We propose an approach for estimating the spherically aberrated PSF of a microscope, directly from the observed samples. The PSF, expressed as a linear combination of 4 basis functions, is obtained directly from the acquired image by minimizing a novel criterion, which is derived from the noise statistics in the microscope. The principle of our PSF estimation approach is sufficiently flexible to be generalized non-spherical aberrations and other microscope modalities.

We propose a calibration-free method to obtain the PSF directly from the image obtained. Specifically, we first parametrize the spherically aberrated PSF as a linear combination of few basis functions. The coefficients of these basis functions are then obtained iteratively by minimizing a novel criterion, which is derived from the mixed Poisson-Gaussian noise statistics. Experiments demonstrate that the proposed approach results in highly accurate PSF estimations.

We propose a non-iterative image deconvolution algorithm for data corrupted by Poisson or mixed Poisson-Gaussian noise. In contrast to existing approaches, the proposed algorithm merely amounts to solving a linear system of equations, which has a fast and exact solution. Simulation experiments over different types of convolution kernels and various noise levels indicate that the proposed method outperforms the state-of-the-art techniques, in terms of both restoration quality and computational complexity.

We extended the PURE-LET deconvolution algorithm to 3D and applied to deconvolution microscopy. The proposed approach is non-iterative and outperforms existing techniques (usually, variants of Richardson-Lucy algorithm) both in terms of computational efficiency and quality. We illustrate its effectiveness on both synthetic and real data.

A realistic and accurately calculated PSF model can significantly improve the performance in deconvolution microscopy and also the localization accuracy in single-molecule microscopy. We propose a fast and accurate approximation to the Gibson-Lanni model by expressing the integral in this model as a linear combination of rescaled Bessel functions, providing an integral-free way for the calculation. Experiments demonstrate that the proposed approach results in significantly smaller computational time compared with the quadrature approach. This approach can also be extended to other microscopy PSF models.

We propose a non-iterative image deconvolution algorithm for data corrupted by Poisson noise. In contrast to existing approaches, the proposed algorithm merely amounts to solving a linear system of equations which has a fast and exact solution. Simulation experiments over various noise levels indicate that the proposed method outperforms current state-of-the-art techniques, in terms of both restoration quality and computational time.