Adaptive penalty likelihood for reconstruction of multidimensional confocal microscopy images

In this paper we devise a penalty likelihood with noise constraints method to restore 2D and 3D confocal microscope images. Regularization is a commonly used technique in image restoration to balance restored image quality and noise suppression, but despite this noise is usually amplified. Taking into account common confocal imaging system degradation, we develop an algorithm by using a gradient descent method (PLGDA) to approach the minimum solution of the penalty likelihood equation. A Lagrange parameter controls the balance between the penalty and likelihood terms and is estimated using an adaptive method. We show that the a priori information is key to the regularization and Lagrange parameter estimation. The convergence characteristics are analysed and discussed. PLGDA and a traditional maximum likelihood expectation maximization are used to restore 2D and 3D confocal images. The point spread function (PSF), used to restore the data is collected from an experiment and modelled by bi-cubic splines to give an accurate noise free representation. Our experimental results show that the restored images are significantly improved by PLGDA.