# Multi-View Synthesis of Sparse Projection of Absorption Spectra Based on Joint GRU and U-Net
## 1 Introduction  
In order to optimize combustion processes, improve combustion efficiency and reduce pollutant emissions, accurate and reliable measurements of temperature and gas component concentrations in combustion fields are of paramount importance. Taking the temperature measurement as an example, although the development of contact temperature measurement methods represented by thermocouples is relatively mature, most of them are single-point or wall temperature distribution measurements. Usually, multiple measurement points need to be deployed to reflect the temperature distribution within the combustion field, which cannot meet the demand for high-quality field distribution measurements, and the contact measurements will destroy the combustion flow field, affecting the measurement results [1, 2]. In contrast, infrared thermography and radiation thermometry, as two types of non-contact measurement methods, do not interfere with the measurement area and more easily achieve the field distribution measurement [3, 4], but these methods usually measure the temperature of the surface of the combustion field, and it is difficult to meet the needs of temperature measurement inside the combustion field. Tunable diode laser absorption spectroscopy (TDLAS), known for its sensitivity, accuracy, reliability, and non-invasiveness, has become one of the most accurate in situ temperature and gas concentration measurement techniques for combustion diagnostics [5, 6]. In particular, the method can optimize the combustion process, improve the efficiency ofenergy utilization, and reduce the generation of emissions by accurately monitoring the temperature, concentration, and other parameters of gasifiers, internal combustion engines, and aircraft engines, thereby achieving more environmentally friendly and efficient energy utilization. The application of this technology enables researchers to gain a deeper understanding of the details of the combustion process, providing strong support for the design, control, and optimization of combustion systems [7; 8; 9; 10; 11]. TDLAS measurement results represent the average values along the optical path and do not directly reflect the spatial distribution of information in the combustion field. To address this limitation, scholars have combined TDLAS technology with computed tomography (CT) imaging technology, proposing tunable diode laser absorption tomography (TDLAT). The two-dimensional distribution of parameters within the combustion field can be obtained by utilizing multiple intersecting laser beams. The bilinear ratio method is used, which involves selecting two laser beams of specific wavelengths and using the integral absorbance ratio obtained from the projection data to reconstruct the temperature and concentration values within each pixel grid. This method offers a dependable way to extract spatial data on temperature and concentration distributions in the combustion field [12]. In the field of combustion, many scholars have contributed to investigating and reconstructing temperature fields. [PERSON] et al., from the University of Virginia, measured the two-dimensional temperature distribution at the exit of a supersonic combustion wind tunnel using multi-angle and direct absorption spectral data from two water vapor lines combined with a classical filtered inverse projection algorithm [13; 14]. Although the method produced satisfactory reconstruction results, it requires a large number of beams, which may be impractical for real-world applications. [PERSON], [PERSON] et al. developed a pentagonal TDLAS detection system and used a modified Landweber algorithm to reconstruct two-dimensional temperature and water vapor concentration distribution in vortex combustion [15; 16]. However, when dealing with a large amount of TDLAS projection data, challenges such as low reconstruction accuracy and slow processing speed arise. The rapid development of artificial intelligence has led to the widespread use of deep learning in combustion diagnostics.