Image Fusion Based on the \({\Delta ^{ - 1}} - T{V_0}\) Energy Function

Abstract

This article proposes a \({\Delta^{-1}}-T{V_0}\) energy function to fuse a multi-spectral image with a panchromatic image. The proposed energy function consists of two components, a \(TV_0\) component and a \(\Delta^{-1}\) component. The \(TV_0\) term uses the sparse priority to increase the detailed spatial information; while the \({\Delta ^{ - 1}}\) term removes the block effect of the multi-spectral image. Furthermore, as the proposed energy function is non-convex, we also adopt an alternative minimization algorithm and the \(L_0\) gradient minimization to solve it. Experimental results demonstrate the improved performance of the proposed method over existing methods.

Keywords

• image fusion
• inverse transform of the Laplace operator (\(\Delta^{-1}\) )
• sparse norm
• total variation