Image denoising using normal inverse gaussian model in quaternion wavelet domain

This paper proposes a novel image denoising algorithm that can more effectively remove Gaussian white noise. The proposed algorithm is based on a design of a Maximum Posteriori Estimator (MAP) combined with a Quaternion Wavelet Transform (QWT) that utilizes the Normal Inverse Gaussian (NIG) Probability Density Function (PDF). The QWT is a near shift-invariant whose coefficients include one magnitude and three phase values. An NIG PDF which is specified by four real-value parameters is capable of modeling the heavy-tailed QWT coefficients, and describing the intra-scale dependency between the QWT coefficients. The NIG PDF is applied as a prior probability distribution, to model the coefficients by utilizing the Bayesian estimation technique. Additionally, a simple and fast method is given to estimate the parameters of the NIG PDF from the neighboring QWT coefficients. Experimental results show that the proposed method outperforms other existing denoising methods in terms of the PSNR, the structural similarity, and the edge preservation. It is clear that the proposed method can remove Gaussian white noise more effectively.