Beam-Shape Effects and Noise Removal from THz Time-Domain Images in Reflection Geometry in the 0.25-6 THz Range

Abstract

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.

Figures (13)

• Figure 1: Scheme of the THz-TDS system in the reflection mode. The instrument is based on an ultrafast laser source, emitter and receiver antennas and motorized raster-scanning stage, where the sample is positioned for measurements in reflection geometry.
• Figure 2: Example of the amplitude signal $A(\omega)$ of a raster-scanned sample taken with three different $\Delta$x and $\Delta$y step sizes, equal to (A) 0.5 mm, (B) 0.2 mm, (C) 0.1 mm. The frequency is fixed at 2.72 THz.
• Figure 3: Typical degradation effects in the representation of the amplitude $A(\omega)$ images. The images are corrupted by noise that increases with the frequency, while at lower frequency value, the blur effects are more dominant.The frequency region with relatively low noise and blur degradation effects stays between 0.5 and 3.5 THz.
• Figure 4: Comparison between simulated reference images and experimental measurements of a hole on a metallic plate at three THz frequencies. From left to right: the denoised bands of raw data on three different frequencies (0.97, 1.94, and 3.11 THz); simulated bands corresponding to the same frequencies; intensity vectors corresponding to the middle cross-section of real (blue) and simulated (red) bands; and theoretical PSFs.
• Figure 5: Results of band-by-band deblurring approaches for restoring amplitude images on 1 Euro cent coin (top) and a silver pendant (bottom). The first rows corresponding to each sample show the optical image of the sample and selected row bands on seven different frequencies (red dashed line). The tested deconvolution approaches: 1) Richardson-Lucy iterative deconvolution 1972_Richardson_Bayesian,1974_Lucy_Iterative (blue dashed line); 2) Fast image deconvolution with a hyper-Laplacian priors by Krishnan et al.2009_Krishnan_Fast (green dashed line); 3) Image deblurring using Wiener filtering 1964_Wiener_Extrapolation (yellow dashed line).