Year: 2019
Type: preprint
Abstract: We introduce a first order Total Variation type regulariser that decomposes a function into a part with a given Lipschitz constant (which is also allowed to vary spatially) and a jump part. The kernel of this regulariser contains all functions whose Lipschitz constant does not exceed a given value, hence by locally adjusting this value one can determine how much variation is the reconstruction allowed to have. We prove regularising properties of this functional, study its connections to other Total Variation type regularisers and propose a primal dual optimisation scheme. Our numerical experiments demonstrate that the proposed first order regulariser can achieve reconstruction quality similar to that of second order regularisers such as Total Generalised Variation, while requiring significantly less computational time.
Source: arXiv (Cornell University)
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1755984640, Peta-5: A National Facility for Petascale Data Intensive Computation and Analytics, Nonlocal Methods for Arbitrary Data Sources, Robust and Efficient Analysis Approaches of Remote Imagery for Assessing Population and Forest Health in India, G2978676218, G358276009, CHallenges in Preservation of Structure, EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, G751609732, PET++: Improving Localisation, Diagnosis and Quantification in Clinical and Medical PET Imaging with Randomised Optimisation, G81539058
OpenAlex ID: W2994418036