Remotely sensed hyperspectral imagery provides, at each pixel, a radiance spectrum with up to hundreds of distinct wavelength channels. This high-dimensional spectral information allows for pixel-level material discrimination, including applications to remotely detecting the presence of particular materials of interest within a scene. Target detection takes a spectrum (or multiple spectra) corresponding to the target material, typically laboratory-measured, field-measured, or image-derived, and uses a detection algorithm to assign a target-likelihood score to each pixel in the image. Here, we explore the tradeoff between spatial accuracy and detection accuracy by presenting the CITRUS algorithm (Cueing Image Target Regions by Unmixing Spectra), which performs target detection on local patches, or tiles. Instead of assigning a detection score to each pixel, we assign a detection score to each tile, indicating the likelihood of the target being contained within that local region; the assumption is that detecting target-containing regions will have lower false alarm rates than when detecting target-containing pixels. Through local spectral unmixing in each tile, we identify the corresponding endmembers using the MaxD algorithm. We hypothesize that for tiles containing the target material in either full-pixel or sub-pixel abundances, the target spectrum will be within - or close to, in a Euclidean sense - the simplex described by those endmembers. The resulting detection map highlights the tiles with low target-to-simplex distances, and serves as a visual cueing tool for an analyst. The ultimate application here is target-region detection in broad-area spectral imagery. The methodology is detailed in this paper, and results are shown on a ground-truthed hyperspectral dataset.