Electrical Impedance Tomography (EIT) can be used to study the hydrodynamic characteristics in multi-phase flows such as gas holdup in bubble columns, air-core in hydrocyclone, etc. In EIT, the main objective is to estimate the electrical properties (conductivity distribution) of an object in a region of interest based on the surface voltage measurements. The main challenge in such reconstruction (estimation of conductivity distribution) is the low spatial resolution. In this paper, a sparse optimization approach for image reconstruction in EIT is presented. The main idea presented in this article is based on considering the L1 norm on the data term, which enhances the reconstruction of conductivity distributions with sharp changes near phase boundaries. Further, this method is also robust to outliers in the data. The accuracy of the proposed method is demonstrated with the help of two phantoms, and a comparison with the existing methods is also presented. Copyright © 2020 The Authors. This is an open access article under the CC BY-NC-ND license