I'm trying to implement color to grayscale method from this paper: http://www.cs.kent.edu/~zhao/papers/SpectralDecolor.pdf
And I'm not really sure what does mean this operator $||$ from this equatation:
$\theta=\frac{|\hat{R}|+|\hat{G}|+|\hat{B}|-|\hat{L}|}{|\hat{R}|+|\hat{G}|+|\hat{B}|}$
In paper it states $||$ represents the spectrum of the complex values, $\hat{R},\hat{G},\hat{B}$ are Fourier transform results of R, G, B channels. $\hat{L}$ is Fourier transform result of luminance.
Given computed coefficients by Fourier transform are complex numbers. I guess the operator could be defined as $|z|=\sqrt{a^2+b^2}$ or $|z|=a^2+b^2$, where $z=a+b\mathrm{i}$. But I'm not really sure.