Visible light communication (VLC) based on light emitting diodes (LEDs) has attracted much attention because of its high data rate and energy efficiency. However, the shadowing caused by any mobile obstacles could block the light-of-sight (LoS) link which may have a dramatical effect on the indoor VLC channel state information (CSI). Instead of investigating the shadowing channel characteristics, we model the link blockages as the incomplete channel matrix with sparse missing elements and reconstruct the transmitted signal by the ℓ ₀ -minimization with additional constraint on shadowing loss. However, the indoor VLC channel is highly correlated especially in cases with small emitter separation. To further improve the accuracy performance, we design the transmit beamforming to reduce the total coherence. Simulation results illustrate the effectiveness of the proposed signal recovery algorithm with incomplete channel and further significant enhancement via the proposed beamforming design.