We consider the problem of estimating receiver coil sensitivity functions in parallel MRI. By exploiting the multichannel nature of the problem, where multiple acquisitions of the same image function are obtained with different sensitivity weightings, we obtain a subspace-based framework for directly solving for the sensitivity functions. The proposed approach does not rely on the sum-of-squares assumption used in existing estimation schemes; this assumption tends to be violated towards the center of the image, thus leading to errors in the sensitivity estimates. Our approach eliminates this problem, producing superior sensitivity estimates in comparsion to the sum-of-squares technique. In addition, the proposed restoration procedure is non-iterative, computationally efficient, and applicable both to cases where pilot scans are available or where auto-calibration data are collected with each scan. We present experimental results using actual and simulated data to assess the performance of our approach in comparison with existing methods.