The shielding of electromagnetic noise is critical in obtaining magnetic resonance imaging measurements in the ultra-low magnetic field regime where the intrinsic signal-to-noise ratio is very small. The traditional approach of using an enclosure for electromagnetic shielding is expensive and hinders system portability. We describe here the use of a CNN-based software gradiometer to suppress the effect of electromagnetic ambient background noise sources that inductively couple into the signal detection coils. The system involves three ambient noise monitoring coils placed at a distance from the magnetic resonance signal detector. The three coils were used to synthesize the ambient noise captured by the signal detector; a convolutional neural network approach was used. Mathematical foundations are provided to justify the noise suppression framework. The results show that as much as 20-fold noise suppression can be achieved using an optimized convolutional neural network and simultaneous ambient noise measurements. The proposed approach has the potential to replace the requirement for magnetically shielded enclosures and make ultra-low field magnetic resonance imaging truly portable.