The autofocus problem in synthetic aperture radar (SAR) is con sidered. We precisely characterize the multichannel nature or the SAR autofocus problem by constructing a low-dimensional subspace where the perfectly-focused image resides. To obtain a unique solution, we perform a sharpness optimization within this subspace. The subspace characterization enables the sharpness optimization to be performed in a vector space, which is conceptually simpler, and allows the SAR autofocus problem to be cast into a similar framework with other image restoration problems where fast algorithms and efficient methods have been established. We present experimental results demonstrating that the proposed framework can be used to bring the ideas of blind multichannel deconvolution techniques to the SAR autofocus problem, allowing the dimension of the solution subspace to be reduced further.