Systems and methods for providing a visualization capability to map magnetic fields. The system utilizes a high-sensitivity magnetic field sensor (e.g., a magnetometer inside a tube made of magnetic shielding material) disposed on one side of a magnetic field modulation screen to acquire measurement data representing an image of a magnetic field. The magnetic field modulation screen includes a multiplicity of magnetic field-generating pixel elements (e.g., current-carrying loops made of electrically conductive material). Optionally, the system also uses compressive sensing techniques to reduce the amount of measurement data required to reconstruct an image of the original magnetic field. Compressive sensing is enabled by not supplying current to a different selected individual magnetic field-generating pixel element of the magnetic field modulation screen at successive sampling times.