Optical sectioning using compressive Fresnel holography with dictionary learning

Abstract

Optical sectioning through the numerical reconstruction of digital holographic data with low diffraction noise is the key process for understanding the structure of a recorded three-dimensional object. Recently, this has been enabled by compressive holography, by virtue of sparse signal processing. However, interpretation of the object signal domain has been limited to predefined domains, such as spatial, discrete cosine transform, and wavelet transform domains. We propose a reconstruction technique of compressive Fresnel holographic data using an overcomplete dictionary learned from natural images to enhance the axial resolution of the sectional images. The redundant (overcomplete) dictionary gives sparser and more flexible solutions for representing the two-dimensional images compared to predefined transforms. We provide simulation results to verify the feasibility of our proposed method.