A sporadic decomposition of Hankel structured matrix in logarithmic and wavelet domain for impulse noise removal

Noise removal from the color images is the most significant and challenging task in image processing. Among different conventional filter methods, a robust Annihilating filter-based Low-rank Hankel matrix (r-ALOHA) approach was proposed as an impulse noise removal algorithm that uses the sparse and low-rank decomposition of a Hankel structured matrix to decompose the sparse impulse noise components from an original image. However, in this algorithm, the patch image was considered as it was sparse in the Fourier domain only. It requires an analysis of noise removal performance by considering the other transform domains. Hence in this article, the r-ALOHA can be extended into other transform domains such as log and exponential. In the log and exponential domain, the logarithmic and exponential functions are used for modeling the multiplicative noise model. But, this model is used only for positive outcomes. Therefore, wavelet transform domain is applied to the noise model that localizes an image pixel in both frequency and time domain simultaneously. Moreover, it separates the most vital information in a given image. Thus, it is feasible for obtaining a better approximation of the considered function using few coefficients. Finally, the experimental results show the performance effectiveness of the proposed algorithm.