An approach to Wavelet-Hermite image representation

The paper proposes a Wavelet-Hermite approach for image representation. The wavelet transform is applied at one or two levels to achieve a certain level of compression, followed by the Hermite transform representation using a reduced number of Hermite functions. The Hermite transform, gained attention in recent years, offering advantages over traditional methods such as the Fourier or discrete cosine transforms for image analysis. With this approach, a one-dimensional Hermite transform is combined with two-dimensional wavelet decomposition. This method can be applied for both image compression and noise reduction, leveraging the Hermite transform’s efficiency in noisy environments. The proposed theory is validated experimentally, and image quality is measured using Peak Signal-to-Noise Ratio.