This paper investigates local reconstruction techniques for extracting region-of-interest (ROI) from a 3-D terahertz imaging setup using a quantum cascade laser (QCL). The advantage of local reconstruction is the reduction in the required measurement time. Difficulties with limited projection angles and image noise make the development of accurate reconstruction algorithms particularly challenging. In this paper, both wavelet-based and traditional filtered back projection (FBP) techniques are investigated. Segmentation algorithms are applied to reconstructed images with low contrast and the resultant segments are compared with a known ground truth to explore the ability of a QCL to image target objects with complex contours. In our experiments, a polystyrene object with a hole drilled inside is used as the imaging target. The region of interest is adjusted through changing the size of the exposure regions. It is found that 3-D local reconstruction of the interior hole suffers from shape distortion, since scattering caused by the target's exterior contours introduces errors in the measured optical parameters of the object. It is found that wavelet-based local computed tomography for terahertz image reconstruction results in lower misclassification of pixels than traditional FBP algorithms.