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Electrical Tomography (ET) technology is widely used in multiphase flow detection due to its advantages of low cost, visualization, fast response, non-radiation, and non-invasiveness. However, ill-posed solutions lead to low image reconstruction resolution, which limits its practical engineering applications. Although existing interpolation approximation algorithms can alleviate the effects of the ill-posed solutions to some extent, the imaging results remain suboptimal due to the limited approximation capability of these methods. This paper proposes a Bivariate Reproducing Kernel-Based Best Interpolation (BRKBI) method, which offers smaller approximation errors and clearer image reconstruction quality compared to existing methods. The effectiveness of the BRKBI method is validated through theoretical analysis and experimental comparisons. [ABSTRACT FROM AUTHOR]