Error correction of noisy reads obtained from high-throughput DNA sequencers is an important problem since read quality significantly affects the complexity and success of sequence assembly. The vast majority of current algorithms only address the correction of substitution errors. In this work, we present PREMIER IDS, an algorithm that simultaneously corrects insertion, deletion and substitution errors by modelling the sequencer output as emissions of an appropriately defined Hidden Markov Model (HMM). Reads are corrected to the corresponding maximum likelihood paths through the HMM. When compared with Coral, the current state of the art algorithm for this problem, PREMIER IDS exhibits better performance across a range of datasets from both Ion Torrent and 454 sequencing platforms.