  The total variation (TV) model and its related variants have already been
proposed for image processing in previous literature. In this paper a novel
total variation model based on kernel functions is proposed. In this novel
model, we first map each pixel value of an image into a Hilbert space by using
a nonlinear map, and then define a coupled image of an original image in order
to construct a kernel function. Finally, the proposed model is solved in a
kernel function space instead of in the projecting space from a nonlinear map.
For the proposed model, we theoretically show under what conditions the mapping
image is in the space of bounded variation when the original image is in the
space of bounded variation. It is also found that the proposed model further
extends the generalized TV model and the information from three different
channels of color images can be fused by adopting various kernel functions. A
series of experiments on some gray and color images are carried out to
demonstrate the effectiveness of the proposed model.
