A novel total variation model based on kernel functions and its application

TL;DR

This paper introduces a new total variation model based on kernel functions that enhances image processing by mapping images into a Hilbert space, allowing for better fusion of color channels and extension of existing TV models.

Contribution

The paper proposes a novel TV model using kernel functions, extending the generalized TV model and enabling multi-channel image fusion in a kernel space.

Findings

The model effectively processes gray and color images.

It theoretically guarantees bounded variation in the kernel space.

Experimental results demonstrate improved image processing performance.

Abstract

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.