DHTSD: On discrete Hankel transform spectral description for effective infrared spectra recovery and identification

Abstract

Infrared spectroscopy has shown promise in the field of biomedicine practice. Nevertheless, its widespread application, particularly in the imaging field, has been hampered by the slow acquisition of spectral data from degraded infrared signals, which is exacerbated by band overlap and random noise. This study presents a novel infrared spectral recovery technique that utilizes discrete Hankel transform regularization and is capable of distinguishing between degraded and high-resolution infrared spectra. To assess the sparse disparity between the captured infrared spectrum and its ground truth counterpart in the frequency domain, we use the discrete Hankel transform to examine their coefficient distributions. Given that the distribution of the ground truth spectrum is significantly sparser than that detected, we propose an infrared spectral recovery framework that regulates the sparsity of the observed spectrum using the L₀ norm. Then, the tracking algorithm of greedy analysis is leveraged to address the challenge of L₀ norm minimization. Experimental results, including both simulated and real spectral data, confirm the effectiveness of the algorithm in preserving the spectral peaks of the infrared while removing the random noise. Furthermore, our algorithm can determine the aperture function of spectrometer instrument and thus significantly increase the significance of the measurement.