Terahertz (THz) spectroscopy is a technique proving extremely useful for investigating various biomedical applications by virtue of its high sensitivity in the measurement of water content and non-ionizing nature. By combining this with sparse deconvolution, the THz response of skin directly underneath transdermal drug delivery (TDD) patches was isolated and reconstructed to determine the skin water content in vivo. Verification for this method was given by a comparison of skin measured through patches using sparse deconvolution, and skin measurements immediately following patch removal processed with standard approaches. It was found that patches with a non-permeable film backing hydrated the skin to a greater extent than permeable woven polyester fiber backed patches and that this hydration effect primarily occurs within the first 30 minutes of patch application and lasts for at least 24 hours given that the patch remains applied. We demonstrate the effectiveness of this sparse reconstruction method to track hydration levels through layers such as patches and identify scope for further applications including TDD patch development and wound healing techniques and monitoring.

Recently, finite rate of innovation methods have been successfully applied to achieve low sampling rates in many areas, such as for ultrasound and radio signals. However, to the best of our knowledge, there are no journal publications applying this to real terahertz signals. In this work, we mathematically describe a finite rate of innovation method applied specifically to terahertz signals both experimentally and in simulation. To demonstrate our method, we applied it to randomized simulated signals with and without the presence of noise and to simple experimental measurements. We found excellent agreement between the simulated signals and those recreated based on results from our method, with this success also being replicated experimentally. These results were obtained at relatively low sampling rates, compared to standard methods, which is a key advantage to using a finite rate of innovation method as it allows for faster data acquisition and signal processing.