Quantum state reconstruction, the computational problem associated with identifying the state most consistent with observed measurement results in quantum state tomography, becomes intractable for large quantum systems due to the exponential scaling of Hilbert space with system size. Here we implement a convolutional neural network (CNN) to perform quantum state reconstruction which allows us to frontload the expensive computational overhead into the training period of the network. After demonstrating the basic functionality of our approach using both synthetic and experimental data, we explore its robustness to noise and missing measurements. Additionally, we compare our system to reconstruction performed with Bayesian Mean Estimation (BME) and using the analogy between a prior distribution in BME and the training set of our CNN develop several techniques for synthetically preparing bespoke distributions of random quantum states that improve the performance of both reconstruction methods.