Local inverse

The local inverse is a kind of inverse function or matrix inverse used in image and signal processing, as well as other general areas of mathematics.

The concept of local inverse came from interior reconstruction of the CT image. One of the interior reconstruction methods was done through that first approximately reconstructs the image outside the ROI (region of interest) and then subtracts the re-projection data of the image at outside the ROI from the original projection data; then the above created data are used to make a new reconstruction. This idea can be widened to inverse. Instead of directly making an inverse, the unknowns at the outside of the local region can be first inverted. Recalculate the data from these unknowns (at outside the local region). Subtract this recalculated data from the original data, then the inverse for the unknowns inside the local region is done through the above newly produced data.