In this paper, we explore a novel method for tomographic image reconstruction in the field of SPECT imaging. Deep Learning methodologies and more specifically deep convolutional neural networks (CNN) are employed in the new reconstruction method, which is referred to as "CNN Reconstruction - CNNR". For training of the CNNR Projection data from software phantoms were used. For evaluation of the efficacy of the CNNR method, both software and hardware phantoms were used. The resulting tomographic images are compared to those produced by filtered back projection (FBP) [1], the "Maximum Likelihood Expectation Maximization" (MLEM) [1] and ordered subset expectation maximization (OSEM) [2].