Conventional two-dimensional structured illumination microscopy (SIM) requires 9 raw images to reconstruct a super-resolved image. In order to increase the frame rate of 2DSIM, attempts are being made to reduce the number of raw SIM images. However, all the proposed SIM reconstruction algorithms (SIM-RA) capable of reconstructing super-resolution (SR) image with a reduced number of raw SIM images operate in the spatial domain. Here, we present a frequency domain SIM-RA based on ordinary least squares technique, which enables reconstruction of SR image using 4 raw SIM images. Unlike the spatial domain RA, which produces the SR image through iterative convergence, the presented RA provides a single step solution. It also reveals the fundamental limitation of least number of raw images required for resolution doubling in SIM.