Spherical microphone arrays (SMAs) are widely used for sound field analysis, and sparse recovery (SR) techniques can significantly enhance their spatial resolution by modeling the sound field as a sparse superposition of dominant plane waves. However, the spatial resolution of SMAs is fundamentally limited by their spherical harmonic order, and their performance often degrades in reverberant environments. This paper proposes a two-stage SR framework with residue refinement that integrates observations from a central SMA and four surrounding linear microphone arrays (LMAs). The core idea is to exploit complementary spatial characteristics by treating the SMA as a primary estimator and the LMAs as a spatially complementary refiner. Simulation results demonstrate that the proposed SMA-LMA method significantly enhances spatial energy map reconstruction under varying reverberation conditions, compared to both SMA-only and direct one-step joint processing. These results demonstrate the effectiveness of the proposed framework in enhancing spatial fidelity and robustness in complex acoustic environments.