Band overlap and random noise are a serious problem in infrared spectra, especially for aging spectrometers. In this paper, we have presented a simple method for spectrum restoration. The proposed method is based on local operations, and involves sparse decompositions of each spectrum piece under an evolving overcomplete dictionary, and a simple averaging calculation. The content of the dictionary is of prime importance for the deconvolution process. Quantitative assessments of this technique on simulated and real spectra show significant improvements over the state-of-the-art methods. The proposed method can almost eliminate the effects of instrument aging. The features of these deconvoluted infrared spectra are more easily extracted, aiding the interpretation of unknown chemical mixtures.