The parallel imaging technique reduces the scan time at the expense of increased noise, due to its ill-conditioned system matrix. Tikhonov regularization has been proposed for SENSE to reduce the noise. However, Tikhonov regularized images suffer from residual aliasing artifacts or image blurring when a low resolution prior image is used. This study used wavelet-based multivariate regularization to overcome this problem, while maintaining the computational efficiency of Tikhonov regularization. In this method, SENSE is formularized as a multilevel-structured problem in the wavelet domain. Regularization is adaptively performed based on the noise behavior for different levels and orientations throughout the wavelet domain. Both Tikhonov regularization and the present method are systematically evaluated using in vivo anatomical brain data and diffusion weighted brain data. Qualitative and quantitative results demonstrate the advantage of multivariate regularization over Tikhonov regularization in the presence of low resolution prior images. This method suits most parallel imaging applications, especially when a high-quality prior image is unavailable, such as diffusion weighed imaging.