A method and apparatus are disclosed for Magnetic Resonance Imaging using specialized signal acquisition and processing techniques for image reconstruction with a generally inhomogeneous static magnetic field. New signal processing methods for image reconstruction and for minimizing dephasing effects are disclosed. Imaging systems with smaller static magnetic field strengths and smaller hardware demands than those with homogeneous static magnetic fields are provided, leading to significant reductions in system size and cost as compared to standard MRI systems. Such systems can also exploit imaging coils having high Signal-to-Noise-Ratio (SNR), including those made from Carbon nanotube conductors, leading to further imaging system efficiencies.