(eng): This paper addresses the estimation of Relative Transfer Function (RTF) between microphones from noisy recordings. We utilize an incomplete initial measurement of the RTF, which is known for only several frequency bins. The measurement is completed by finding its sparsest representation in the time domain. We propose to perform this reconstruction by solving a Second-Order Cone Program (SOCP). Free parameters of this formulation represent distance of the completed RTF from the initial estimate. We select these parameters based on the theoretical performance of the initial estimate. In experiments with realworld data, this approach achieves a significant refinement of the RTF, especially in scenarios with low signal-to-noise ratios.