Modified Uniformly Redundant Array

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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.[1]

Mathematical Construction of MURAs[edit]

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:


  1. ^ Fenimore, E. E.; Gottesman, Stephen R. (1989-10-15). "New family of binary arrays for coded aperture imaging". Applied Optics. 28 (20): 4344–4352. doi:10.1364/AO.28.004344. ISSN 2155-3165.