Unsupervised noise removal algorithms for three-dimensional confocal fluorescence microscopy

Algorithms are presented for effective suppression of the quantum noise artifact that is inherent to three-dimensional confocal fluorescence microscopy images of extended spatial objects such as neurons. The specific advances embodied in these algorithms are as follows: (i) they incorporate an automatic and pattern-constrained three-dimensional segmentation of the image field, and use it to limit any smoothing to the interiors of specified image regions and hence avoid the blurring that is inevitably associated with conventional noise removal algorithms; (ii) they are ‘unsupervised’ in the sense that they automatically estimate and adapt to the unknown spatially and temporally varying noise level in the microscopy data. Fast computation is achieved by parallel computation methods, rather than by algorithmic or modelling compromises.

The quantum noise artifact is modelled using a mixture of spatially non-homogeneous Poisson point processes. The intensity of each component process is constrained to lie in specific intervals. A set of segmentation and edge-site variables are used to determine the intensity of the mixture process. Using this model, the noise-removal process is formulated as the joint optimal estimation of the segmentation labels, edge-sites and intensity of the mixture Poisson point process, subject to a combination of stochastic priors and syntactic pattern constraints. The computations proceed iteratively, starting from a set of approximate user-supplied, or default initial guesses of the underlying random process parameters. An Expectation Maximization algorithm is used to obtain a more precise characterization of these parameters, that are then input to a joint estimation algorithm.

Stereoscopic renderings of processed three-dimensional images of murine hippocampal neurons are presented to demonstrate the effectiveness of the method. The processed images exhibit increased contrast and significant smoothing and reduction of the background intensity while avoiding any blurring of the foreground neuronal structures.