Estimation Methods of the Point Spread Function Axial Position: A Comparative Computational Study

• Published in: Journal of imaging Vol. 3; no. 1; p. 7
• Main Authors: Diaz Zamboni, Javier, Casco, Víctor
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2017
• Subjects: accuracy; Advantages; Algorithms; Comparative studies; Cramer–Rao lower bound; Csiszár I-divergence; Dependence; Divergence; Fluorescence; fluorescence wide-field microscopy; inverse problems; Iterative methods; Localization; Lower bounds; Mathematical models; maximum likelihood; Maximum likelihood estimation; Methods; Microscopy; Noise; Noise levels; non-linear least square; optical sectioning; Optics; Parameter estimation; Point spread functions; precision; R&D; Research & development; Studies; three-dimensional point spread function; New York; United States > US
• ISSN: 2313-433X; 2313-433X
• DOI: 10.3390/jimaging3010007

The precise knowledge of the point spread function is central for any imaging system characterization. In fluorescence microscopy, point spread function (PSF) determination has become a common and obligatory task for each new experimental device, mainly due to its strong dependence on acquisition conditions. During the last decade, algorithms have been developed for the precise calculation of the PSF, which fit model parameters that describe image formation on the microscope to experimental data. In order to contribute to this subject, a comparative study of three parameter estimation methods is reported, namely: I-divergence minimization (MIDIV), maximum likelihood (ML) and non-linear least square (LSQR). They were applied to the estimation of the point source position on the optical axis, using a physical model. Methods’ performance was evaluated under different conditions and noise levels using synthetic images and considering success percentage, iteration number, computation time, accuracy and precision. The main results showed that the axial position estimation requires a high SNR to achieve an acceptable success level and higher still to be close to the estimation error lower bound. ML achieved a higher success percentage at lower SNR compared to MIDIV and LSQR with an intrinsic noise source. Only the ML and MIDIV methods achieved the error lower bound, but only with data belonging to the optical axis and high SNR. Extrinsic noise sources worsened the success percentage, but no difference was found between noise sources for the same method for all methods studied.