A modified uniformly redundant array (MURA) is a type of mask used in coded aperture imaging. They were first proposed by Gottesman and Fenimore in 1989.
Mathematical Construction of MURAs
MURAs can be generated in any length L that is prime and of the form
the first six such values being . The binary sequence of a linear MURA is given by , where
These linear MURA arrays can also be arranged to form hexagonal MURA arrays. One may note that if and , a uniformly redundant array(URA) is a generated.
As with any mask in coded aperture imaging, an inverse sequence must also be constructed. In the MURA case, this inverse G can be constructed easily given the original coding pattern A:
Rectangular MURA arrays are constructed in a slightly different manner, letting , where
A rectangular MURA mask of size 101
The corresponding decoding function G is constructed as follows: