In this paper, we use the voice samples recorded from laryngectomised patients to develop a novel method for speech enhancement and regeneration of natural sounding speech for laryngectomees. By leveraging recent advances in computational methods for speech reconstruction, our proposed method takes advantages of both non-training and training-based approaches to improve the quality of reconstructed speech for voice-impaired individuals. Since the proposed method has been developed based on the samples obtained from post-laryngectomised patients (and not based on the characteristics of other alternative modes of speech such as whispers and pseudo-whispers), it can address the limitations of current computational methods to some extent. Furthermore, by focusing on English vowels, objective evaluations are carried out to show the efficiency of the proposed method.