3D localization for light-field microscopy via convergent accelerated inertial algorithm

Light-field microscopy (LFM) enables the rapid, light-efficient, and volumetric imaging of target samples within a three-dimensional (3D) scene. The capture of depth and phase information provides insight into the 3D morphology, which is of particular interest in the field of neuroscience. This paper presents an enhanced version of an existing 3D localization method for light-field microscopy offering a notable improvement in both localization accuracy and efficiency. To address the issue of patch overlap, a slice-based convolutional sparse coding problem with a synthesized depth-correlated dictionary is proposed for 3D localization. As the ADMM algorithm does not guarantee convergence, a convergent Nesterov’s accelerated inertial proximal gradient with dry friction (NIPGDF) algorithm is proposed. Furthermore, we have augmented NIPGDF with asymptotic vanishing damping, thereby facilitating rapid convergence. The experimental results demonstrate that NIPGDF offers rapid convergence and high accuracy, effectively detecting the 3D location of target samples in both ideal and noisy environments, and outperforming the ADMM algorithm. Additionally, NIPGDF has been demonstrated to be an effective approach for tracking moving targets in 3D localization experiments with dynamic point sources in a simulated microfluidic environment. This provides a basis for further research into the task of dynamic target tracking. The code is available.