Nowadays High-Performance Computing (HPC) suffer from an ever-growing gap between computational power, I/O bandwidth and storage capacity. Typical runs of HPC simulations produce Terabytes of data every day. This poses a serious problem when it comes to storing and manipulating such high amount of data. In this thesis I will present a method for compressing time-dependent volume data using an overcomplete dictionary learned from the input data. The proposed method comprises of two steps. In the first step the dictionary is learned over a number of training examples extracted from the volume that we want to compress. This process is an iterative one and at each step the dictionary is updated to better sparsely represent the training data. The second step expresses each block of the volume as a sparse linear combination of the dictionary atoms that were trained over that volume. In order to establish the performance of the proposed method different aspects were tested such as: training speed vs sparsifying speed, compression ratio vs reconstruction error, dictionary reusabilty for multiple time steps and how does a dictionary perform when it is used on a different volume than the one it was trained on. Finally we compare the quality of the reconstructed volume to the original volume and other lossy compression techniques in order to have a visual understanding about the quality of the reconstruction.