Infrared small target enhancement via phase spectrum of Quaternion Fourier Transform

Small target enhancement is one of the crucial stages in infrared small target detection. In this paper, we propose a new method using phase spectrum of Quaternion Fourier Transform to enhance small targets while suppressing backgrounds for infrared images. This is inspired by the property that regularly Gaussian-like shape small targets could be considered as attractively salient signal in infrared images and the location information of such signal is implicitly contained in the phase spectrum from frequency domain. Formally, in the proposed method, we adopt the phase spectrum of Quaternion Fourier Transform instead of using traditional Fourier Transform to enhance the targets since the quaternion provides at most four data channels than only one for the latter, which could be helpful to broad types of background clutters by adding more information. For the construction of the quaternion, we present a second-order directional derivative filter via facet model to compute four second order directional derivative maps from four directions respectively as the four data channels. This filter is used to suppress noises and distinguish the targets and backgrounds into separably different textures so that it would boost the robustness of small target enhancement. In experiments, some typical infrared images with various scenes are tested to validate the effectiveness of the proposed method. The results demonstrate that our method actually has good performance and outperforms several state-of-the-art methods, which can be further used for infrared small target detection and tracking.