Using non-redundant components to increase calculation efficiency for structured illumination microscopy

A non-transitory computer readable storage medium impressed with computer program instructions to produce an enhanced resolution image from images of a target captured under structured illumination, the instructions, when executed on a processor, implement a method comprising:

• transforming at least three images of the target, captured by a sensor in a spatial domain from at least three phase displacements of the structured illumination along one angle, 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;
• using estimated reconstruction parameters, applying an inverse mixing matrix to the first blocks to produce at least three phase-separated half-matrices in the Fourier domain, which are an unshifted half-matrix and shifted half-matrices;
• performing one or more intermediate transformations on the phase-separated half-matrices to produce realigned shifted half-matrices;
• calculating complex coefficients of second blocks in the Fourier domain to produce full matrices from the half-matrices, after the intermediate transformations, by copying complex coefficients from the unshifted half-matrix and the realigned shifted half-matrices, as conjugates, into respective second block positions to produce unshifted full matrix and shifted full matrices from the half-matrices, including changing a sign of imaginary parts of the copied complex coefficients;
• aligning and summing overlapping complex coefficients of the unshifted matrix and the shifted full matrices to produce an expanded frequency coverage matrix;
• and
• inversely transforming the expanded frequency coverage matrix into the spatial domain to produce an enhanced resolution image.

A system including one or more processors coupled to memory, the memory loaded with computer instructions to produce an enhanced resolution image from images of a target captured under structured illumination, the instructions, when executed on the processors, implement actions comprising:

• transforming at least three images of the target, captured by a sensor in a spatial domain from at least three phase displacements of the structured illumination along one angle, 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;
• using estimated reconstruction parameters, applying an inverse mixing matrix to the first blocks to produce at least three phase-separated half-matrices in the Fourier domain, which are an unshifted half-matrix and shifted half-matrices;
• performing one or more intermediate transformations on the phase-separated half-matrices to produce realigned shifted half-matrices;
• calculating complex coefficients of second blocks in the Fourier domain to produce full matrices from the half-matrices, after the intermediate transformations, by copying complex coefficients from the unshifted half-matrix and the realigned shifted half-matrices, as conjugates, into respective second block positions to produce unshifted full matrix and shifted full matrices from the half-matrices, including changing a sign of imaginary parts of the copied complex coefficients;
• aligning and summing overlapping complex coefficients of the unshifted matrix and the shifted full matrices to produce an expanded frequency coverage matrix;
• and
• inversely transforming the expanded frequency coverage matrix from the Fourier domain to produce an enhanced resolution image in the spatial domain.