This paper addresses performing Inverse Radon Transform (IRT) with Artificial Neural Network (ANN) or Deep Learning, along with motion correction. The purported application domain is cardiac image reconstruction in emission or transmission tomography where IRT is relevant. Our main contribution is in proposing an ANN architecture that is particularly suitable for this purpose. We validate our approach with two types of datasets. First, we use an abstract object that looks like a heart to simulate motion-blurred Radon Transform (RT). With the known ground truth in hand, we train our proposed ANN architecture and validate its effectiveness in Motion Correction (MC). Second, we used human cardiac gated datasets for training and validation of our approach. Gating mechanism time-bins data using electro-cardiogram (ECG) signals for cardiac motion correction. We have shown that trained ANNs can perform motion-corrected image reconstruction directly from motion-corrupted sinogram. We have compared our model against the existing ANN-based approach. Our approach paves the way for eliminating the need for any hardware gating in medical imaging.