By applying compressive sensing to infrared imaging systems, the sampling and transmitting time can be remarkably reduced. Therefore, in order to meet the real-time requirements of infrared small target detection tasks in the remote sensing field, many approaches based on compressive sensing have been proposed. However, these approaches need to reconstruct the image from the compressive domain before detecting targets, which is inefficient due to the complex recovery algorithms. To overcome this drawback, in this paper, we propose a two-dimensional adaptive threshold algorithm based on compressive sensing for infrared small target detection. Instead of processing the reconstructed image, our algorithm focuses on directly detecting the target in the compressive domain, which reduces both the time and memory requirements for image recovery. First, we directly subtract the spatial background image in the compressive domain of the original image sampled by the two-dimensional measurement model. Then, we use the properties of the Gram matrix to decode the subtracted image for further processing. Finally, we detect the targets by employing the advanced adaptive threshold method to the decoded image. Experiments show that our algorithm can achieve an average 100% detection rate, with a false alarm rate lower than 0.4%, and the computational time is within 0.3 s, on average.
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