Recently, compressed-sensing (CS) was proposed to jointly reconstruct undersampled multi-contrast datasets to exploit the common structural features therein. Here, we propose a method to improve joint reconstruction of multi-contrast acquisitions. Inspired by the SPIRiT framework for parallel imaging, our method linearly synthesizes missing data for each contrast from neighboring k-space data for all contrasts. To improve reconstruction quality, the proposed method high-pass filters calibration data to emphasize the weight of intermediate spatial frequencies in the interpolation operator. Phantom and in vivo results at 3T indicate that the proposed method outperforms reconstructions with conventionally estimated interpolators.