Noise Removal for Medical X-ray images in Multiwavelet Domain

When a signal is embedded in an additive Gaussian noise, its estimation is often done by finding a wavelet basis that concentrates the signal energy in few coefficients and then thresholding the noisy coefficients. However, in many practical problems such as medical X-ray image, astronomical and low-light images, the recorded data is not modeled by Gaussian noise but as the realization of a Poisson process. Multiwavelet is a new development to the body of wavelet theory. Multiwavelet simultaneously offers orthogonality, symmetry and short support which are not possible in scalar 2-channel wavelet systems. After reviewing this recently developed theory, a new theory and algorithm for denoising medical X-ray images using multiwavelet multiple resolution analysis (MRA) are presented and investigated in this paper. The proposed covariance shrink (CS) method is used to threshold wavelet coefficients. The form of thresholds is carefully formulated which is the key to more excellent results obtained in the extensive numerical simulations of medical image denoising compared to conventional methods