To accommodate displays with varying dynamic ranges, image encoding frameworks are emerging that propose to include metadata within a standard dynamic range (SDR) image to encode an arbitrary, user-defined residual which allows the SDR image’s pixel values to be transformed into its intended high dynamic range (HDR) version. The suggested metadata is a compressed version of the gain map computed as the pixel-wise ratio between the HDR and SDR image. Multiplying the gain map with the SDR image reconstructs the HDR image. This paper proposes an effective alternative for HDR recovery in the form of a pixel-wise exponent map instead of the multiplicative gain map. We demonstrate experimentally that the exponent map approach produces higher quality HDR reconstructions over the gain map strategy according to several metrics.