The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
A unified approach for inversion problems in intensity-modulated radiation therapy
Open accessAbstract
We propose and study a unified model for handling dose constraints (physical dose, equivalent uniform dose (EUD), etc) and radiation source constraints in a single mathematical framework based on the split feasibility problem. The model does not impose on the constraints an exogenous objective (merit) function. The optimization algorithm minimizes a weighted proximity function that measures the sum of the squares of the distances to the constraint sets. This guarantees convergence to a feasible solution point if the split feasibility problem is consistent (i.e., has a solution), or, otherwise, convergence to a solution that minimally violates the physical dose constraints and EUD constraints. We present computational results that demonstrate the validity of the model and the power of the proposed algorithmic scheme.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Image reconstruction from projections : the fundamentals of computerized tomography
Herman, G. T. (1980) · Academic Press eBooks · Cited by 1,993
On Projection Algorithms for Solving Convex Feasibility Problems
Bauschke, H. H., & Borwein, J. M. (1996) · SIAM Review · doi:10.1137/s0036144593251710 · Cited by 1,654
Fundamentals of Convex Analysis
Hiriart-Urruty, J.-B., & Lemaréchal, C. (2001) · Springer eBooks · doi:10.1007/978-3-642-56468-0 · Cited by 1,402
A multiprojection algorithm using Bregman projections in a product space
Censor, Y., & Elfving, T. (1994) · Numerical Algorithms · doi:10.1007/bf02142692 · Cited by 1,392
Self-citationReporting and analyzing dose distributions: A concept of equivalent uniform dose
Niemierko, A. (1997) · Medical Physics · doi:10.1118/1.598063 · Cited by 1,227
Iterative oblique projection onto convex sets and the split feasibility problem
Byrne, C. L. (2002) · Inverse Problems · doi:10.1088/0266-5611/18/2/310 · Cited by 1,057
(1986) · Acta Applicandae Mathematicae · doi:10.1007/bf00046728 · Cited by 1,022
Parallel optimization: Theory, algorithms, and applications
(1998) · Computers & Mathematics with Applications · doi:10.1016/s0898-1221(98)90713-1 · Cited by 813
Optimization of intensity-modulated radiotherapy plans based on the equivalent uniform dose
Wu, Q., Mohan, R., Niemierko, A., & Schmidt-Ullrich, R. (2002) · International Journal of Radiation Oncology*Biology*Physics · doi:10.1016/s0360-3016(01)02585-8 · Cited by 412
Cited by
A Douglas–Rachford Splitting Approach to Nonsmooth Convex Variational Signal Recovery
Combettes, P. L., & Pesquet, J.-C. (2007) · IEEE Journal of Selected Topics in Signal Processing · doi:10.1109/jstsp.2007.910264 · Cited by 490
Metadata
- Authors
- Censor, Y., Bortfeld, T., Martin, B., & Trofimov, A.
- Venue
- Physics in Medicine and Biology
- Publisher
- IOP Publishing
- Published
- 2006-04-26
- Volume
- 51
- Issue
- 10
- Pages
- 2353-2365
- ISSN
- 0031-9155 (ISSN-L)
- 1361-6560
- OpenAlex
- W2155161834
- Cited by
- 831
- References
- 11
- FWCI
- 6.85
- Type
- journal article
- Language
- en
- Open access
- bronze
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
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: A unified approach for inversion problems in intensity-modulated radiation therapy. https://app.cochat.ai/papers/10.1088/0031-9155/51/10/001
- The paper
- Censor, Y., Bortfeld, T., Martin, B., & Trofimov, A. (2006). A unified approach for inversion problems in intensity-modulated radiation therapy. Physics in Medicine and Biology. https://doi.org/10.1088/0031-9155/51/10/001
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
