In this paper we present a compressed sensing (CS) method adapted to 3D ultrasound imaging (US). In contrast to previous work, we propose a new approach based on the use of learned overcomplete dictionaries that allow for much sparser representations of the signals since they are optimized for a particular class of images such as US images. In this study, the dictionary was learned using the K-SVD algorithm and CS reconstruction was performed on the non-log envelope data by removing 20% to 80% of the original data. Using numerically simulated images, we evaluate the influence of the training parameters and of the sampling strategy. The latter is done by comparing the two most common sampling patterns, i.e., point-wise and line-wise random patterns. The results show in particular that line-wise sampling yields an accuracy comparable to the conventional point-wise sampling. This indicates that CS acquisition of 3D data is feasible in a relatively simple setting, and thus offers the perspective of increasing the frame rate by skipping the acquisition of RF lines. Next, we evaluated this approach on US volumes of several ex vivo and in vivo organs. We first show that the learned dictionary approach yields better performances than conventional fixed transforms such as Fourier or discrete cosine. Finally, we investigate the generality of the learned dictionary approach and show that it is possible to build a general dictionary allowing to reliably reconstruct different volumes of different ex vivo or in vivo organs.