Super-resolution MAP algorithms applied to fluorescence imaging

We have developed efficient image restoration algorithms for restoration of images that are acquired by conventional and confocal fluorescence microscopy. Assuming additive Gaussian noise or Poisson noise in the image and Gaussian or entropy prior distributions, functionals are formulated that must be minimized to obtain maximum a posteriori (MAP) and maximum likelihood (ML) estimations. We propose computationally efficient algorithms to find the solutions. The quality of the MAP restorations is determined largely by the choice of the regularization parameter, which determines the tradeoff between fitting and smoothing the solution. We propose a normalization method to ease the interactive choice of the regularization parameter if the variance of the noise is known. The performance of the algorithms was tested using simulated fluorescence conventional microscopy and fluorescence confocal laser scanning microscopy. Several error measures and quantitative measurements were used to evaluate the quality of the restoration result. We have tested the super-resolution capabilities and have found that the algorithms are capable of recovering partially the frequencies that were lost. The performance of the algorithms was compared to two existing algorithms that are commonly used for fluorescence imaging: the accelerated EM algorithm of Holmes and the regularized algorithm of Carrington.