Two sound power measurement approaches were developped that are easy to install and have the ability to detect the dominant modal content by applying the modern signal processing method, Compressed Sensing. In general Compressed Sensing requires only few measurement positions for an exact reconstruction of sparse acoustic mode fields. For a current study we have chosen two Compressed Sensing algorithms. Each require separate sensor array arrangements and deliver different modal contents, from which the sound power can be derived. Firstly, an Azimuthal Mode Analysis is conducted by applying the Enhanced Orthogonal Matching Pursuit (EOMP) algorithm to a sound pressure measurement vector. The measurements are obtained by using a sensor ring array with optimized positions. In a subsequent step, the sound power is calculated by referring the detected azimuthal mode spectrum to a model describing the energy distribution over the radial mode content. Secondly, using the Block Orthogonal Matching Pursuit (BOMP) algorithm, the radial mode amplitudes are determined directly. This algorithm requires the sensors to be placed at optimized azimuthal and axial positions and reconstructs a set of dominant radial modes that occur in groups. With the objective to verify both methods, the newly designed and optimized arrays in combination with the aforementioned mode reconstruction algorithms are applied to a numerical data set. This data was provided by URANS simulations of a radial compressor set-up, which is an exact replication of an actual test rig located at the RWTH Aachen University. The introduced estimation methods perform well as shown by comparison with an exact and high resolution Radial Mode Analysis Method. In the near future, the presented measurement approaches will be applied in an experimental study performed at the radial compressor test rig.