Recently, a novel approach to color image compression based on colorization has been presented. The conventional method for colorization-based image coding tends to lose the local oscillation of chrominance components that the original images had. A large number of color assignments is required to restore these oscillations. On the other hand, previous studies suggest that an oscillation of a chrominance component correlates with the oscillation of a corresponding luminance component. In this paper, we propose a new colorization-based image coding method that utilizes the local correlation between texture components of luminance and chrominance. These texture components are obtained by a total variation regularized energy minimization method. The local correlation relationships are approximated by linear functions, and their coefficients are extracted by an optimization method. This key idea enables us to represent the oscillations of chrominance components by using only a few pieces of information. Experimental results showed that our method can restore the local oscillation and code images more efficiently than the conventional method, JPEG, or JPEG2000 at a high compression rate.