This paper presents a novel technique for the dense reconstruction of light fields (LFs) from sparse input views. Our approach leverages the Epipolar Focus Spectrum (EFS) representation, which models the LF in the transformed spatial-focus domain, avoiding the dependence on the scene depth and providing a high-quality basis for dense LF reconstruction. Previous EFS-based LF reconstruction methods learn the cross-view, occlusion, depth and shearing terms simultaneously, which makes the training difficult due to stability and convergence problems and further results in limited reconstruction performance for challenging scenarios. To address this issue, we conduct a theoretical study on the transformation between the EFSs derived from one LF with sparse and dense angular samplings, and propose that a dense EFS can be decomposed into a linear combination of the EFS of the sparse input, the sheared EFS, and a high-order occlusion term explicitly. The devised learning-based framework with the input of the under-sampled EFS and its sheared version provides high-quality reconstruction results, especially in large disparity areas. Comprehensive experimental evaluations show that our approach outperforms state-of-the-art methods, especially achieves at most dB advantages in reconstructing scenes containing thin structures.