Filter for speckle noise reduction based on compressive sensing

Abstract

In holographic reconstruction, speckle noise is a serious factor that may degrade the image quality greatly. Several methods have been proposed, so far, to filter speckle from hologram reconstruction. The first approach is based on averaging several speckle patterns. The second solution is to apply a filter on the reconstructed image. In the first case, several holograms should be acquired, while compromise between speckle reduction and edge preservation is usually a challenge in the case of digital filtering. We propose a method to filter speckle noise based on compressive sensing (CS). CS is a method that has been demonstrated recently to reconstruct images with a sampling inferior to the Nyquist rate. By applying several times the CS algorithm on the hologram reconstruction with different initial downsampling, several versions of the same images can be reconstructed with slightly different speckle patterns. Then, speckle noise can be greatly decreased while preserving sharpness of the image. We demonstrate the effectiveness of our proposed method with simulations as well as with holograms acquired by phase-shifting method.