Setting:

• Image denoising imposes a compromise between noise reduction and preserving significant image details. To achieve a good performance in this respect, a denoising algorithm has to adapt to image discontinuities. The wavelet representation naturally facilitates the construction of such spatially adaptive algorithms. It compresses the essential information in a signal into relatively few, large coefficients, which represent image details at different resolution scales.

• In this thesis, we further develop some emerging wavelet domain denoising methods. Also, we propose new denoising approaches. Throughout the work, we emphasize the use of spatial context and accurate statistical modeling. For spatial context modeling, we consider two approaches: (1) encoding pixel interactions in a Markov Random Field prior model and (2) a lower complexity local approach, which computes a local spatial activity indicator whose marginal densities are characterized. In practical applications, we often simplify the theory using heuristics, when this leads to algorithms with lower complexity or higher flexibility. Also, we do not propose a universal denoising method, but rather build a library of algorithms suitable for a diversity of applications in close range and remote sensing and in medical imaging.

• Practical results of new algorithms are demonstrated in different applications: in infrared imaging, Ground Penetrating Radar (GPR) imaging, Synthetic Aperture Radar (SAR) im-aging, medical ultrasound and magnetic resonance imaging (MRI).