Speckle filtering of ultrasonic images using weighted nuclear norm minimization in wavelet domain

Abstract

Medical images such as ultrasound images suffer from multiplicative speckle noise which reduces the contrast of ultrasound images and adversely affects the diagnosis process. Discrete Wavelet transform (DWT) is widely accepted in the area of image processing due to its time localization, multi-resolution and sparseness properties. DWT decomposes the noisy image into approximation coefficients and detail coefficients. The detail wavelet coefficients of clean image have sparsity property, whereas in the case of noisy image, sparsity of detail coefficients is reduced due to the presence of speckle noise. Thus, in the proposed method, low rank based Weighted Nuclear Norm Minimization (WNNM) is applied on detail coefficients to reveal the sparsity property of DWT. WNNM is applied on the group matrix of non-local similar patches of detail subbands of DWT to approximate the low-rank denoised version of the subbands. Moreover, less amount of edge and structure information is present in the approximation coefficients of DWT. Thus, in the proposed method, Non-local Means (NLM) filter with Square-Chord distance is also used to denoise speckle noise from approximation coefficients of DWT. Exhaustive experiments are conducted on various images such as real US images, simulated kidney image and synthetic image. It is observed that the mean improvement in terms of PSNR and CNR values of the proposed hybrid method are 1.50% and 3.81% respectively over WNNM based Despeckling using Low-Rank Approximation (DLRA) method. Qualitative and quantitative analyses show that the proposed hybrid method performed better than existing speckle reduction methods in terms of both speckle reduction and edge preservation.