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Most noisy speech enhancement methods result in partial suppression and distortion of speech spectrum. At instances when the local signal-to-noise ratio at a frequency band is very low speech partials are often obliterated. In this paper a method for enhancement and restoration of noisy speech based on a harmonic-noise model (HNM) is introduced. A HNM imposes a temporal-spectral structure that may reduce processing artifacts. The restoration process is enhanced through incorporation of a prior HNM of clean speech stored in a pre-trained codebook. The restored speech is a SNR-dependent combination of the de-noised observation and the speech obtained from weighted codebook mapping. The additional improvements of speech quality resulting from the proposed method in comparison to conventional and modern speech enhancement systems are evaluated. The results show that the proposed method improves the quality of noisy speech and restores much of the information lost to noise.