Described here are systems and methods for reconstructing images of a subject using a magnetic resonance imaging (“MRI”) system. As part of the reconstruction, synthesized data are estimated at arbitrarily specified k-space locations from measured data at known k-space locations. In general, the synthesized data is estimated using a convolution operation that is based on measured or estimated covariances in the acquired data. The systems and methods described here can thus be referred to as Convolution Operations for Data Estimation from Covariance (“CODEC”).