In this paper, a multi-resolution method for depth estimation from dense image arrays is presented. Recent progress in consumer electronics has enabled the development of low cost hand-held plenoptic cameras. In these systems, multiple views of a scene are captured in a single shot by means of a micro-lens array placed on the focal point of the first camera lens, in front of the imaging sensor. These views can be processed jointly to obtain accurate depth maps. In this contribution, to reduce the computational complexity associated to global optimization schemes based on match cost functions, we make a local estimate based on the maximization of the total log-likelihood spatial density aggregated along the epipolar lines corresponding to each view pair. This method includes the local maximum likelihood estimation of the depth field based on epipolar plane images. To face the potential accuracy losses associated to the ambiguity problem that arises in flat surface regions while preserving bandwidth in correspondence of the edges, we adopt a multi-resolution scheme. In practice, the depth map resolution is reduced in regions where maximizing the higher resolution functional is ill-conditioned. The main benefits of the proposed system are in a reduced computational complexity and a high accuracy of the estimated depth. Experimental results show that the proposed scheme represents a good tradeoff among accuracy, robustness, and discontinuities handling.