Convolutional Neural Networks (CNNs) are the state-of-the-art algorithms used in computer vision. However, these models often suffer from the lack of interpretability of their information transformation process. To address this problem, we introduce a novel model called Sparse Deep Predictive Coding (SDPC). In a biologically realistic manner, SDPC mimics how the brain is efficiently representing visual information. This model complements the hierarchical convolutional layers found in CNNs with the feed-forward and feed-back update scheme described in the Predictive Coding (PC) theory and found in the architecture of the mammalian visual system. We experimentally demonstrate on two databases that the SDPC model extracts qualitatively meaningful features. These features, besides being similar to some of the biological Receptive Fields of the visual cortex, also represent hierarchically independent components of the image that are crucial to describe it in a generic manner. For the first time, the SDPC model demonstrates a meaningful representation of features within the hierarchical generative model and of the decision-making process leading to a specific prediction. A quantitative analysis reveals that the features extracted by the SDPC model encode the input image into a representation that is both easily classifiable and robust to noise.