In the context of next-generation radio interferometers, we are facing a big challenge of how to economically process data. The classical dimensionality reduction technique, averaging visibilities on time, may dilute fast radio transients (FRT). We propose a robust fast approximate SVD-based dimensionality reduction method for FRT imaging. For each time slice of FRT imaging, our dimensionality reduction defines a linear embedding operator to reduce the space spanned by the left singular vectors of the measurement operator and this operator can be fast obtained via a weighted fft on adjoint measurement operator instead of expensive SVD. The preliminary results showcase that the proposed dimensionality reduction can simultaneously reduce the data significantly and recover FRT correctly, while the averaging technique causes the FRT dilution problem.