Deep learning has been developing rapidly, and many holographic applications have been investigated using deep learning. They have shown that deep learning can outperform previous physically-based calculations using lightwave simulation and signal processing. This review focuses on computational holography, including computer-generated holograms, holographic displays, and digital holography, using deep learning. We also discuss our personal views on the promise, limitations and future potential of deep learning in computational holography.
Recently, holographic displays have gained attention owing to their natural presentation of three-dimensional (3D) images; however, the enormous amount of computation has hindered their applicability. This study proposes an oriented-separable convolution accelerated using the wavefront-recording plane (WRP) method and recurrence formulas. We discuss the orientation of 3D objects that affects computational efficiency, which is overcome by reconsidering the orientation, and the suitability of the proposed method for hardware implementations.
Computational holography, encompassing computer-generated holograms and digital holography, utilizes diffraction calculations based on complex-valued operations and complex Fourier transforms. However, for some holographic applications, only real-valued holograms or real-valued diffracted results are required. This study proposes a real-valued diffraction calculation that does not require any complex-valued operation. Instead of complex-valued Fourier transforms, we employ a pure real-valued transform. Among the several real-valued transformations that have been proposed, we employ the Hartley transformation. However, our proposed method is not limited to this transformation, as other real-valued transformations can be utilized.
The Ramanujan sum, introduced by S. Ramanujan, has been utilized-among other applications-for signal processing. It has recently been suggested that transforms using the Ramanujan sums may also provide the benefit of data compression. This study presents a lossless hologram-compression method that employs transforms using the Ramanujan sums. In general, lossless compression of holograms is difficult, because the statistical properties of holograms are different from natural images. We compared the compression ratios of different hologram datasets, both with and without using Ramanujan-sums-based transforms. We found that the Ramanujan periodic transform improves the compression ratio of hologram data when using data having prime number dimensions.
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