SummaryPractical applications of structured illumination microscopy (SIM) often suffer from various artefacts that result from imprecise instrumental hardware and certain bleaching properties of the sample. These artefacts can be observed as residual stripe patterns originating from the illumination grating. We investigated some significant causes of these artefacts and developed a correction approach that can be applied to images after acquisition. Most of the artefacts can be attributed to changes in illumination and detection intensities during acquisition. The proposed correction algorithm has been shown to be functional on noisy image data, and produces exceptional, artefact-free results in everyday laboratory work.

SummaryFor deconvolution applications in three-dimensional microscopy we derived and implemented a generic, accelerated maximum likelihood image restoration algorithm. A conjugate gradient iteration scheme was used considering either Gaussian or Poisson noise models. Poisson models are better suited to low intensity fluorescent image data; typically, they show smaller restoration errors and smoother results. For the regularization, we modified the standard Tikhonov method. However, the generic design of the algorithm allows for more regularization approaches. The Hessian matrix of the restoration functional was used to determine the step size. We compared restoration error and convergence behaviour between the classical line-search and the Hessian matrix method. Under typical working conditions, the restoration error did not increase over that of the line-search and the speed of convergence did not significantly decrease allowing for a twofold increase in processing speed. To determine the regularization parameter, we modified the generalized cross-validation method. Tests that were done on both simulated and experimental fluorescence wide-field data show reliable results.

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Three-dimensional (3D) imaging with optical sectioning microscopy uses computational methods to obtain the true fluorescence distribution by ameliorating the effect of defocus, spherical aberration and noise. Inverse algorithms improve image quality at a fraction of the cost of implementing an optical system by accurate modeling of the imaging system. Good inverse imaging algorithms need to be accurate as well as fast. Better understanding of the image formation model is vital to obtain improved restoration through model-based algorithms. Forward imaging models based on a depth-varying point-spread function (DV-PSF) leads to a substantial improvement in the resulting images because it accounts for depth-induced aberrations present in the imaging system. PSFs at every layer can be represented using their principal components. Computation of the forward imaging model using a principal component analysis (PCA) representation of the DV-PSF requires fewer convolutions than a strata based approach investigated in the past. In this paper we present a new algorithm for maximum likelihood image restoration developed based on a PCA representation of the DV-PSF and an accelerated conjugate gradient (CG) iteration scheme. Results obtained with this PCA-CG algorithm from both simulated and experimental fluorescence microscope data are discussed and compared with results obtained from a CG iteration method based on the strata model and linear interpolation of the DV-PSF. The performance of the PCA-CG algorithms is shown to be promising for practical applications.

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