Overparameterized models for vector fields

Keren Rotker, Dafna Ben Bashat, Alex M. Bronstein

Research output: Contribution to journalArticlepeer-review

Abstract

Vector fields arise in a variety of quantity measure and visualization techniques, such as fluid flow imaging, motion estimation, deformation measures, and color imaging, leading to a better under-standing of physical phenomena. Recent progress in vector field imaging technologies has emphasized the need for efficient noise removal and reconstruction algorithms. A key ingredient in the successful extraction of signals from noisy measurements is prior information, which can often be represented as a parameterized model. In this work, we extend the overparameterization variational framework in order to perform model-based reconstruction of vector fields. The overparameterization methodol-ogy combines local modeling of the data with global model parameter regularization. By considering the vector field as a linear combination of basis vector fields and appropriate scale and rotation coefficients, we can reduce the denoising problem to a simpler form of coefficient recovery. We in-troduce two versions of the overparameterization framework: a total variation-based method and a sparsity-based method, which relies on the cosparse analysis model. We demonstrate the efficiency of the proposed frameworks for two-and three-dimensional vector fields with linear and quadratic overparameterization models.

Original languageEnglish
Pages (from-to)1386-1414
Number of pages29
JournalSIAM Journal on Imaging Sciences
Volume13
Issue number3
DOIs
StatePublished - 2020
Externally publishedYes

Keywords

  • Cosparsity
  • Denoising
  • Inverse problems
  • Overparameterization
  • Regularization
  • Sparsity
  • Total variation
  • Variational methods
  • Vector fields

Fingerprint

Dive into the research topics of 'Overparameterized models for vector fields'. Together they form a unique fingerprint.

Cite this