Wavelet methods for a weighted sparsity penalty for region of interest tomography

We consider region of interest (ROI) tomography of piecewise constant functions. Additionally, an algorithm is developed for ROI tomography of piecewise constant functions using a Haar wavelet basis. A weighted ℓp–penalty is used with weights that depend on the relative location of wavelets to the region of interest. We prove that the proposed method is a regularization method, i.e., that the regularized solutions converge to the exact piecewise constant solution if the noise tends to zero. Tests on phantoms demonstrate the effectiveness of the method.FWF, T 529-N18, Mumford-Shah models for tomography IINSF, 1311558, Tomography and Microlocal AnalysisFWF, W 1214, Doktoratskolleg "Computational Mathematics