3D-DeepZern: a deep convolutional neural network for tomographic reconstruction based on Zernike polynomials

Abstract

Traditional analytical Zernike methods for tomographic encoding require multiplying large Zernike polynomial matrices, which leads to substantial computational overhead. Moreover, the inverse Zernike matrices must be precomputed and stored, resulting in significant memory consumption—an issue that becomes increasingly severe as the Zernike order or tomogram resolution grows. To address these limitations, we propose 3D-DeepZern, a deep learning-based Zernike polynomials that replaces the matrix-based encoding with neural networks. The method efficiently maps a 3D tomogram to its 1D Zernike descriptor vector and reconstructs the tomogram from this encoding. Compared with the analytical approach, 3D-DeepZern provides dramatically faster encoding, substantially lower memory usage, and comparable reconstruction accuracy. The improvements become even more pronounced at higher Zernike orders or larger voxel grids, demonstrating the scalability and practicality of the proposed method for high-resolution tomographic applications.

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