Sparse reconstruction for integral Fourier holography using dictionary learning method

A simplified (i.e., single shot) method is demonstrated to generate a Fourier hologram from multiple two-dimensional (2D) perspective images (PIs) under low light level imaging conditions. It was shown that the orthographic projection images (OPIs) can be synthesized using PIs and then, following incorporation of corresponding phase values, a digital hologram can be generated. In this work, a fast dictionary learning (DL) technique, known as Sequential Generalised K-means (SGK) algorithm, is used to perform Integral Fourier hologram reconstruction from fewer samples. The SGK method transforms the generated Fourier hologram into its sparse form, which represented it with a linear combination of some basis functions, also known as atoms. These atoms are arranged in the form of a matrix called a dictionary. In this work, the dictionary is updated using an arithmetic average method while the Orthogonal Matching Pursuit algorithm is opted to update the sparse coefficients. It is shown that the proposed DL method provides good hologram quality, (in terms of peak signal-to-noise ratio) even for cases of ~ 90% sparsity.