In recent years there has been a great interest in the study of morphological decomposition of image into cartoon and texture

and its hierarchical decomposition. The existing algorithms suffer from high computational complexity and are not very well suited for decomposing images hierarchically. We propose an operator-based image decomposition method

in which a local linear singular operator characterizes the texture component and the residual signal is treated as a cartoon component. With proper changes to the adaptive parameter

it can decompose the image hierarchically through the decomposition of the residual signal. The adaptive parameter is determined according to the change rate of local total variation. The experimental results demonstrate that this method is effective and shows better visual effects.