Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and emphasizing the echoes from the reflectors that we wish to locate. We consider a detection and filtering approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm applies to general clutter, but its analysis depends on the model of the medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging.