Three-dimensional noisy image restoration using filtered extrapolation and deconvolution

The problem of restoration in fluorescence 1 microscopy has to deal at the same time with blurring 2 and photon noise. Their combined effects corrupt the 3 image by inserting elements that do not belong to the 4 real object and distort the contrast. This hinders the 5 possibility of using the images for visualization, recog6 nition and analysis using the three-dimensional data. 7 The algorithms developed to restore the lost frequen8 cies and perform band extrapolation, in general, as9 sume absence of noise or an additive noise. This paper 10 presents a restoration approach through band extrap11 olation and deconvolution that deals with the noise. 12 An extrapolation algorithm using constraints on both 13 spatial and frequency domains with a smoothing op14 erator were combined with the Richardson-Lucy iter15 ative algorithm. The results of the method for simu16 lated data are compared with those obtained by the 17 original Richardson-Lucy algorithm and also regular18 ized by Total Variation. The extrapolation of frequen19 This study was partially supported by CAPES with a PhD/PDEE scolarship. Moacir P. Ponti-Jr Institute of Mathematical and Computer Sciences — University of São Paulo — 13560-970 São Carlos, SP, Brazil E-mail: [email protected] – Homepage: http://www.icmc. usp.br/~moacir — Phone.: +55-16-3373-9686, Fax.: +55-163373-9650 Nelson D.A. Mascarenhas · Claudio A.T. Suazo Universidade Federal de São Carlos — 13565-905 São Carlos, SP, Brazil E-mail: [email protected], [email protected] — Phone.: +55-16-3351-8232, Fax.: +55-16-3351-8233 Paulo J.G.S. Ferreira Signal Processing Laboratory, IEETA — Universidade de Aveiro — 3810-193 Aveiro Portugal E-mail: [email protected] — Phone.: +351 234 370 500, Fax.: +351 234 370 545 cies is also analysed both in synthetic and real images. 20 The method improved the results with higher signal-to21 noise ratio and quality index values, performing band 22 extrapolation and achieving a better visualization of the 23 3D structures. 24