The synthesis of two-dimensional antenna arrays that allows to optimize the number of its elements is of great interest for long term evolution (LTE)-advanced wireless systems. In this communication we present a novel synthesis approach which focuses on reducing the number of antenna elements using independent compression regions (ICR). We base our approach on the non-iterative matrix pencil method (MPM) and the iterative Bayesian compressive sampling (BCS) method. Both of these techniques have been previously used for the compression of linear arrays and now we apply them in the context of two-dimensional arrays. Our compression method is based on the idea of segmenting the array in independent regions. A set of numerical experiments (small and large 2D arrays, shaped-beam antenna patterns) are presented to assess the performance and potentialities of ICR design approach.