Wavelet based denoising is an effective way to improve the quality of images. Various methods have been proposed for denoising using real-valued wavelet transform. Complex valued wavelets exist but are rarely used. The complex wavelet transform provides phase information and it is shift invariant in nature. In medical image denoising, both removal of phase incoherency as well as maintaining the phase coherency are needed. This paper is an attempt to explore and apply the complex Daubechies wavelet transform for medical image denoising. We have proposed a method to compute a complex threshold, which does not depend on any assumed model of noise. In this sense this is a "universal" method. The proposed complex-domain shrinkage function depends on mean, variance and median of wavelet coefficients. To test the effectiveness of the proposed method, we have computed the input and output SNR and PSNR of various types of medical images. The method gives an improvement for Gaussian additive, Speckle and Salt-&-Pepper noise as well as for the mixture of these noise types for a range of noisy images with 15 db to 30 db noise levels and outperforms other real-valued wavelet transform based methods. The application of the proposed method to Ultrasound, X-ray and MRI images is demonstrated in the experiments.
Fast Registration Algorithm for 3D Medical Images using Double Density Dual Tree Complex Wavelet Transform and Bi-directional Prediction
