The use of contrast agents and tracers in medical imaging has a long history. They provide important information for diagnosis and therapy, but for some desired applications, a higher resolution is required than can be obtained using the currently available medical imaging techniques. Consider, for example, the use of magnetic tracers in magnetic resonance imaging: detection thresholds for in vitro and in vivo imaging are such that the background signal from the host tissue is a crucial limiting factor. A sensitive method for detecting the magnetic particles directly is to measure their magnetic fields using relaxometry; but this approach has the drawback that the inverse problem (associated with transforming the data into a spatial image) is ill posed and therefore yields low spatial resolution. Here we present a method for obtaining a high-resolution image of such tracers that takes advantage of the nonlinear magnetization curve of small magnetic particles. Initial 'phantom' experiments are reported that demonstrate the feasibility of the imaging method. The resolution that we achieve is already well below 1 mm. We evaluate the prospects for further improvement, and show that the method has the potential to be developed into an imaging method characterized by both high spatial resolution as well as high sensitivity.