Abstract
Applications abound in remote sensing, medical imaging, and target detection; rely on relative noise fee images to draw essential inferences for machine learning and for eventual human interaction. Denoising images can be challenging due not only to the stochastic nature of additive noise but also to the complex, varied, and unpredictable nature of the actual image to be recovered. For these reasons, image-processing techniques are developed to provide a solution to generate relatively noise-free images from corrupted measurements. The Discrete Wavelet Transform is widely used within the image processing community as they provide a bases that concentrates energy in relatively few coefficients for images. The wavelet coefficients provide a computationally fast orthogonal projection of the image onto the spatially localized bases. Unlike the conventional Fourier bases, which rely on phase across the entire set of bases, the discrete wavelet transform captures scale and spatially localized features in a very small subset of bases. This particular property of wavelets proves useful as many two-dimensional signals prove quite sparse in the wavelet domain, making the discrete wavelet transform more computationally efficient. This thesis focuses on denoising images via two-dimensional wavelet-based thresholding and explores different adaptive and non-adaptive wavelet-based thresholding methods: VISU-Shrink, SURE-Shrink, and Bayes-Shrink. For clarity, we focus on four test images corrupted by Additive White Gaussian Noise at several noise variance levels. To establish practical performance metrics, numerical results are based on the following image quality metrics: mean-squared error, Peak-Signal-to-Noise Ratio, and Structural Similarity Index. The relative merits of soft and hard thresholding are also explored. Based on MATLAB simulations performed, Bayes-Shrink soft thresholding outperforms VISU-Shrink and SURE-Shrink regardless of the test image, and the amount of additive white Gaussian noise implemented in the noisy image, because of the adaptive nature allowing for more thresholding customization at each sub-band level. Bayes-Shrink soft thresholding, on average, generates an improvement of peak-signal-to-noise ratio of roughly 14.5 dB when comparing the noisy test image with the denoised test image.