Characterising the functional relationship between sensory stimuli and neural responses in the brain is one of the main goals of neuroscience. From an encoding perspective, building models that are able to predict neural responses from arbitrary stimuli is the preferred approach to the understanding of neural coding strategies. From a decoding perspective, instead, explaining the neural code means describing how the information about the stimulus could be extracted from the neural responses. Such a decoding task has both theoretical and practical relevance, as well as implications for brain-machine interface devices. However, the complexity and high-dimensionality of the data make this a challenging task. In this thesis, the main goal is to perform pixel-wise reconstruction of visual scenes from neural responses recorded with 2-photon calcium imaging in mouse V1. The reconstruction algorithm is then used to probe specific aspects of the neural code and to explore the relationship between the encoding and the decoding perspectives. To this end, I first introduce a pyramid wavelet model of neural responses and show how it is affected by different sparsity inducing optimisation techniques. Then, I present the outcome of applying an optimal linear estimator (OLE) to stimulus reconstruction from both recorded and synthetic data (generated using the pyramid wavelet model). The OLE was used to study how pairwise correlations between neurons, and the use of different forward models to generate data, affect the accuracy of the reconstruction. Then, I investigated the efficacy of non-linear approaches, such as Bayesian inference and fully connected artificial neural networks (ANNs), comparing it to the linear one. Results show that solely the ANN provides better performance, although the improvements are not always significant. This would suggest that, despite the highly non-linear encoding, a linear decoding strategy suffices.