Image filtering based on the one-dimensional Hermite transform combining triangular filter and fusion approach

The paper introduces a novel image filtering method that combines smoothing in the Hermite transform using a triangular filter with image fusion for noise reduction and quality enhancement. The Hermite transform is employed due to its desirable properties in block-based image processing and the possibility to represent images using a reduced number of functions. The proposed approach involves computing multiple image representations with a reduced number of Hermite functions, applying subsequent smoothing to mitigate Gaussian noise impact. A type of low-pass filter in the Hermite domain is applied. This reduces the influence of the higher-order Hermite functions on the image reconstruction, diminishing the Gaussian noise at the same time. The proposed approach is based on one-dimensional Hermite transform, applied on image rows and columns separately. This can facilitate practical application by allowing the proposed procedure to be parallelized, enabling the simultaneous processing of multiple image rows and columns. To compensate for the loss of some high-frequency components due to reducing the impact of the higher-order Hermite functions, the image fusion technique is applied for detail retrieval and overall image quality refinement. The procedure is experimentally verified, demonstrating improved values of standard image quality measures compared to traditional approaches.