Image reconstruction from continuous Gaussian–Hermite moments implemented by discrete algorithm

The problem of image reconstruction from its statistical moments is particularly interesting to researchers in the domain of image processing and pattern recognition. Compared to geometric moments, the orthogonal moments offer the ability to recover much more easily the image due to their orthogonality, which allows reducing greatly the complexity of computation in the phase of reconstruction. Since the 1980s, various orthogonal moments, such as Legendre moments, Zernike moments and discrete Tchebichef moments have been introduced early or late to image reconstruction. In this paper, another set of orthonormal moments, the Gaussian–Hermite moments, based on Hermite polynomials modulated by a Gaussian envelope, is proposed to be used for image reconstruction. Especially, the paperʹs focus is on the determination of the optimal scale parameter and the improvement of the reconstruction result by a post-processing which make Gaussian–Hermite moments be useful and comparable with other moments for image reconstruction. The algorithms for computing the values of the basis functions, moment computation and image reconstruction are also given in the paper, as well as a brief discussion on the computational complexity. The experimental results and error analysis by comparison with other moments show a good performance of this new approach.