  The increasing need of restoring high-resolution Hyper-Spectral (HS) images
is determining a growing reliance on Computer Vision-based processing to
enhance the clarity of the image content. HS images can, in fact, suffer from
degradation effects or artefacts caused by instrument limitations. This paper
focuses on a procedure aimed at reducing the degradation effects,
frequency-dependent blur and noise, in Terahertz Time-Domain Spectroscopy
(THz-TDS) images in reflection geometry. It describes the application of a
joint deblurring and denoising approach that had been previously proved to be
effective for the restoration of THz-TDS images in transmission geometry, but
that had never been tested in reflection modality. This mode is often the only
one that can be effectively used in most cases, for example when analyzing
objects that are either opaque in the THz range, or that cannot be displaced
from their location (e.g., museums), such as those of cultural interest.
Compared to transmission mode, reflection geometry introduces, however, further
distortion to THz data, neglected in existing literature. In this work, we
successfully implement image deblurring and denoising of both uniform-shape
samples (a contemporary 1 Euro cent coin and an inlaid pendant) and samples
with the uneven reliefs and corrosion products on the surface which make the
analysis of the object particularly complex (an ancient Roman silver coin). The
study demonstrates the ability of image processing to restore data in the 0.25
- 6 THz range, spanning over more than four octaves, and providing the
foundation for future analytical approaches of cultural heritage using the
far-infrared spectrum still not sufficiently investigated in literature.
