Sound field analysis and reconstruction has been a topic of intense research in the last decades for its multiple applications in spatial audio processing tasks. In this context, the identification of the direct and reverberant sound field components is a problem of great interest, where several solutions exploiting spherical harmonics representations have already been proposed. However, the available techniques demand a large number of high-order microphones (HOMs) and high computational power in order to fulfill the necessary spatial sampling requirements, which can only be reduced by prior information obtained through acoustic measurements. Inspired by compressed sensing approaches, this paper proposes an alternative sparse formulation for estimating the exterior and interior sound field components in the spherical harmonics domain that allows to reduce hardware requirements without the need for additional acoustic measurements. The results show that a considerable reduction in the number of HOMs can be achieved while improving the estimation of the sound field components.