In this paper, we have proposed and implemented ViSpA, a novel software tool for quasispecies spectrum reconstruction from high-throughput sequencing reads. The ViSpA assembler takes into account sequencing errors at multiple steps, including mapping-based read preprocessing, path selection based on maximum bandwidth, and candidate sequence assembly using probability-weighted consensus techniques. Sequencing errors are also taken into account in ViSpA's EM-based estimation of quasispecies sequence frequencies.