# An Extremely Sparse Tomography Reconstruction of a Multispectral Temperature Field without Any a Priori Knowledge

## TL;DR

This paper introduces a new tomography method that can reconstruct temperature fields with very few projection angles and no prior information.

## Contribution

The novel algorithm uses radiation similarity and dynamic time warping to reconstruct temperature fields without a priori knowledge.

## Key findings

- The method achieves a temperature reconstruction accuracy of 1.53–12.05% with only two projection angles.
- It outperforms existing methods in terms of projection angle requirements and robustness.

## Abstract

When undertaking optical sparse projection reconstruction, the reconstruction of the tested field often requires the utilization of a priori knowledge to compensate for the lack of information due to the sparse projection angle. In order to reconstruct the radiation field of unknown materials or in situations where a priori knowledge cannot be obtained, this paper proposes an extremely sparse tomography multispectral temperature field reconstruction algorithm that analyzes the similarity (the similarity here compares and calculates the Euclidean distance of the spectral emissivity values at various wavelengths between different spectral curves) of radiation characteristics of materials under the same pressure and concentration but different temperature, describes the similarity between the radiation information of the tested field using the dynamic time warping (DTW) algorithm, and uses the similarity sum of the radiation information among the subregions of the temperature field as the optimization objective. This is combined with the equation-constrained optimization algorithm and multispectral thermometry to establish the statistical law between the missing information and finally realize the reconstruction of the temperature field. Simulation experiments show that, without any a priori knowledge, the method in this paper can realize reconstruction of the temperature field with an accuracy of 1.53–12.05% under two projection angles and has fewer projection angles and stronger robustness than other methods.