Infrared dim target detection plays an important role in remote surveillance, infrared warning, infrared target recognition and tracking system, and so on. The thermal sensors are far away from the imagery sensors in respect of target size and features. The size of dim targets is commonly less than 80 pixels in the imaging plane.Also, there are no fixed shapes and textures for the infrared dim targets.Moreover, the infrared dim targets are often interfered by non-uniform backgrounds such as houses, trees, and clouds. It has been shown that the infrared dim target might be completely submerged in the complicated cluttered background, and is imaged with low signal-to-clutter ratio (SCR<0.3) and low signal-to-noise ratio (SNR<2dB).Thus, it is difficult to detect dim targets in infrared image for their complex imaging characteristics.

Over the last decade, in order to improve the efficiency and accuracy, a wide range of theories and methods of infrared dim target detection have been presented by many scientists and hundreds of papers published in related journals covering scientific and engineering field. In general, the method of target detection in the single-frame infrared image can be divided into two categories, which are of global feature-based or local feature-based. The detection approaches based on the global features of image include maximum entropy estimation, spatial filtering, modification of partial differential equations, non-convex rank approximation minimization, non-convex optimization with Lp-norm, partial sum of tensor nuclear norm etc.However, its global features corresponding to infrared dim target are not obvious, and its performances of target detection may be degraded due to the dim feature with local maximums in region. Recently, the target detection based on local features is developed as wellsuch as facet-based, filter-based, cellular automata, contrast-based features and so on. In addition, the artificial neural networks (ANNs) and the wavelet transform are also used for the target detection of single-frame infrared images.However, it is difficult for them to distinguish the dim target from the cluttered background in infrared images with low SNR and SCR.

Compared with the traditional wavelets, the multi-scale geometric analysis (MGA), also called “the beyond wavelets”, contains novel harmonic analysis and sparse representation ideas for a signal or an image. It is very efficient to deal with sharp transitions such as edges in high dimension function or signal space, and can overcome the limitation of the traditional wavelet transform that handles pointwise singularities only.It has been proved that MGA isgood at dealing with directional information and anisotropic features to capture singularities accurately and efficiently in infrared images. Furthermore, MGA can enhance target by eliminating the background and noises in the image, so that improve the performances of dim target detection. So far, curvelets, nonsubsampled contourlets and shearlets are presented as MGA methods, which make lots of achievements and are applied in the field of infrared dim target detection. As a new MGA approach, the shearlet transform is derived from the curvelet, and nonsubsampled contourlet transforms (NSCT). Shearlet is much related to them in idealized frequency decomposition for the image, only differing in their construction and implementation model.

In addition to suppress the background, it is also necessary to enhance the targets.Kurtosis is a statistical measure that is used to describe the shape of distribution’ tails and the degree of steepness. It represents the characteristics of peakedness of a probability distribution curve at the average value. Any distribution that is Leptokurtic corresponds to a greater kurtosis than a mesokurtic distribution.Furthermore, the Leptokurtic distribution is characterized with long tails. By comparison, the Platykurtic distribution has shorter tails and is flatter than normal distribution. Due to the presence of the target, the distribution of the target is similar to that of the Leptokurtosis.Moreover, the kurtosis measure is sensitive to target and thus can be used to measure the deviation of background distribution to detect the target.Small target corresponds to large and positive coefficients of Kurtosis. But for large target, the corresponding coefficients of kurtosis are smaller, even be negative.

A novel method for detecting dim targets in infrared images by using maximum kurtosis in the shearlet domain is proposed in this paper. Firstly, the image is decomposed by the shearlet transform and is fused with various directions of high frequency on each scale. Then, the maximum kurtosis coefficient is found to enhance the target.Finally, high frequency images of all scales are merged and the dim targets are detected by an adaptive threshold with a maximum contrast criterion (MCC). The experimental results show that the proposed method has better performance on infrared dim target detection compared to the nonsubsampled contourlet transform (NSCT) method.

The paper is organized as follows. Section 2 briefly introduces the shearlet transform and multi-scale and multi-direction representation for the infrared image. Section 3 describes the principle of multiscale features fusion and the process of dim target detection in sheartlet transform domain by the maximum kurtosis and adaptive threshold. The experimental results of the proposed method and its performance evaluation for the dim target detection is shown in Section 4. We conclude this paper with a summary in Section5.