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To benefit from the learned multiple graphs\u2019 property and enhance interpretability, we study the spectral property of speech samples in the joint vertex-frequency domain by using the new graph weight matrix. Moreover, we propose the representation of minimum mean-square error (MMSE) graph spectral magnitude estimator for speech signals residing on undirected multiple graphs. We use the MMSE graph spectral magnitude estimator to improve speech enhancement performance. The numerical simulation results show that the proposed method outperforms the existing methods in graph signal processing (GSP) and the baseline methods for speech enhancement in discrete signal processing (DSP) in terms of PESQ, LLR, output SNR, and STOI results. These results also demonstrate the validity of the learned multiple graphs.<\/jats:p>","DOI":"10.1186\/s13636-023-00272-z","type":"journal-article","created":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T13:03:51Z","timestamp":1675429431000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An MMSE graph spectral magnitude estimator for speech signals residing on an undirected multiple graph"],"prefix":"10.1186","volume":"2023","author":[{"given":"Tingting","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haiyan","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zirui","family":"Ge","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiquan","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhen","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,2,3]]},"reference":[{"issue":"5","key":"272_CR1","doi-asserted-by":"publisher","first-page":"808","DOI":"10.1109\/JPROC.2018.2820126","volume":"106","author":"A Ortega","year":"2018","unstructured":"A. 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