IntroductionCorrelation averaging (CAV) is meanwhile an established technique in image processing of two-dimensional crystals /1,2/. The basic idea is to detect the real positions of unit cells in a crystalline array by means of correlation functions and to average them by real space superposition of the aligned motifs. The signal-to-noise ratio improves in proportion to the number of motifs included in the average. Unlike filtering in the Fourier domain, CAV corrects for lateral displacements of the unit cells; thus it avoids the loss of resolution entailed by these distortions in the conventional approach. Here we report on some variants of the method, aimed at retrieving a maximum of information from images with very low signal-to-noise ratios (low dose microscopy of unstained or lightly stained specimens) while keeping the procedure economical.
Speech enhancement using the constrained-optimization technique