A method is proposed to estimate the surface impedance of a large absorptive panel from free-field measurements with a spherical microphone array. The method relies on the reconstruction of the pressure and the particle velocity on the studied surface using an equivalent source method based on spherical array measurements. The sound field measured by the array is mainly composed of an incident and a reflected wave, so it can be represented as a spatially sparse problem. This makes it possible to use compressive sensing in order to enhance the resolution and the quality of the estimation. The results indicate an accurate reconstruction for angles of incidence between 0° and 60°, and between approximately 200 and 4000 Hz. Additionally, experimental challenges are discussed, such as the sample's finiteness at low frequencies and the estimation of the background noise.