Iteratively Reweighted Nuclear Norm based Distortion Compensation for THz-TDS

We address the compensation of distortions in terahertz time-domain spectroscopy (THz-TDS) systems. In this context, the main sources of possible distortions are misalignment of the hardware and the sample during the scan, vibration of the measurement system and time delay variations due to the unevenness of the material surface. This heavily affects the achievable accuracy of material characterization by the THz-TDS system. Therefore, it is important to develop approaches to mitigate these effects. In this work, we profit from the low-rankness of the distortion profile. To this end, we formulate an iterative algorithm based on rank minimization to estimate the material parameters in the presence of the aforementioned impairments. In contrast to the standard convex relaxation of the rank, we propose an iteratively reweighted nuclear norm for improved estimation performance. Further, we compare our approach with the state-of-the-art maximum a posteriori (MAP) approach, which utilizes prior knowledge to mitigate the distortions. Our numerical results show that our proposed approach achieves similar performance to the MAP approach without using any prior knowledge.