Boron Neutron Capture Therapy (BNCT) is an innovative binary form of radiation therapy with high selectivity towards cancer tissue based on the neutron capture reaction 10B(n,$\alpha$)7Li, consisting in the exposition of patients to neutron beams after administration of a boron compound with preferential accumulation in cancer cells. The high linear energy transfer products of the ensuing reaction deposit their energy at cell level, sparing normal tissue. Although progress in accelerator-based BNCT has led to renewed interest in this cancer treatment modality, in vivo dose monitoring during treatment still remains not feasible and several approaches are under investigation. While Compton imaging presents various advantages over other imaging methods, it typically requires long reconstruction times, comparable with BNCT treatment duration. This study aims to develop deep neural network models to estimate the dose distribution by using a simulated dataset of BNCT Compton camera images. The models pursue the avoidance of the iteration time associated with the maximum-likelihood expectation-maximization algorithm (MLEM), enabling a prompt dose reconstruction during the treatment. The U-Net architecture and two variants based on the deep convolutional framelets framework have been used for noise and artifacts reduction in few-iterations reconstructed images, leading to promising results in terms of reconstruction accuracy and processing time.