This paper proposes a frequency-domain Magnetic Resonance (MR) spectral processing method based on sparse representation for accurate quantification of prostate spectra. Generally, an observed prostate spectrum can be considered as a mixture of resonances of interest, a baseline and noise. As the resonances of interest often overlap and the baseline is unknown, their separation and quantification can be difficult. In the proposed method, based on the commonly used signal model of prostate spectra and some a priori knowledge of nonlinear model parameters, a dictionary is constructed which can sparsely represent the resonances of interest as well as the baseline in an input spectrum. The estimation of the resonances of interest is achieved by finding their sparse representations with respect this dictionary. A linear pursuit algorithm based on regularized FOCUSS (Focal Underdetermined System Solver) algorithm is proposed to estimate these sparse representations. The robustness and accuracy of prostate spectrum quantification of the proposed method are improved compared with two classical spectral processing methods: model-based time domain fitting and frequency-domain analysis based on peak integration when tested on simulation data. Quantification on in vivo prostate spectra is also demonstrated and the results appear encouraging.