Measurement of neural currents constitutes an important tool in cognitive neuroscience. The purpose of this thesis was to devise a new CSD-reconstruction method capable of determining the membrane currents of a single neuron from extracellular potential data. This task is essentially equivalent to solving an ill-posed Poisson-type inverse problem. The algorithm is based on a previous method called spike CSD, which employs a priori knowledge about the currents of a spiking neuron to solve the problem of CSD-reconstruction. The new algorithm aims to improve the abilities of its predecessor by using ideas borrowed from super-resolution approaches developed for image processing. Testing with simulated data indicated an improvement in the algorithm's parameter-estimation on idealized potential-patterns. Surprisingly, this did not lead to an increase in the accuracy of the reconstructed current-source densities. Suitability of the new solution was demonstrated by testing on real-world data.