Laser instruments often suffer from the problem of baseline drift and random noise, which greatly degrade spectral quality. In this article, we propose a variation model that combines baseline correction and denoising. First, to guide the baseline estimation, morphological operations are adopted to extract the characteristics of the degraded spectrum. Second, to suppress noise in both the spectrum and baseline, Tikhonov regularization is introduced. Moreover, we describe an efficient optimization scheme that alternates between the latent spectrum estimation and the baseline correction until convergence. The major novel aspect of the proposed algorithms is the estimation of a smooth spectrum and removal of the baseline simultaneously. Results of a comparison with state-of-the-art methods demonstrate that the proposed method outperforms them in both qualitative and quantitative assessments.