Three-dimensional noisy image restoration using filtered extrapolation and deconvolution

The problem of restoration in fluorescence microscopy has to deal at the same time with blurring and photon noise. Their combined effects corrupt the image by inserting elements that do not belong to the real object and distort the contrast. This hinders the possibility of using the images for visualization, recognition, and analysis using the three-dimensional data. The algorithms developed to restore the lost frequencies and perform band extrapolation, in general, assume absence of noise or an additive noise. This paper presents a restoration approach through band extrapolation and deconvolution that deals with the noise. An extrapolation algorithm using constraints on both spatial and frequency domains with a smoothing operator were combined with the Richardson-Lucy iterative algorithm. The results of the method for simulated data are compared with those obtained by the original Richardson-Lucy algorithm and also regularized by Total Variation. The extrapolation of frequencies is also analyzed both in synthetic and in real images. The method improved the results with higher signal-to-noise ratio and quality index values, performing band extrapolation, and achieving a better visualization of the 3D structures.