This research is focused on biomedical sensing and imaging, specifically skin cancer imaging and detection. In this domain, the core of this research resides in designing mathematical models and signal-processing technologies for investigating the non-invasive interrogation of materials at terahertz (THz) frequencies using a THz quantum cascade laser (QCL) as a radiation source in a laser feedback interferometry (LFI) sensing configuration. Such a system is particularly well-suited to the biomedical imaging of skin, as THz radiation is biologically safe (non-ionising), extremely sensitive to water content and the low penetration depth of THz waves in biological tissue makes them suitable for imaging the epidermis layer of the skin. QCLs are high-power coherent sources that can generate tunable continuous wave (CW) emissions in the THz frequency range with enough output power for imaging. In an LFI system, the emitted THz wave reflected from the external target will be partially reinjected into the laser cavity and will interfere with the electrical field that exists within the laser cavity, leading to changes in the parameters of the laser. This self-mixing (SM) effect can be exploited for THz CW detection with the benefits of low cost, small size and fast response time.In the last two decades, the application of LFI in imaging and material identification has continued to develop. However, extraction of the optical constants of materials using LFI at THz frequencies requires the target under test to be prepared before detection. Most of the imaging systems based on LFI to date are only applicable to a flat and homogeneous target. There is a requirement for mathematical models and signal-processing technology built on the LFI model, which can interrogate a granular target, such as skin tissue, which has an irregular surface, is an inhomogeneous material and contains multiple layers. The desired outcome of this thesis is an optical analysis technology, which includes determining the complex refractive index of the target and the shape of the target surface. To be practically useful, the optical analysis method must be robust, able to operate automatically and in real time, and able to cope with noise both from the environment and arising from operating the LFI system. The model and signal-processing techniques make LFI with THz QCLs practically useful for skin cancer detection in vivo and tissue imaging.The two main difficulties in applying THz imaging using LFI to skin cancer detection are that the skin tissue sample under test has an irregular surface and that the sample test typically has a cover slip window. Covering skin tissue with a cover slip window is common practice in the medical field. However, the noisy reflections from the irregular surface and reflections from the cover slip window interfere through the nonlinear process of SM, creating complicated signals from which it is challenging to extract information only from the target. These noisy reflections prevent the direct imaging of skin in the presence of a cover slip window. This thesis therefore describes how to image skin tissue in the presence of a cover slip window in three parts. The first part models an LFI imaging system and designs a fast and robust iterative algorithm to automatically extract the complex refractive index of the target. This optical analysis system provides the foundation for imaging skin tissue with LFI. The second part extends the mathematical model and signal-processing technology, making it possible to apply LFI to the extraction of optical constants for granular targets with an irregular surface, addressing the first main difficulty noted above. The third part develops understanding of how simultaneous optical feedback from multiple different layers of the target will affect the imaging result and proposes a complete solution that minimises reflection from the glass on the surface of the object. By combining the methods from these three parts, this research demonstrates the practical feasibility of using the THz LFI imaging system for skin cancer detection by imaging samples of mouse skin with lesions that are not visible.