Statistical Modeling in the Wavelet Domain and Applications

In this thesis, we study statistical models for transform coefficients of two different wavelet transform variants, the pyramidal Discrete Wavelet Transform (DWT) and the Dual-Tree Complex Wavelet Transform (DTCWT). The work is motivated by the high computational demand of many state-of-the-art modeling approaches, although a variety of applications require computationally efficient, yet accurate models which facilitate straightforward parameter estimation and possess an analytically tractable form. In case of the DTCWT, there is also very little literature on (joint) statistical modeling of complex wavelet coefficients, even though it is a wellestablished fact that complex wavelet transforms exhibit striking advantages compared to the DWTwhen it comes to image analysis applications. The statistical models we develop throughout this thesis are utilized in three different areas of image processing. We address the research branches of (probabilistic) texture image retrieval, medical image classification and image watermarking. For each particular field, we provide a brief introduction of the problem, then introduce our contribution and conclude with an extensive experimental section. This includes a comparative study to existing work in literature and, depending on whether computational effort is a crucial issue, a thorough computational analysis of the main building blocks. Our results reveal, that the proposed models are beneficial in the aforementioned areas and improve upon state-of-the-art work. In addition, application of statistical models is not limited to the presented fields. In fact, we presume that other areas of transform domain based image processing, such as denoising or segmentation, can benefit in a similar manner.