Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks

Andrade-Loarca, Hector; Kutyniok, Gitta ; Öktem, Ozan und Petersen, Philipp C. (2019): Extraction of Digital Wavefront Sets Using Applied Harmonic Analysis and Deep Neural Networks. In: SIAM Journal on Imaging Sciences, Vol. 12, No. 4: pp. 1936-1966

Abstract

Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct extraction of those. In this paper, we introduce the first algorithmic approach to extract the wavefront set of images, which combines data-based and model-based methods. Based on a celebrated property of the shearlet transform to unravel information on the wavefront set, we extract the wavefront set of an image by first applying a discrete shearlet transform and then feeding local patches of this transform to a deep convolutional neural network trained on labeled data. The resulting algorithm outperforms all competing algorithms in edge-orientation and ramp-orientation detection.

• 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