Abstract

(Higher order) total variation regularization methods are examined in the context of image reconstruction and denoising. With the staircasing effect and the loss of contrast, two well known drawbacks of the total variation (TV) as regularizer are addressed and thus higher order extensions to prevent the former one, namely infimal convolution total variation (ICTV) and generalized total variation (GTV), are discussed. The presented methods are finally applied to image reconstruction in positron emission tomography (PET). In particular in cases where standard reconstruction algorithms (as e.g. EM) only produce noisy images, extensions with TV and GTV regularization, further improved by Bregman iterations, produce superior results.