Complex Wavelet Based Image Denoising

The discrete wavelet transform (DWT) is undoubtedly a powerful tool for signal and image processing. However, it has few disadvantages like shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, this work focuses on the dual-tree complex wavelet transform which has two important properties: It is nearly shift invariant and directionally selective in two and higher dimensions. Further, it is generally assumed that the wavelet coefficients are independent, but the coefficients of natural images have strong dependencies. The performance of image denoising algorithms using wavelet transforms can be improved significantly by taking into account these statistical dependencies among wavelet coefficients. In this work, both intrascale and interscale dependencies have been considered in detail and accordingly, an improved shrinkage function has been proposed. The denoising performance is improved because parameters are estimated in a local neighborhood as well as across different scales.