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Sparsity in the resulting estimator of the cross\u2013power is induced through\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\ell _1$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:msub>\n                            <mml:mi>\u2113<\/mml:mi>\n                            <mml:mn>1<\/mml:mn>\n                          <\/mml:msub>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    regularization and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) is used for computing such an estimator. With respect to a standard implementation, we prove that a proper initialization step is sufficient to guarantee the required symmetric and antisymmetric properties of the involved quantities. Further, we show how structural properties of the forward operator can be exploited within the FISTA update in order to make our approach adequate also for large\u2013scale problems such as those arising in the context of brain functional connectivity. The effectiveness of the proposed approach is shown in a practical scenario where we aim at quantifying the statistical relationships between brain regions in the context of non-invasive electromagnetic field recordings. Our results show that our method provides results with a higher specificity than classical approaches based on a two\u2013step procedure where first the hidden process describing the brain activity is estimated through a linear optimization step and then the cortical cross\u2013power spectrum is computed from the estimated time\u2013series.\n                  <\/jats:p>","DOI":"10.1007\/s10957-026-02967-7","type":"journal-article","created":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T04:49:10Z","timestamp":1775882950000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Sparse Optimization of Cross-Power Spectra in Linear Inverse Models from Brain Connectivity"],"prefix":"10.1007","volume":"209","author":[{"given":"Laura","family":"Carini","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Isabella","family":"Furci","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1835-9399","authenticated-orcid":false,"given":"Sara","family":"Sommariva","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2026,4,11]]},"reference":[{"issue":"4","key":"2967_CR1","doi-asserted-by":"publisher","first-page":"3259","DOI":"10.1137\/23M158961X","volume":"34","author":"JF Aujol","year":"2024","unstructured":"Aujol, J.F., Calatroni, L., Dossal, C., Labarri\u00e8re, H., Rondepierre, A.: Parameter-free fista by adaptive restart and backtracking. 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