Wavelet methods for a weighted sparsity penalty for region of interest tomography. (21st January 2015)

• Record Type: Journal Article
• Authors: Klann, Esther; Quinto, Eric Todd; Ramlau, Ronny
• Is Part Of: Inverse problems. Volume 31:Number 2(2015:Feb.)
• Publication Date: 2015-01-21
• Subjects: region of interest tomography -- uniqueness -- wavelets -- sparsity -- piecewise constant; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/31/2/025001
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: 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 ℓ p –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.