Wavelet methods for a weighted sparsity penalty for region of interest tomography. - Quinto, Eric Todd.; Klann, Esther.; Ramlau, Ronny. (Tufts University. Tisch Library., 2016)
We consider region of interest (ROI) tomography of piecewise constant functions.We prove that continuous ROI data determine piecewise constant functions. Additionally,an algorithm is developed for ROI tomography of piecewise constant functionsusing a Haar wavelet basis. A weighted `p–penalty is used with weights that depend on therelative location of wavelets to the region of interest. We prove that the proposed method isa regularization method, i.e., that the regularized solutions converge to the exact piecewiseconstant solution if the noise tends to zero. Tests on phantoms demonstrate the effectivenessof the method.