Removal of defocused images using three-dimensional nonlinear diffusion based on digital holography

We combine the 3D hybrid-Weickert nonlinear diffusion regularizer with digital holography, which can distinguish the locations of certain small-sized particles that are overlapped along the z-axis, to realize autofocusing of multiple micro-objects and simultaneously remove the defocused images. The proposed method is applied to all the reconstruction slices generated from the hologram after each back-propagation. After applying the proposed scheme for certain small-sized particles, the reconstructed image at the ground truth z position is retained, the defocused images are diffused out when the reconstruction range along the z-axis is sufficiently long and the reconstruction depth spacing is sufficiently fine. The results demonstrated that the proposed scheme can diffuse out the defocused images that are 20 mu m from the ground truth z position, despite several scattering particles of different diameters being completely overlapped along the z-axis with a distance of 800 mu m when the hologram pixel pitch is 2 mu m. In addition, the results revealed that the sparsity distribution of the ground truth z slice is not affected by the sparsity distribution of the corresponding defocused images when the diameter of the particle is less than 35 mu m and the reconstruction depth spacing is more than 20 mu m.