The Fourier transform, named after Joseph Fourier, is a mathematical transformation employed to transform signals between time (or spatial) domain andfrequency domain, which has many applications in physics and engineering. The new function is then known as the Fourier transform and/or the frequency spectrum of the function f. The Fourier transform is also a reversible operation. Thus, given the function , one can determine the original function, f. (See Fourier inversion theorem.) f and are also respectively known as time domain and frequency domain representations of the same “event”. Most often perhaps, f is a real-valued function, and is complex valued, where a complex number describes both the amplitude and phase of a corresponding frequency component. In general, f is also complex, such as the analytic representation of a real-valued function. The term “Fourier transform” refers to both the transform operation and to the complex-valued function it produces.
The Hounsfield unit (HU) scale is a linear transformation of the original linear attenuation coefficient measurement in one in which the radiodensity of distilled water at standard pressure and temperature (STP) is defined as zero Hounsfield units (HU), while the radiodensity of air at STP is defined as -1000 HU.
For a material X with linear attenuation coefficient μX, the corresponding HU value is therefore given by where is the linear attenuation coefficient of water.
Thus, a change of one Hounsfield unit (HU) represents a change of 0.1% of the attenuation coefficient of water since the attenuation coefficient of air is nearly zero.
It is the definition for CT scanners that are calibrated with reference to water.
Tissue CT number (HU)
40 - 60
10 - 40
-50 - -100
A voxel (volumetric pixel or Volumetric Picture Element) is a volume element, representing a value on a regular grid in three dimensional space. This is analogous to a texel, which represents 2D image data in a bitmap (which is sometimes referred to as a pixmap). As with pixels in a bitmap, voxels themselves do not typically have their position (their coordinates) explicitly encoded along with their values. Instead, the position of a voxel is inferred based upon its position relative to other voxels (i.e., its position in the data structure that makes up a single volumetric image). In contrast to pixels and voxels, points and polygons are often explicitly represented by the coordinates of their vertices. A direct consequence of this difference is that polygons are able to efficiently represent simple 3D structures with lots of empty or homogeneously filled space, while voxels are good at representing regularly sampled spaces that are non-homogeneously filled.
mottle caused by the statistical fluctuation of the number of photons absorbed by the intensifying screens to form the light image on the film; faster screens produce more quantum mottle.
Event-related field, the magnetic equivalent of an event-related potential in functional brain imaging