A new wavelet-based reconstruction algorithm for twin image removal in digital in-line holography

•We present an algorithm for blind separation of convolutively mixed images.•Wavelet-based transform (AQLS) is coupled with a statistical unmixing algorithm.•Firstly, the convolutively mixed images are decomposed by AQLS.•Statistical unmixing algorithm is applied to digital holography problems.•The obtained images are reconstructed using the inverse AQLS transform.

Two original methods are proposed here for digital in-line hologram processing. Firstly, we propose an entropy-based method to retrieve the focus plane which is very useful for digital hologram reconstruction. Secondly, we introduce a new approach to remove the so-called twin images reconstructed by holograms. This is achieved owing to the Blind Source Separation (BSS) technique. The proposed method is made up of two steps: an Adaptive Quincunx Lifting Scheme (AQLS) and a statistical unmixing algorithm. The AQLS tool is based on wavelet packet transform, whose role is to maximize the sparseness of the input holograms. The unmixing algorithm uses the Independent Component Analysis (ICA) tool. Experimental results confirm the ability of convolutive blind source separation to discard the unwanted twin image from in-line digital holograms.