A preliminary structure + texture image decomposition is very useful for a number of digital image processing tasks, as different strategies are supposed to be employed for processing the structure and texture image components. In this paper, a new variational structure + texture image decomposition method is developed. The main ingredients of the proposed approach are: (1) using a low-pass filtered level-set curvature of the input image as a guidance image; (2) texture suppressing by minimizing a variable exponent energy, where the variable exponent is learned from the result of the curvature-guided image filtering. Numerical experiments demonstrate that the method is competitive with the current state of the art in structure + texture image decomposition. Several applications are considered.