## 1 Introduction  
The diagnosis of combustion processes is a vital tool for both scientific research and industrial applications. Over the years, various techniques have been devised and implemented for this purpose. Acoustic thermometry (AT) [1; 2; 3; 4], coherent anti-Stokes Raman scattering spectrometry (CARS) [5], planar laser-induced fluorescence (PLIF) [6], radiation thermometry [7; 8] and laser absorption spectroscopy (LAS) are examples of such techniques [9; 10]. As a typical non-contact measurement method, tunable diode laser absorption spectroscopy (TDLAS) has many advantages, such as a fast measurement response, high accuracy, high sensitivity, the simultaneous measurement of multiple parameters, etc. TDLAS has been widely used in combustion diagnostics and trace-gas detection, and its performance is particularly demonstrated when multiple-parameter measurement is required. A more recent development in this field is the tunable diode laser absorption tomography (TDLAT) technique [11; 12], which combines the TDLAS technique and the computed tomography (CT) technique. TDLAT has been gradually developed and has been widely applied [13]. By detecting the spectral data for multiple angles and laser paths through the measured field, combined with image reconstruction algorithms, the visualization of temperature and component concentration distributions in complex combustion fields is achieved using TDLAT, which was used in the experiments in this research [14; 15]. Two-dimensional distribution reconstruction is essentially the process of solving the physical properties of each reconstruction parameter of a target region based on the measured projection values and sensitivity matrix of a measurement system. Reconstruction algorithms play a key role as a bridge between the physical parameters and measured projection values. Algebraic iterative-type reconstruction algorithms allow for the incorporation of a priori knowledge about the target field into the iterative process, and they are widely used in incomplete data reconstruction. However, the reconstruction process itself is an inverse problem that is often ill posed. In order to solve this type of ill-posed problem, it is usually necessary to regularize the constraints on the reconstructed and true distributions with the aid of additional a priori information to suppress the noise and artifacts introduced by data incompleteness and to effectively improve the instability of the inverse problem of process tomography. Therefore, the establishment of suitable and accurate regularization terms becomes key to the success of a regularization method. [PERSON] et al. (2016) developed a Modified Adaptive Algebraic Reconstruction Technique (MAART) to reconstruct the distributions of concentration and temperature simultaneously under incomplete projections for fast computation and high quality. In this method, the author introduced two correction coefficients, the relaxation factor and the smoothing factor, on the basis of the traditional algebraic reconstruction algorithm. Through numerical simulations, the influence of the correction coefficients on the convergence of the algorithm and the imaging accuracy were analyzed, and the value interval of the correction coefficients was optimized ([PERSON] et al., 2017; [PERSON] et al., 2018). In this paper, a new reconstruction algorithm, named the Multi-iterative Adaptive Regular Optimization (MIARO) algorithm, is proposed, which is a further development of MAART, and the initial value and adaptive regularization parameter selections are its main added features.