Abstract. Much interest has arisen in the problem of detecting weak optical subpixel objects in a sequence of images immersed in a heavy homogeneous Gaussian clutter background. In optical systems, the presence of the objects changes the background plus the channel noise covariance matrix. Hence, this matrix may be different under null and alternative hypotheses. Because the maximum likelihood estimate of the background covariance matrix is not available when using the primary data set, we use an approximate estimate of a certain number of eigenvalues of the background covariance matrix that are available for estimation. We derived the general likelihood ratio test for the problem at hand and obtained the modified spectrum matching detector (MSpMD). Using the simulation results, we contrast it with well-known spectrum matching detectors and the hypothesis-independent matched subspace detectors. We also present experimental results of small subpixel objects detection on an agitated sea surface, using digital optical experiments that demonstrate the validation of the simulating results. We show the advantage of the MSpMD that allows to detect small subpixel floating objects on an agitated sea surface even with the same means and variances of the reflected signals from the sea surface and the object.

中文翻译：

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具有假设相关背景协方差矩阵的光学子像素目标检测的广义似然比检验

摘要。在沉浸在重的均匀高斯杂波背景中的图像序列中检测弱光学子像素对象的问题引起了很多兴趣。在光学系统中，物体的存在会改变背景加上通道噪声协方差矩阵。因此，该矩阵在原假设和替代假设下可能不同。由于在使用原始数据集时背景协方差矩阵的最大似然估计不可用，因此我们使用可用于估计的背景协方差矩阵的一定数量的特征值的近似估计。我们导出了手头问题的一般似然比检验，并获得了改进的频谱匹配检测器 (MSpMD)。使用模拟结果，我们将它与众所周知的频谱匹配检测器和假设独立的匹配子空间检测器进行对比。我们还展示了在搅动的海面上检测小子像素物体的实验结果，使用数字光学实验证明了模拟结果的有效性。我们展示了 MSpMD 的优势，即使在来自海面和物体的反射信号的均值和方差相同的情况下，它也允许检测搅动海面上的小型亚像素漂浮物体。