{"doi":"10.1002/mrc.5289","title":"Input layer regularization for magnetic resonance relaxometry biexponential parameter estimation","abstract":"Many methods have been developed for estimating the parameters of biexponential decay signals, which arise throughout magnetic resonance relaxometry (MRR) and the physical sciences. This is an intrinsically ill-posed problem so that estimates can depend strongly on noise and underlying parameter values. Regularization has proven to be a remarkably efficient procedure for providing more reliable solutions to ill-posed problems, while, more recently, neural networks have been used for parameter estimation. We re-address the problem of parameter estimation in biexponential models by introducing a novel form of neural network regularization which we call input layer regularization (ILR). Here, inputs to the neural network are composed of a biexponential decay signal augmented by signals constructed from parameters obtained from a regularized nonlinear least-squares estimate of the two decay time constants. We find that ILR results in a reduction in the error of time constant estimates on the order of 15%-50% or more, depending on the metric used and signal-to-noise level, with greater improvement seen for the time constant of the more rapidly decaying component. ILR is compatible with existing regularization techniques and should be applicable to a wide range of parameter estimation problems.","journal":"Magnetic Resonance in Chemistry","year":2022,"id":277719,"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":7,"citer_count":0,"citers_with_citation_signal":0,"citers_with_endowment":0,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":0.9458,"is_data_producer":false,"deposit_databanks":null,"is_oa":true,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":"2022-01-01","fair_score":null,"fair_percentile":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":949780,"name":"Jonathan Palumbo","orcid":null,"position":1,"is_corresponding":false},{"id":949781,"name":"Jay Bisen","orcid":null,"position":2,"is_corresponding":false},{"id":916749,"name":"Chuan Bi","orcid":"0000-0001-8498-5422","position":3,"is_corresponding":false},{"id":317798,"name":"Mustapha Bouhrara","orcid":"0000-0001-6184-669X","position":4,"is_corresponding":false},{"id":539551,"name":"Wojciech Czaja","orcid":"0000-0002-9956-1881","position":5,"is_corresponding":false},{"id":291058,"name":"Richard G. Spencer","orcid":"0000-0001-7101-4328","position":6,"is_corresponding":false},{"id":949329,"name":"Michael Rozowski","orcid":"0000-0002-4348-3685","position":0,"is_corresponding":true}],"reference_count":57,"raw_metadata":null,"created_at":"2026-07-19T00:28:39.226969Z","pmid":"35593385","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":[]}