De-noising and contrast enhancement via wavelet shrinkage and nonlinear adaptive gain

This paper presents an approach which addresses both de-noising and contrast enhancement. In a multiscale wavelet analysis framework, we take advantage of both soft thresholding and hard thresholding wavelet shrinkage techniques to reduce noise. In addition, we carry out nonlinear processing to enhance contrast within structures and along boundaries. Feature restoration and enhancement are accomplished by modifying the gain of a signal's variational energy. The multiscale discrete dyadic wavelet transform adapted in this paper is treated as a process for the diffusion of variational energy from a signal stored as the power (scaled variational energy) of wavelet coefficients. We show that a discrete dyadic wavelet transform has the capability to separate feature variational energy from noise variational energy. De- noising and feature enhancement are achieved by simultaneously lowering noise variational energy and raising feature variational energy in the transform domain. We present methods for achieving this objective, including regulated soft thresholding and adaptive nonlinear processing combined with hard thresholding. We have applied this algorithm to synthetic and real signals as well as images with additive Gaussian white noise. Experimental results show that de-noised as well as enhanced signals and images are free from artifacts. Sample analysis and experimental results are presented.