veins—throughout the human body. Using contrast injected into the blood vessels, images are created to look for blockages, aneurysms (dilations of walls), dissections (tearing of walls), and stenosis (narrowing of vessel). CTA can be used to visualize the vessels of the heart, the aorta and other large blood vessels, the lungs, the kidneys, the head and neck, and the arms and legs.

Bézier surface

Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central control points; rather, it is "stretched" toward them as though each were an attractive force. They are visually intuitive and, for many applications, mathematically convenient.