Disclosed are techniques for an improved method for performing Acoustic Wave Decomposition (AWD) processing that reduces a complexity and processing consumption. The improved method enables a device to perform AWD processing to decompose an observed sound field into directional components, enabling the device to perform additional processing such as sound source separation, dereverberation, sound source localization, sound field reconstruction, and/or the like. The improved method splits the solution to two phases: a search phase that selects a subset of a device dictionary to reduce a complexity, and a decomposition phase that solves an optimization problem using the subset of the device dictionary.