Three kinds of color total-variation semi-norms and its application to color-image denoising

This paper extends the total-variation (TV) semi-norm of a scalar-valued image to a new color TV semi-norm of a color image, in the definition of which interdependence among the three primary color channels is taken into account. This paper defines a 12-D color-gradient operator that treats primary color signals and color-difference signals collectively; and then with the color-gradient operator this paper defines three kinds of color-TV semi-norms: isotropic, semi-isotropic, and anisotropic color TV semi-norms. By introducing dual definitions of the color-TV semi-norms, this paper reformulates color-TV variational denoising problems, and solves their dual problems with the projected gradient solver. Experimental simulations of color-image denoising demonstrate that the color TV semi-norms achieve selective noise-removal much more efficiently than the classic TV semi-norm, and show the merits and demerits among the three color TV semi-norms.