Velocity analysis is crucial in reflection seismic data processing and imaging. Velocity picking is widely used in the industry for building the initial velocity model. When the size of the seismic data becomes extremely large, we cannot afford the corresponding human endeavor that is required by the velocity picking. In such situations, an automatic velocity-picking algorithm is highly demanded. We have developed a novel automatic velocity-analysis algorithm that is based on the high-resolution hyperbolic Radon transform. We formulate the automatic velocity-analysis problem as a constrained optimization problem. To solve the optimization problem with a hard constraint on the sparsity and distribution of the velocity spectrum, we relax it to a more familiar L1-regularized optimization problem in two steps. We use the iterative preconditioned least-squares method to solve the L1-regularized problem, and then we apply the hard constraint of the target optimization during the iterative inversion. Using synthetic and field-data examples, we determine the successful performance of our algorithm.