Multiwavelet-domain filtering for degraded images with Gaussian noise

Multiwavelet is a new development to the body of wavelet theory. Multiwavelet simultaneously offers orthogonality, symmetry and short support which is not possible in scalar 2-channel wavelet systems. After reviewing this recently developed theory, a new theory and algorithm for images with Gaussian noise with multiwavelet multiple resolution analysis (MRA) are presented and investigated in this paper. Denoising with the multiwavelet transform sometimes exhibits visual artifacts (Gibbs phenomena in the neighborhood of discontinuities). Translation-invariant (TI) denoising scheme is applied to suppress such artifacts. A multiwavelet transform is applied to denoise, and the proposed covariance shrink (CS) method is used to threshold wavelet coefficients. The form of thresholds are carefully formulated which is the key to the more excellent results obtained. The proposed method gives better results in the extensive numerical simulations of image denoising than conventional methods.