目的 红外弱小目标检测是红外图像处理领域中难度大且实际意义相当重要的一项研究热点问题，其在侦察预警系统、飞行器跟踪系统与导弹制导系统中都扮演了十分重要的角色。自然背景下的红外图像一般具有较低信噪比，其中背景占据着绝大部分面积，而目标尺寸很小且不具有明显形状和纹理信息，这为红外图像中弱小目标的检测增加了难度。本文提出一种将Facet方向导数特征与稀疏表示相结合的红外弱小目标检测算法。方法 首先利用Facet模型提取原红外图像在0°、90°、45°和-45° 4个方向上的一阶导数特征，然后通过稀疏表示方法，在方向导数信息基础上对图像进行分块逐一处理，利用求解出的稀疏系数和导数图像块的重建残差构建检测数值图，最后分割出小目标所在具体位置。结果 通过对4组不同红外图像序列进行实验验证，绘制了检测率与虚警率ROC曲线图。从结果可以看出，本文算法相较于对比算法在小目标检测中具有较高检测率。结论 本文算法将Facet方向导数特征与稀疏表示相结合，在红外弱小目标检测上具有较高检测精度和较强抗噪声干扰能力，相比于传统检测算法具有一定优势，同时可根据不同检测背景训练出相应背景字典，从而得到较好检测效果，在实际工程应用中具有良好针对性。

Objective Infrared dim and small target detection is a research interest in the field of infrared image processing, which is difficult but practical. It plays a crucial role in reconnaissance and warning, aircraft tracking, and missile guidance systems. The process of detecting infrared small targets in natural scenes is characterized by the fact that the target area can frequently be expressed as a small, uniform, compact area with a significant discontinuity or contrast compared with the surrounding background. The detection of a small target in an infrared image is affected by many factors, such as the small number of target pixels, low contrast between a target and a background, dim edges of the targets, complex image background, and lack of texture information of the small targets, thereby resulting in the difficulty of infrared small target detections. The existing methods have achieved effective results in detecting small targets in infrared images; however, drawbacks, such as low adaptability to complex background, low detection rate, and high false alarm rate, still remain. In addition, methods related to sparse representation have the following shortcomings:the construction of a dictionary directly from the original images ignores the feature extraction of the target, or does not establish the target and the background dictionaries simultaneously, thus resulting in a weak representation capability of the entire dictionary. Thus, an infrared small target detection algorithm that combines facet directional derivative features with sparse representation is proposed. Method A dictionary must initially be constructed. A background dictionary is constructed by intercepting 1 000 small blocks and then obtaining their derivatives in a certain direction. K-SVD algorithm is used to train the blocks after merging them into column vectors. A background dictionary with 500 atoms is achieved. The construction method of the target dictionary is as follows:325 small blocks containing small targets are generated in accordance with the characteristics of the small target. The first-order derivative in one direction is calculated for these small blocks containing small targets, and then the columns are converted into column vectors. The target dictionary containing 325 atoms is obtained in that direction after normalizing. We combine the target and the background dictionaries into one large dictionary with 825 atoms, which will be used in the subsequent sparse solution section. The facet model is utilized to extract the first-order derivative features of the original infrared image in four directions, that is 0°, 90°, 45°, and -45°. Then, the blocks separated from the image are processed from top to bottom and left to right on the basis of the directional derivative information through the sparse representation method. The detection result map is constructed using the sparse coefficients and reconstruction residuals of the derivative image blocks. Finally, a threshold is calculated from the detection result map to separate the target from the background. Result The classical max-mean and max-median algorithms are selected as the algorithms for comparison. Comparative results show that the max-mean and max-median algorithms are sensitive to the edges in the infrared image. The traditional algorithms perform ineffectively in removing these clusters when the infrared image has clusters due to distance, atmospheric refraction, lens aberration, and optical defocus. A 3D image of the detection result shows that our method has better performance, is insensitive to noise, and can achieve an excellent target detection effect. Therefore, our algorithm has certain advantages over the traditional algorithms. Receiver operating characteristic (ROC) curves of detection and false alarm rates are plotted through experimental verification of four infrared image sequences. The results evidently show that the proposed algorithm has a higher detection rate and lower false alarm rate in a small target detection than other algorithms. Conclusion Our algorithm extracts image directional derivative information through the facet model, combines the directional derivative features of infrared imagery with sparse representation theory, analyzes the characteristics of the small target in a single direction in detail, and extends it to feature information presented in multiple directions. The difference between the target and the background is discussed. The final test results of the small target are obtained using sparse representation theory as a medium. Experiments show that the proposed algorithm has a high detection accuracy and strong anti-noise capability. The proposed algorithm has certain advantages, improves detection rate, and reduces false alarm rate over the traditional detection algorithms. Another important advantage of our algorithm is that it can generate different background dictionaries in accordance with a certain background under different conditions to obtain improved detection results and perform an effective pertinence in practical applications.