2014/07/09 by Kati Niinimäki, Niinimäki, Kati, Matti Lassas +11
Engineering · Medicine · #Advanced MRI Techniques and Applications #Advanced X-ray and CT Imaging #FOS: Mathematics #Medical Imaging Techniques and Applications #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1407.2386
openalex publication_date 2014/07/09 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
A computational method is introduced for choosing the regularization\nparameter for total variation (TV) regularization. The approach is based on\ncomputing reconstructions at a few different resolutions and various values of\nregularization parameter. The chosen parameter is the smallest one resulting in\napproximately discretization-invariant TV norms of the reconstructions. The\nmethod is tested with X-ray tomography data measured from a walnut and compared\nto the S-curve method. The proposed method seems to automatically adapt to the\ndesired resolution and noise level, and it yields useful results in the tests.\nThe results are comparable to those of the S-curve method; however, the S-curve\nmethod needs a priori information about the sparsity of the unknown, while the\nproposed method does not need any a priori information (apart from the choice\nof a desired resolution). Mathematical analysis is presented for (partial)\nunderstanding of the properties of the proposed parameter choice method. It is\nrigorously proven that the TV norms of the reconstructions converge with any\nchoice of regularization parameter.\n