Tone mapping or range reduction is often used in High Dynamic Range (HDR) visual signal compression to take advantage of the existing image/video coding architectures. Thus, it is important to study the impact of tone mapping on the visual quality of decompressed HDR visual signals. To our knowledge, most of the existing studies focus only on the quality loss in the resultant low dynamic range (LDR) signal (obtained via tone mapping) and typically employ LDR displays for subjective viewing experiments. As a result, it is not clear how tone mapping affects the perceptual quality of the decompressed HDR signal produced by inverse tone mapping. To address that, we present the results and analysis of a comprehensive subjective study in which the decompressed HDR images were displayed on an HDR display. Our study reveals that, indeed, the perceptual quality of the decompressed HDR signal is dependent on the tone mapping method employed.