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Several magnetic resonance parallel imaging techniques require explicit estimates of the receive coil sensitivity profiles. These estimates must be accurate over both the object and its surrounding regions to avoid generating artifacts in the reconstructed images. Regularized estimation methods that involve minimizing a cost function containing both a data-fit term and a regularization term provide robust sensitivity estimates. However, these methods can be computationally expensive when dealing with large problems. In this paper, we propose an iterative algorithm based on variable splitting and the augmented Lagrangian method that estimates the coil sensitivity profile by minimizing a quadratic cost function. Our method, ADMM-Circ, reformulates the finite differencing matrix in the regularization term to enable exact alternating minimization steps. We also present a faster variant of this algorithm using intermediate updating of the associated Lagrange multipliers. Numerical experiments with simulated and real data sets indicate that our proposed method converges approximately twice as fast as the preconditioned conjugate gradient method over the entire field-of-view. These concepts may accelerate other quadratic optimization problems.