Abstract: This paper applies the K-Singular Value Decomposition method and its non-negative variant to enhance the contaminated speech. In the proposed approach, noise is categorized as structured and unstructured noise. Firstly, the noise dictionary is learned from a training noise database. Then, we remove the structured noise iteratively by using the noise dictionary. Finally, the approach adopts sparse and redundant representations over trained dictionary to separate the clean speech from the unstructured noise. Extensive experimental results show that the enhancement method proposed outperforms state-of-the-art methods like multi-band spectral subtraction and the non-negative sparse coding based noise reduction algorithm.