High-density analysis methods for localization microscopy increase acquisition speed but produce artifacts. We demonstrate that these artifacts can be eliminated by the combination of Haar wavelet kernel (HAWK) analysis with standard single-frame fitting. We tested the performance of this method on synthetic, fixed-cell, and live-cell data, and found that HAWK preprocessing yielded reconstructions that reflected the structure of the sample, thus enabling high-speed, artifact-free super-resolution imaging of live cells.