In this talk we present an iterative method to reconstruct diffusion coefficients in linear elliptic partial differential equations from interior (incomplete) measurements of solutions. By making use of continuous data assimilation (CDA), the proposed approach aims to minimize an error functional which measures the mismatch between the observed data and the data-assimilated solutions. The advantage of this approach is that the introduction of CDA allows us to derive a simple gradient formula for the error functional, thus avoiding the computation of adjoint problems in each iteration. With the proposed gradient formula, we formulate the numerical reconstruction scheme, and discuss its error analysis in a semi-discrete situation. Specifically, we establish $L^2$ reconstruction error estimates in terms of both observation error and PDE model error.