Phase-preserving speckle reduction based on soft thresholding in quaternion wavelet domain

Abstract. Speckle reduction is a difficult task for ultrasound image processing because of low resolution and contrast. As a novel tool of image analysis, quaternion wavelet (QW) has some superior properties compared to discrete wavelets, such as nearly shift-invariant wavelet coefficients and phase-based texture presentation. We aim to exploit the excellent performance of speckle reduction in quaternion wavelet domain based on the soft thresholding method. First, we exploit the characteristics of magnitude and phases in quaternion wavelet transform (QWT) to the denoising application, and find that the QWT phases of the images are little influenced by the noises. Then we model the QWT magnitude using the Rayleigh distribution, and derive the thresholding criterion. Furthermore, we conduct several experiments on synthetic speckle images and real ultrasound images. The performance of the proposed speckle reduction algorithm, using QWT with soft thresholding, demonstrates superiority to those using discrete wavelet transform and classical algorithms.