基于高斯空间低秩稀疏分解的红外小目标检测

Infrared Small Target Detection Based on Low Rank Sparse Decomposition in Gaussian Space

摘要: 针对红外图像中小目标尺寸未知，空域中不同高斯核模板对图像平滑效果不同，传统高斯差分滤波在小目标检测中容易造成漏检。提出利用多尺度模板对图像进行处理，同时结合目标的稀疏性与背景的低秩性，对不同尺度高斯平滑后的图像进行低秩稀疏分解，以增强差分图像中目标的完整度。首先利用三个不同尺度的高斯模板与图像进行卷积，得到三个不同尺度抑制目标后的平滑图像；进一步对平滑后的图像使用加速近端梯度法进行低秩稀疏分解，保留低秩部分，以抑制高斯平滑图像中残留的目标信息，取每个尺度低秩矩阵的最大值为最终的背景图像；接着将原始图像与背景图像做差得到目标显著性图，最后利用图像的均值及方差对显著性图进行阈值分割，得到最终的目标检测结果。实验结果表明，将原始图像与融合不同尺度低秩矩阵得到的背景图像做差，在提高目标与背景对比度的同时也尽可能地保证了目标的完整性，与其它算法对比有较高的检测率以及较低的误警率。

Abstract: In view of the unknown size of small targets in infrared images, different Gaussian kernel templates in the airspace have different smoothing effects on images. Traditional Gaussian differential filtering is likely to cause missed detections in small target detection. It is proposed to use multi-scale templates to process the image, and at the same time combine the sparseness of the target with the low rank of the background, perform low-rank sparse decomposition of the Gaussian smoothed images of different scales to enhance the integrity of the target in the differential image. Firstly, three Gaussian templates with different scales are used to convolve with the image to obtain a smooth image after suppressing the target at three different scales; the smoothed image is further subjected to low-rank sparse decomposition using the accelerated near-end gradient method to retain the low-rank part. In order to suppress the target information remaining in the Gaussian smooth image, the maximum value of the low-rank matrix of each scale is taken as the final background image; then the original image and the background image are subtracted to obtain the target saliency map, and finally the image mean and variance pairs are used. The saliency map is the thresh-old to obtain the final target detection result. The experimental results show that the difference between the original image and the background image obtained by fusing low-rank matrices of different scales can improve the contrast between the target and the background while ensuring the integrity of the target as much as possible. Compared with other comparison algorithms, it has higher detection rate and lower false alarm rate.