Noise removal in medical images remains a challenge for the researchers because noise removal introduces artifacts and blurring of the image. Developing medical image denoising algorithm is a difficult operation because a tradeoff between noise reduction and the preservation of actual features of image has to be made in a way that enhances and preserves the diagnostically relevant image content. A special member of the emerging family of multiscale geometric transforms is the contourlet transform which effectively captures the image edges and contours. This overcomes the limitations of the existing method of denoising using wavelet and curvelet. But due to down sampling and up sampling, the contourlet transform is shift-variant. However, shift-invariance is desirable in image analysis applications such as edge detection, contour characterization, and image enhancement. In this chapter, nonsubsampled contourlet transform (shift-invariance transform)-based denoising is presented which more effectively represents edges than contourlet transform.
