Linear inverse problems in imaging
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.
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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].”
From A Comprehensive Review of Blind Deconvolution Techniques for Image Deblurring (2020) · cites this paper as [1]
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- Authors
- Ribes, A., & Schmitt, F.
- ORCID
- Schmitt, Francis
- 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.
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