Bilateral two-dimensional least mean square filter for infrared small target detection

•Variance of Gaussian filter and step size are adjusted adaptively.•Leftward filter is added.•Prediction error is separated by its plus–minus sign.•Four images of prediction error are fused.•Clouds and noises are significantly suppressed.

The basic TDLMS (Two-Dimensional Least Mean Square) filter fails to detect infrared small targets consistently, especially under conditions of heavy noise and distinct cloud edges. This paper proposes a robust and efficient small-target detection method based on the basic TDLMS filter. The method first smooths the input image with a Gaussian filter of adaptive variance, and then employs TDLMS with a selected step size to filter the image with rightward and leftward iterations. Two prediction error images are obtained by subtracting the prediction images of the bilateral filtering from the original input image. Each prediction error image is separated into positive and negative prediction error images. That is, four images are generated in the bilateral filtering. The final image is obtained by fusing these four images. Experimental results show that the proposed method achieves significant improvement in background suppression and detection performance over the basic TDLMS filter and other improved TDLMS filters.