{"doi":"10.3389/fphy.2021.678171","title":"EM Estimation of the X-Ray Spectrum With a Genetically Optimized Step-Wedge Phantom","abstract":"The energy spectrum of an X-ray tube plays an important role in computed tomography (CT), and is often estimated from physical measurement of dedicated phantoms. Usually, this estimation problem is reduced to solving a system of linear equations, which is generally ill-conditioned. In this paper, we optimize a phantom design to find the most effective combinations of thicknesses for different materials. First, we analyze the ill-posedness of the energy spectrum inversion when the number of unknown variables ( N ) and measurements ( M ) are equal, and show the condition number of the system matrix increases exponentially with N if the transmission thicknesses are linearly changed. Then, we present a genetic optimization algorithm to minimize the condition number of the system matrix in a general case ( M < N ) with respect to the selection of thicknesses and types of phantom materials. Finally, in the simulation with Poisson noise we study the accuracy of the spectrum estimation using the expectation-maximum algorithm. Our results indicate that the proposed method allows high-quality spectrum estimation, and the number of measurements is reduced over two thirds of that required by the widely-used method using a phantom with linearly-changed thicknesses.","journal":"Frontiers in Physics","year":2021,"id":203492,"datarank":0.0,"base_score":0.0,"endowment":0.0,"self_citation_contribution":0.0,"citation_network_contribution":0.0,"self_endowment_contribution":0.0,"citer_contribution":0.0,"corpus_percentile":null,"corpus_rank":null,"citation_count":5,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9499,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2021-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":292743,"name":"Fenglei Fan","orcid":"0000-0003-3691-5141","position":1,"is_corresponding":false},{"id":458714,"name":"Wenxiang Cong","orcid":"0000-0003-2908-1759","position":2,"is_corresponding":false},{"id":277821,"name":"Ge Wang","orcid":"0000-0002-2656-7705","position":3,"is_corresponding":false},{"id":542683,"name":"Mengzhou Li","orcid":"0000-0002-0192-5422","position":0,"is_corresponding":true}],"reference_count":23,"raw_metadata":null,"created_at":"2026-07-18T23:51:18.050175Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"fair_f":null,"fair_a":null,"fair_i":null,"fair_r":null,"fair_zscore":null,"fair_rationale":null,"fair_model":null,"fair_agent_version":null,"fair_fulltext_source":null,"fair_has_llm":null,"fair_computed_at":null,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}