The rapid decrease in the dimensions of integrated circuits with a simultaneous increase in component density have introduced resolution challenges for optical failure analysis techniques. Although optical microscopy efforts continue to increase resolution of optical systems through hardware modifications, signal processing methods are essential to complement these efforts to meet the resolution requirements for the nanoscale integrated circuit technologies. In this work, we focus on laser voltage imaging as the optical failure analysis technique and show how an overcomplete dictionary-based sparse representation can improve resolution and localization accuracy. We describe a reconstruction approach based on this sparse representation and validate its performance on simulated data. We achieve an 80% reduction of the localization error.