Machine-learning based approaches to speech enhancement have recently shown great promise for improving speech intelligibility for hearing-impaired listeners. Here, the performance of three machine-learning algorithms and one classical algorithm, Wiener filtering, was compared. Two algorithms based on neural networks were examined, one using a previously reported feature set and one using a feature set derived from an auditory model. The third machine-learning approach was a dictionary-based sparse-coding algorithm. Speech intelligibility and quality scores were obtained for participants with mild-to-moderate hearing impairments listening to sentences in speech-shaped noise and multi-talker babble following processing with the algorithms. Intelligibility and quality scores were significantly improved by each of the three machine-learning approaches, but not by the classical approach. The largest improvements for both speech intelligibility and quality were found by implementing a neural network using the feature set based on auditory modeling. Furthermore, neural network based techniques appeared more promising than dictionary-based, sparse coding in terms of performance and ease of implementation.