USING NON-REDUNDANT COMPONENTS TO INCREASE CALCULATION EFFICIENCY FOR STRUCTURED ILLUMINATION MICROSCOPY

The technology disclosed present systems and methods to produce an enhanced resolution image from images of a target using structured illumination microscopy (SIM). The method includes transforming at least three images of the target captured by a sensor in a spatial domain into a Fourier domain to produce at least three frequency domain matrices that each include first blocks of complex coefficients and redundant second blocks of complex coefficients that are conjugates to the first blocks. The method includes reducing computing resources required to produce the enhanced resolution image by using first blocks of complex coefficients to produce at least three phase-separated half-matrices in the Fourier domain. The method includes performing one or more intermediate transformation on the phase-separated half-matrices to produce realigned shifted half-matrices. The method includes calculating complex coefficients of second blocks in the Fourier domain to produce full matrices from half-matrices.