Two-stage Geometric Information Guided Image Reconstruction

Jing Qin, Weihong Guo

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


In compressive sensing, it is challenging to reconstruct image of high quality from very few noisy linear projections. Existing methods mostly work well on piecewise constant images but not so well on piecewise smooth images such as natural images, medical images that contain a lot of details. We propose a two-stage method called GeoCS to recover images with rich geometric information from very limited amount of noisy measurements. The method adopts the shearlet transform that is mathematically proven to be optimal in sparsely representing images containing anisotropic features such as edges, corners, spikes etc. It also uses the weighted total variation (TV) sparsity with spatially variant weights to preserve sharp edges but to reduce the staircase effects of TV. Geometric information extracted from the results of stage I serves as an initial prior for stage II which alternates image reconstruction and geometric information update in a mutually beneficial way. GeoCS has been tested on incomplete spectral Fourier samples. It is applicable to other types of measurements as well. Experimental results on various complicated images show that GeoCS is efficient and generates high-quality images.

Original languageEnglish
Title of host publicationAssociation for Women in Mathematics Series
Number of pages21
StatePublished - 2021

Publication series

NameAssociation for Women in Mathematics Series
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741

Bibliographical note

Publisher Copyright:
© 2021, The Authors and the Association for Women in Mathematics.


  • ADMM
  • Compressive sensing
  • Shearlet transform
  • Split Bregman
  • Weighted TV

ASJC Scopus subject areas

  • Gender Studies
  • General Mathematics


Dive into the research topics of 'Two-stage Geometric Information Guided Image Reconstruction'. Together they form a unique fingerprint.

Cite this