## 1 Introduction  
Exhaled air contains a plethora of volatile compounds of endogenous origin, being products of various metabolic pathways. Examination of volatile molecular biomarkers (VMBs) in the patient's breath is a promising way of developing new noninvasive medical screening tests [1, 2]. This approach is a kind of \"omics\" test (genomics, metabolomics, proteomics, etc. ), often referred to as \"breathomics\" [3, 4]. Ideally, in the future, exhaled air analysis can become a noninvasive analog of laboratory blood tests with detection of the level of specific VMBs, and medical decisions can be based on analysis of the profile of such VMBs' concentrations. This approach is associated with qualitative and quantitative analysis of gas mixtures. Qualitative analysis means determining the presence or absence of a specific molecular substance in a gas sample or making decisions about the health state of a person from whom this sample was taken. Quantitative analysis includes a volatile substance concentration evaluation. The qualitative and quantitative analysis of gas mixtures can be implemented experimentally by methods of gas chromatography, absorption spectroscopy, and chemical sensor arrays (e-nose) [5]. Absorption spectroscopy is simple to use and has low-cost operation, high sensitivity, and selectivity. In breathomics, IR and THz absorption spectroscopy are usually used [6, 7, 8, 9] because IR spectra represent information about vibrational absorption bands of volatile molecules, while THz spectra describe rotational absorption bands of polar molecules [10; 11]. From the experimental techniques point of view, two options can be highlighted: terahertz (THz) time-domain spectroscopy (THz-TDS) and THz frequency-domain spectroscopy (THz-PDS). These classes can be referred to as time-resolved THz spectroscopy and continuous wave THz spectroscopy, respectively [12; 13]. THz-TDS is characterized by a high-speed data acquisition rate (with femtoseconds-long pulses) but with a relatively low spectra resolution. On the other hand, THz-FDS, as a rule, can achieve a high resolution (\(10^{-3}\) Hz and higher) but requires more time to measure a wide frequency range spectrum [14; 15]. To improve the sensitivity of THz quartz-based spectroscopy, THz quartz-based spectroscopy devices were suggested [12; 13; 16]. This variant involves the THz quartz tuning fork-based light-induced thermoelastic spectroscopy and quartz-enhanced photoacoustic spectroscopy [8]. These techniques are characterized by an enormously high resolution and sensitivity. But experimental implementation of quartz-enhanced photoacoustic spectroscopy requires achieving several mechanical resonances: a very sharp resonance in a quartz fork and, in addition, tube-shape acoustic resonators [17], which is a nontrivial task due to the influence on them of a studied gas sample pressure, temperature, and composition. Typical absorption spectral data (spectra) are a plot of the dependence of a studied sample's absorption intensity on the wavelength of light. In the absence of noise and with sufficient resolution of the spectroscopic device, each biomarker has a unique spectrum. However, in reality, the spectra of different substances have overlapping regions with close values that are hard to distinguish, which causes difficulties for IR and THz absorption spectra analysis. From a mathematical point of view, a multicomponent gas mixture absorption spectrum \(S(\lambda)\) can be represented as a linear combination of the absorption spectra \(s_{i}(\lambda)\) of the individual molecular substances:  
\[S(\lambda)=\sum_{i}c_{i}s_{i}(\lambda), \tag{1}\]  
where \(c_{i}\) is the \(i\)-th substance concentration, and \(\lambda\) is wavelength. This presentation allows conducting the qualitative (\(c_{i}=0,1\)) and the quantitative (\(c_{i}\in[0,c_{max}]\)) analysis. The problem of finding unknown \(c_{i}\) can be formulated in a matrix form. Let us introduce a matrix \(S\) combining absorption spectra of \(m\) known substances measured at \(n\) wavelengths:  
\[S=