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Infrared (IR) spectrometers, particularly the aging ones, often suffer from the band overlap and random noise. In this paper, a blind estimation method based on discrete cosine transform (DCT) regularization is proposed for IR spectrum measured from an aging spectrometer instrument. Motivated by the observation that the DCT coefficient distribution of the ground-truth spectrum is sparser than that of the observed spectrum, an IR spectral deconvolution model is formulated in our method to regularize the distribution of the observed spectrum by total variation regularization. Then, the split Bregman method is exploited to solve the resulting optimization problem. The experimental results demonstrate an encouraging performance of the proposed approach to suppress noise and preserve spectral details. The novelty of our method lies on its ability to estimate instrument function and latent spectrum in a joint framework; thus, mitigating the effects of instrument aging to a large extent. The recovered IR spectra can efficiently capture the spectral features and interpret the unknown chemical mixture in industrial applications. [ABSTRACT FROM AUTHOR]