The following paper proposes a combination of a supervised encoder-decoder neural network with coded apertures. Coded apertures provide improved sensitivity and signal-to-noise ratio (SNR) in planar images. The unique array design of this method overcomes the spatial frequency cutoff found in standard multi-pinhole arrays. In this design, the pinholes were positioned to minimize loss in spatial frequencies. The large number of pinholes results in significant overlapping on the detector. To overcome the overlapping issue, reconstruction of the object from the obtained image is done using inverse filtering methods. However, traces of duplications remain leading to a decline in SNR, contrast, and resolution. The proposed technique addresses the challenge of image distortion caused by the lack of accuracy in the inverse filter methods, by using a deep neural network. In this work, the coded aperture is combined with a deep convolutional neural network (CNN) to remove noise caused by pinhole imaging and inverse filter limitations. Compared to only using Wiener filtering, the proposed method delivers higher SNR, contrast, and resolution. The imaging system is presented in detail with experimental results that illustrate its efficiency.