Optimal Compressive Imaging of Fourier Data

Kutyniok, Gitta und Lim, Wang-Q (2018): Optimal Compressive Imaging of Fourier Data. In: SIAM Journal on Imaging Sciences, Vol. 11, No. 1: pp. 507-546

Abstract

Applications such as magnetic resonance imaging acquire imaging data by point samples of their Fourier transform. This raises the question of balancing the efficiency of the sampling strategies with the approximation accuracy of an associated reconstruction procedure. In this paper, we introduce a novel sampling-reconstruction scheme based on a random anisotropic sampling pattern and a compressed sensing--type reconstruction strategy with a variant of dualizable shearlet frames as sparsifying representation system. For this scheme, we prove asymptotic almost optimality in an approximation theoretic sense for cartoon-like functions as a model class for the imaging data. Finally, we present numerical experiments showing the superiority of our scheme over other approaches.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1936-4954
• Language: English