Surface-related multiple elimination (SRME) is one of the most commonly used methods for suppressing surface multiples. However, to obtain an accurate surface multiple estimation, dense source and receiver sampling is required. The traditional approach to this problem is performing data interpolation prior to multiple estimation. Although appropriate in many cases, this methodology fails when big data gaps are present or when relevant information is not recovered, e.g., near-offset data in shallow-water environments. We have developed a solution in which multiple estimation was performed simultaneously with data reconstruction, such that data reconstruction helped obtain better multiple estimates and in which the physical primary-multiple relationship helped constrain the data interpolation. To accomplish this, we proposed to extend the recently introduced closed-loop SRME (CL-SRME) algorithm to account for primary estimation in the case of coarsely sampled data. We achieved this by introducing a focal-domain parameterization of the primaries in a sparsity-promoting CL-SRME method. Results proved that the method was capable of reliably estimating primaries data in case of shallow water and with large undersampling factors.