As radio telescope data is now increasingly high-dimensional, data reduction has become essential to reduce computational load while preserving accurate signal reconstruction. Gridding the continuous Fourier visibilities represents the standard approach to dimension reduction in radio interferometric imaging. This abstract describes a novel dimension embedding technique relying on the multiplication of the data vector by a fat matrix whose entries are drawn from an i.i.d. random Gaussian distribution. Preliminary results suggest that this approach may provide significant improvement in the reduction of data size with respect to standard gridding, for a given target imaging quality.