A signal-model-based SAR image formation algorithm is proposed in this paper. A model is used to describe the received signal, and each scatterer can be characterized by a set of its parameters. Two parameter estimation methods via atomic decomposition are presented: (1) applying 1-D matching pursuit to azimuthal projection data; (2) applying 2-D matching pursuit to raw data. The estimated parameters are mapped to form a SAR image, and the mapping procedure can be implemented under application guidelines. This algorithm requires no prior information about the relative motion between the platform and the target. The Cramer-Rao bounds of parameter estimation are derived, and the root mean square errors of the estimates are close to the bounds. Experimental results are given to validate the algorithm and indicate its potential applications.