Image Denoising of Gaussian and Poisson Noise Based on Wavelet Thresholding

Noise on images is generally undesirable and disturbing. It always plays a negative role on higher level processing tasks such as image registration and segmentation. Thus, image denoising becomes a fundamental step necessarily required for better image understanding and interpretation. During the last couple of years, wavelet has been extensively employed in the application of suppressing noise and proven to be a successful tool which outperforms many conventional denoising filters due to its preferred properties.;Basically, two generic scenarios occur during the acquisition of images. First, when the detected intensities on the image are sufficiently high, the noise can be suitably modeled as following an additive independent Gaussian distribution. Second, when only a few photons are detected, this observed image is usually modeled as a Poisson process and the intensities to be estimated are assumed to be the underlying Poisson parameters. In this dissertation, these two scenarios are discussed respectively in Part I and Part II.;In part I, we consider to reduce the typical additive white Gaussian noise (AWGN). Our driving principle is to decrease the upper bound of the error restricted by the soft-thresholding strategy between the investigated image and noise-free image. Thus we develop a new context modeling method to group coefficients with similar statistics and construct a smoothed version of the noisy image prior to the actual denoising operation. Then, we propose an optimized soft-thresholding denoising function with parameters derived from a modification of a closed form solution which has a more flexible shape and is adaptively pointwise. Furthermore, we extend it to its overcomplete representation by employing the "cycle spinning" method so that the property of shift invariance is achieved which leads to a boost of the denoising performance. By combining these strategies, the denoising results in our experiments confirm that theapproach is very competitive to some state-of-the-art denoising methods in terms of quantitative measurements and computational simplicity.;In Part II, a new denoising method for Poisson noise corrupted images is proposed which is based on the variance stabilizing transformation (VST) with a new inverse. The VST is used to approximately convert the Poisson noisy image into Gaussian distributed, so that the denoising methods aiming at Gaussian noise can be applied subsequently. The motivation for the improved inverse comes from a main drawback existing in the conventional VSTs such as the Anscombe transformation: its efficiency degrades significantly when the pixel intensities of the observed images are very low due to the biased errors generated by its inverse transformation. In order to correct the biased errors, we introduce a polynomial regression model based on weighted least squares as an alternate to its inverse. Moreover, we incorporate our developed wavelet thresholding strategy for Gaussian noise presented in Part I into the proposed method. We also extend it to the overcomplete representation to suppress the Pseudo-Gibbs phenomena and therefore gains additional denoising effects. Experimental analysis indicates that this method is very competitive.