This paper introduces a novel, model-based chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI), in which asymmetric spectra of interest are directly estimated from complete or incomplete measurements by incorporating subspace-based spectral signal decomposition into the measurement model of CEST MRI for a robust z-spectrum analysis. Spectral signals are decomposed into symmetric and asymmetric components. The symmetric component, which varies smoothly, is delineated by the linear superposition of a finite set of vectors in a basis trained from the simulated (Lorentzian) signal vectors augmented with data-driven signal vectors, while the asymmetric component is to be inherently lower than or equal to zero due to saturation transfer phenomena. Spectral decomposition is performed directly on the measured spectral data by solving a constrained optimization problem that employs the linearized spectral decomposition model for the symmetric component and the weighted Frobenius norm regularization for the asymmetric component while utilizing additional spatial sparsity and low-rank priors. The simulations and in vivo experiments were performed to demonstrate the feasibility of the proposed method as a reliable molecular MRI.