To meet the increasing fabrication quality standards and the high throughput requirements NDE techniques are reliant on efficient reconstruction tools and visualization tools. In this work we present an inverse algorithm for a modern electromagnetic non-destructive testing approach using a small GMR sensor array to inspect superconducting wires. Four sensitive GMR sensors are positioned around the wire. Small defects of 100 μm in size could be detected in a depth of 200 μm with a signal-to-noise ratio of better than 400. Surface defects could be detected with a SNR of up to 10,000. This remarkably SNR and the small extent of GMR sensors results in a spatial resolution which offers new visualisation techniques for defect localisation, defect characterization and future tomography-like mapping techniques. We developed several inverse algorithms based on either a Finite Element Method or an analytical approach leading to defect localization with an accuracy of a few 10 μm.