Inherent filtration refers to a permanently implemented filter in the useful beam. Inherent filtration includes the window of the x-ray tube and any permanent enclosure for the tube or source.

Added filtration refers to filters, used in addition to the inherent filtration.

Different filter types are used in medical imaging to improve image quality.
Filter materials such as aluminum, iron or copper, located in the primary x-ray beam between tube and collimator, filter out lower energetic x-rays (for example bow-tie filter). Filters partially absorb or attenuate the x-ray beam to prevent radiation overexposure. The sum of filtration consists of inherent and added filters. This filtration affects the beam energy and ability to penetrate materials.
Mathematical filter procedures are used for the convolution of the attenuation profiles and reconstruction of computed tomography (CT) images.

X-rays contain a range of energies (polychromatic photons), the higher energies pass through the patient, the lower energies are absorbed or scattered by the body. Ideally, the x-ray beam should be monochromatic or composed of photons having the same energy. Strong filtration of the beam results in more uniformity. The more uniform the beam, the more accurate the attenuation values or CT numbers are for the scanned anatomical region.
There are two types of filtration utilized in CT:
Inherent tube filtration and filters made of aluminum or Teflon are utilized to shape the beam intensity by filtering out the undesirable x-rays with low energy. Filtration of the x-ray beam is usually done by the manufacturer prior to installation. The half value layer provides information about the energy characteristics of the x-ray beam. Too much filtration produces a loss of contrast in the x-ray image.
A mathematical filter such as a bone or soft tissue algorithm is included into the CT reconstruction process to enhance resolution of a particular anatomical region of interest.