Cited by 156Numerical methods in inverse problemsImage and Signal Denoising MethodsMedical Imaging Techniques and Applications

Linear inverse problems in imaging

Ribes, Alejandro, Schmitt, Francis·2008·IEEE Signal Processing Magazine

Abstract

Classical techniques for solving linear inverse problems have been presented. Our aim was to show how these classical techniques are applied in current state-of-the-art imaging systems. Moreover, we have provided a classification of the techniques into four families: FT-based, direct reconstruction, indirect reconstruction, and interpolation. We hope that this classification will guide the curious reader into a discipline with a rich bibliography and sometimes sophisticated mathematics. In this survey, we skipped complicated methods to solve inverse problems. Through our examples, we have tried to emphasize the large variety of applications of linear inverse problems in imaging. Two main examples have been examined more deeply in this survey. We hope they have helped the reader to understand the application of the general techniques in two interesting contexts: multispectral imaging and magnetic resonance imaging.

Integrity signals

Registry

Crossref · 10.1109/msp.2008.923099

Cites

31 of 31 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The process of sensing light and converting it into image components is mathematically represented as integration.

    “The process of sensing the light, both incident and reflected from the objects of a scene and converting this sensed component of light into image components is mathematically represented as integration as shown by Ribes and Schmitt [1].”

Cites

Flagged first, then by citations

4 of the 35 references couldn’t be matched to a known paper.

Cited by

Sorted by citations

Authors
Ribes, A., & Schmitt, F.
Venue
IEEE Signal Processing Magazine
Published
2008-07
Volume
25
Issue
4
Pages
84-99
ISSN
1053-5888 (ISSN-L)
OpenAlex
W2100522270
Cited by
154
References
35
Citations by year
2026: 5 · 2025: 10 · 2024: 14 · 2023: 10 · 2022: 12 · 2021: 12 · 2020: 11 · 2019: 7 · 2018: 13 · 2017: 5 · 2016: 6 · 2015: 8 · 2014: 5 · 2013: 6 · 2012: 7
FWCI
9.62
Type
journal article
Language
en
Open access
closed
Locations
IEEE Signal Processing Magazine (publishedVersion)
Funders
Télécom Paris
Topics
  • Physical Sciences › Mathematics › Mathematical Physics › Numerical methods in inverse problems
  • Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
  • Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Medical Imaging Techniques and Applications
Keywords
linear inverse problems, image reconstruction, direct reconstruction, interpolation, multispectral imaging, magnetic resonance imaging

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review