Information processing by a population of neurons is studied using two-photon calcium imaging techniques. A neuronal spike results in an increased intracellular calcium concentration. Fluorescent calcium indicators change their brightness upon a change in the calcium concentration, and this change is captured in the imaging technique. The task of estimating the actual spike positions from the brightness variations is formally referred to as spike estimation. Several signal processing and machine learning-based algorithms have been proposed in the past to solve this problem. However, the task is still far from being solved. Here we present a novel neural network-based data-driven algorithm for spike estimation. Our method takes the fluorescence recording as the input and synthesizes the spike information signal, which is well-correlated with the actual spike positions. Our method outperforms state-of-the-art methods on a standard evaluation framework. We further analyze different components of the model and discuss its benefits.