## 1 Introduction  
The infrared sensor can capture the thermal radiation emitted by the objects, which is less impacted by the dark condition. It is widely applied in detection, scene surveillance, reconnaissance, and navigation, etc. due to its ability to operate 24 h a day. However, IR images do have many obvious shortcomings, including low contrast, weak details, and blurred resolution, when compared with visible images, which may trigger much inconvenience when people observe the images. Consequently, infrared sensors in high dynamic range (\(>\)8 bit) are always applied in practical application to capture more details in these years. If displaying the HDR images on normal facilities (8 bit) directly, some information in the original image could not be represented. The procedure to achieve high-quality visualization of HDR infrared image must take the following problems into consideration. First and foremost, the dynamic range of the output should be mapped to be acceptable for the display device. Meanwhile, in order to take advantage of the HDR sensor and guarantee convenience for the following work, weak details should be enhanced. Last but not least, the output should be as visually pleasing as possible. The core idea of many conventional approaches is adjusting the distribution of the gray level. Those methods usually include linear stretching and curve stretching (logarithmic, gamma, and sigmoid) methods based on histogram equalization [1] (HE) and gradient domain methods. Linear stretching can compress the dynamic range to be acceptable for the display equipment, while it leads to detail losing. Curve stretching like Gamma transformations can increase the image contrast, while the fitting parameters change when the images are different. For each image, manual selection of parameters with experience is required. HE enlarges the contrast of the image by redistributing the image pixel values so that the number of pixels in each gray level is approximately equal. Researchers have made plenty of efforts based on HE [2; 3; 4; 5; 6; 7; 8], including global HE-based approaches and local HE-based approaches. The global HE-based approaches like Plateau HE [3; 4] and its improved ones [2; 7] can make the gray levels distribute more reasonably, but the ability to preserve the details is insufficient. The local HE-based approaches like the partially overlapped sub-block histogram equalization (POSHE) [8] and contrast-limited adaptive histogram equalization (CLAHE) [5] can generate more details, but they are intended to induce artifacts, over-enhancement, and blocking effects. In short, most of the existing HE-based methods cannot avoid the contradiction between the maintaining of local details and the global consistency of the entire image, because they only take the histogram information into consideration. The main idea of gradient domain [9; 10] methods is attenuating the large gradient while expanding the small gradient to produce the modified gradient field, and then reconstruct the result image by solving a Poisson equation. Generally, gradient domain operators are capable of achieving appropriate dynamic range compression and avoiding artifacts like halo and gradient reversal. However, they may be limited in enhancing the local details effectively, and cautious selection of parameters is necessary, which limits the practical application of these methods. Recently, multiscale decomposition methods are critical and prevalent in the domain of HDR image display. These methods introduce filters to decompose the image into several components followed by processing each component separately, then compose the processed components to yield the result image. [PERSON] et al. [11] introduced a method to display HDR images. In their method, the image is decomposed into the base layer and the detail layer by the bilateral filter. Then, they attenuate the contrast of base layer, while the contrast of the detail layer is kept, thereby the details are preserved.