The dimensionality of light field data is typically very large for efficient implementation of sparse representation algorithms, such as for dictionary training and sparse coding. We propose a framework for creating light field dictionary using the method of perspective-shearing. Such a dictionary has a special organized structure for different central view patterns and perspective disparities. Based on this dictionary structure, a two-stage sparse coding algorithm is proposed to speed up the reconstruction process by incorporating an interim Winner- Take-All (WTA) hash coding stage into the Orthogonal Matching Pursuit (OMP) algorithm; this stage proves to speed up the sparse coding process by almost three times but still maintains the reconstruction quality. The proposed scheme produces impressive light field reconstruction qualities for compressed light field sensing.