A denoising technique based on filtering the coefficients of a redundant wavelet transform is proposed for the purpose of reducing statistical noise in images without blurring sharp edges. The wavelet coefficients in the higher-spatial-frequency components are denoised using a function that has been used in nonlinear diffusion filtering. With this function, edge and noise points were correctly distinguished. This resulted in the elimination of the wavelet coefficients at the noise points and the preservation of the wavelet coefficients at the edge points. As a result, most of the image noise was successfully eliminated without appreciable losses in the sharp edges. Thus, the denoising technique coped with both noise reduction and edge preservation.
A wavelet-based smoothing technique based on hard and soft thresholding is proposed to eliminate statistical noise interference in the reconstruction of emission computed tomography. The interference is due to Poisson noise in the projection data. Pre-smoothing for projection data is performed to reduce the noise interference, together with post-smoothing for reconstructed images from the pre-smoothed projection data. The present work also investigates not only optimal parameter values for hard and soft thresholding but also the reason why the parameter values produced
good smoothing results. An analysis was made about parameter values for thresholding with which good smoothing results were produced for the purpose of explaining the reason. Based on this analysis, an ad-hoc denoising algorithm is proposed for pre- and post- smoothing.