Blended surveys have recently appeared in production environments. This underlines the need for processing tools that will either process the recorded data directly or perform the separation into single source data (deblending). An inversion technique for the separation of such data is described here. The problem parameterization utilises the surface-related multiples in order to regularise the inversion. In this way, the separation and surface-related multiple elimination are performed in one step. Also, the physical meaning of the model space is exploited during the inversion by formulating the problem as a Basis Pursuit Denoise problem. The method has been applied on a synthetic dataset and it produced promising results.