Despeckling method of ultrasound images using closed-form shrinkage function based on cauchy distribution in wavelet domain

Abstract

Speckle suppression and elimination are very important to improve the visual quality of ultrasound image and the diagnostic ability of the diseases. An effective technique of image denoising based on discrete wavelet transform is to employ a Bayesian maximum a posteriori (MAP) estimator. To suppress and remove the speckle noise using MAP estimator effectively, it must assign correctly the shrinkage function based on appropriate probability density functions (PDFs) for the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise. In this paper, we introduce a new closed-form shrinkage function that is an analytical solution of a Bayesian MAP estimator for despeckling of the ultrasound images effectively in wavelet domain. We employ a Cauchy prior and Gaussian PDF to model the wavelet coefficients of logarithmically transformed noise-free ultrasound image and speckle noise, respectively. Firstly, we derive the CauchyShrinkGMAP that is a closed-form shrinkage function. In addition, we estimate the noise variance and parameter of MAP estimator. Next, we evaluate the despeckling performance of wavelet image denoising method using the CauchyShrinkGMAP compared to various despeckling method using median and Wiener filters, hard and soft thresholding and GaussShrinkGMAP and MCMAP3N shrinkage function. The experiment results show that PSNR of new closed-form shrinkage function is highest, MSE is smallest, and the correlation coefficient ([Formula: see text]) and SSIM are closer to one than the other existing image denoising methods for noisy synthetic ultrasound images at different speckle noise levels. Also, experiment results show that ENL of new closed-form shrinkage function is highest and that of EN and SD is smallest than the other existing image denoising methods for noisy real ultrasound image.