This paper presents a novel approach to capture light field in camera arrays based on the compressive sensing framework. Light fields are captured by a linear array of cameras with overlapping field of view. In this work, we design a redundant dictionary to exploit cross-cameras correlated structures to sparsely represent cameras image. Our main contributions are threefold. First, we exploit the correlations between the set of views by making use of a specially designed redundant dictionary. We show experimentally that the projection of complex scenes onto this dictionary yields very sparse coefficients. Second, we propose an efficient compressive encoding scheme based on the random convolution framework. Finally, we develop a joint sparse recovery algorithm for decoding the compressed measurements and show a marked improvement over independent decoding of CS measurements.