(n, k, p)-Gray code for image systems

This paper introduces a new parametric
n
-ary Gray code, the (
n
,
k
,
p
)-Gray code, which includes several commonly used codes such as the binary-reflected, ternary, and (
n
,
k
)-Gray codes. The new (
n
,
k
,
p
)-Gray code has potential applications in digital communications and signal/image processing systems. This paper focuses on three illustrative applications of the (
n
,
k
,
p
)-Gray code, namely, image bit-plane decomposition, image denoising, and encryption. The computer simulations demonstrate that the (
n
,
k
,
p
)-Gray code shows better performance than other traditional Gray codes for these applications in image systems.