Tone mapping operators (TMOs) and inverse TMOs (iTMOs) are important for scalable coding of high dynamic range (HDR) images. Because of the high nonlinearity of local TMOs, it is very difficult to estimate the iTMO accurately for a local TMO. In this letter, we present a two-layer local iTMO estimation algorithm using an edge-preserving decomposition technique. The low dynamic range (LDR) image is first linearized and then decomposed into a base layer and a detail layer via a fast edge-preserving decomposition method. The base layer of the HDR image is generated by subtracting the LDR detail layer from the HDR image. An iTMO function is finally estimated by solving a novel quadratic optimization problem formulated on the pair of base layers rather than the pair of HDR and LDR images as in existing methods. Experimental results show that the proposed two-layer iTMO can recover the HDR accurately so that it is possible to use these local TMOs in scalable HDR image coding schemes.