Modified Uniformly Redundant Array - Alchetron, the free social encyclopedia

A modified uniformly redundant array (MURA) is a type of mask used in coded aperture imaging.

Mathematical Construction of MURAs

MURAs can be generated in any length L that is prime and of the form

L = 4 m + 1 , m = 1 , 2 , 3 , . . . ,

the first six such values being L = 5 , 13 , 17 , 29 , 37 . The binary sequence of a linear MURA is given by A = A i i = 0 L − 1 , where

A i = { 0 if i = 0 , 1 if i is a quadratic residue modulo L , i ≠ 0 , 0 otherwise

These linear MURA arrays can also be arranged to form hexagonal MURA arrays. One may note that if L = 4 m + 3 and A 0 = 1 , 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:

G i = { + 1 if i = 0 , + 1 if A i = 1 , i ≠ 0 , − 1 if A i = 0 , i ≠ 0 ,

Rectangular MURA arrays are constructed in a slightly different manner, letting A = { A i j } i , j = 0 p − 1 , where

A i j = { 0 if i = 0 , 1 if j = 0 , i ≠ 0 , 1 if C i C j = + 1 , 0 otherwise,

and

C i = { + 1 if i is a quadratic residue modulo p , − 1 otherwise,

The corresponding decoding function G is constructed as follows:

G i j = { + 1 if i + j = 0 ; + 1 if A i j = 1 , ( i + j ≠ 0 ) ; − 1 if A i j = 0 , ( i + j ≠ 0 ) , ;

References

Modified Uniformly Redundant Array Wikipedia

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