A number of successful tone mapping operators (TMOs) for contrast compression have been proposed due to the need to visualize high dynamic range (HDR) images on low dynamic range devices. This paper proposes a novel inverse tone mapping (TM) operation and a new remapping framework with the operation. Existing inverse TM operations require either the store of some parameters calculated in forward TM, or data-depended operations. The proposed inverse TM operation enables to estimate HDR images from LDR ones mapped by the Reinhard's global operator, not only without keeping any parameters but also without any data-depended calculation. The proposed remapping framework with the inverse operation consists of two TM operations. The first TM operation is carried out by the Reinhard's global operator, and then the generated LDR one is stored. When we want different quality LDR ones, the proposed inverse TM operation is applied to the stored LDR one to generate an HDR one, and the second TM operation is applied to the HDR one to generate an LDR one with desirable quality, by using an arbitrary TMO. This framework allows not only to visualize an HDR image on low dynamic range devices at low computing cost, but also to efficiently store an HDR one as an LDR one. In simulations, it is shown that the proposed inverse TM operation has low computational cost, compared to the conventional ones. Furthermore, it is confirmed that the proposed framework allows to remap the stored LDR one to another LDR one whose quality is the same as that of the LDR one remapped by the conventional inverse TMO with parameters.