The camera array is an important tool to obtain the light field of target in space. The method of obtaining high angular resolution light field by a large-scaled dense camera array increases the difficulty of sampling and the equipment cost. At the same time, the demand for synchronization and transmission of a large number of data also limits the sampling rate of light field. In order to complete the dense reconstruction of sparse sampling of light field, we analyze the correlation and redundancy of multi-view images in the same scene based on sparse light field data, then establish an effective mathematical model of light field dictionary learning and sparse coding. The trained light field atoms can sparsely express the local spatial-angular consistency of light field, and the four-dimensional (4D) light field patches can be reconstructed from a two-dimensional (2D) local image patch centered around each pixel in the sensor. The global and local constraints of the four-dimensional light field are mapped into the low-dimensional space by the dictionary. These constraints are shown as the sparsity of each vector in the sparse representation domain, the constraints between the positions of non-zero elements and their values. According to the constraints among sparse encoding elements, we establish the sparse encoding recovering model of virtual angular image, and propose the sparse encoding recovering method in the transform domain. The atoms of light field in dictionary are screened and the patches of light field are represented linearly by the sparse representation matrix of the virtual angular image. In the end, the virtual angular images are constructed by image fusion after sparse inverse transform. According to multi-scene dense reconstruction experiments, the effectiveness of the proposed method is verified. The experimental results show that the proposed method can recover the occlusion, shadow and complex illumination in satisfying quality. That is to say, it can be used for dense reconstruction of sparse light field in complex scene. In our study, the dense reconstruction of linear sparse light field is achieved. In the future, the dense reconstruction of nonlinear sparse light field will be studied to promote the practical application of light field imaging.