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Imaging Sci."],"published-print":{"date-parts":[[2023,9,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Parallel imaging (PI), relying on multicoils to sense [Formula: see text]-space data, is an effective technique to accelerate magnetic resonance imaging by exploiting spatial sensitivity coding of multiple coils, with an integrated compressive sensing (CS) technology to achieve higher acceleration. In this paper, we propose a novel nonconvex reconstruction model and its proximal alternating linearized minimization (PALM) algorithm for PI in a blind setting that MR image and multichannel sensitivity maps are jointly estimated, regularized by image and sensitivity regularizers. Instead of hand-crafting the image and sensitivity regularizers, we propose unrolling the PALM algorithm to be a deep network for Blind Parallel MRI, dubbed as BPMRI-Net, with two learnable subnetworks to substitute the proximal operators of the image and sensitivity regularizers. We theoretically prove the linear convergence of BPMRI-Net as an iterative algorithm, which alternately updates two variables based on the learnable proximal operators. The learned BPMRI-Net can simultaneously output the MR image and sensitivity maps from undersampled multichannel [Formula: see text]-space data even when the number of low-frequency sampling lines in the center of [Formula: see text]-space is small. Numerical results demonstrate the effectiveness of our method with state-of-the-art reconstruction accuracy.<\/jats:p>","DOI":"10.1137\/22m1502094","type":"journal-article","created":{"date-parts":[[2023,9,6]],"date-time":"2023-09-06T08:07:02Z","timestamp":1693987622000},"page":"1791-1824","source":"Crossref","is-referenced-by-count":6,"title":["An Unrolled Implicit Regularization Network for Joint Image and Sensitivity Estimation in Parallel MR Imaging with Convergence Guarantee"],"prefix":"10.1137","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6227-5235","authenticated-orcid":true,"given":"Yan","family":"Yang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, 710049, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1601-9649","authenticated-orcid":true,"given":"Yizhou","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Northeastern University, Boston, MA 02115 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiazhen","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Xi\u2019an Jiaotong University, Xi\u2019an, Shaanxi, 710049, People\u2019s Republic of China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jian","family":"Sun","sequence":"additional","affiliation":[{"name":"Corresponding author. 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