Sparse representation has been applied in many domains, such as signal processing, image processing and machine learning. In this paper, a redundant dictionary with each column composed of a Voigt-like
lineshape is constructed to represent the pure spectrum of the sample. With the prior knowledge that the baseline is smooth and sparse representation coefficient for a pure spectrum, a method simultaneously
fitting the pure spectrum and baseline is proposed. Since the pure spectrum is nonnegative, the representation coefficients are also made to be nonnegative. Then through alternating optimization, a surrogate
function based algorithm is used to obtain the sparse coefficients. Finally, we adopt one simulated data set and two real data sets to evaluate our method. The results of quantitative analysis show that our
method successfully estimates the baseline and pure spectrum and is superior compared to other baseline correction and preprocessing methods.