{"ID":2884857,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.06490","arxiv_id":"2508.06490","title":"Multivariate Fields of Experts for Convergent Image Reconstruction","abstract":"We introduce the multivariate fields of experts, a new framework for the learning of image priors. Our model generalizes existing fields of experts methods by incorporating multivariate potential functions constructed via Moreau envelopes of the $\\ell_\\infty$-norm. We demonstrate the effectiveness of our proposal across a range of inverse problems that include image denoising, deblurring, compressed-sensing magnetic-resonance imaging, and computed tomography. The proposed approach outperforms comparable univariate models and achieves performance close to that of deep-learning-based regularizers while being significantly faster, requiring fewer parameters, and being trained on substantially fewer data. In addition, our model retains a high level of interpretability due to its structured design. It is supported by theoretical convergence guarantees which ensure reliability in sensitive reconstruction tasks.","short_abstract":"We introduce the multivariate fields of experts, a new framework for the learning of image priors. Our model generalizes existing fields of experts methods by incorporating multivariate potential functions constructed via Moreau envelopes of the $\\ell_\\infty$-norm. We demonstrate the effectiveness of our proposal acros...","url_abs":"https://arxiv.org/abs/2508.06490","url_pdf":"https://arxiv.org/pdf/2508.06490v2","authors":"[\"Stanislas Ducotterd\",\"Michael Unser\"]","published":"2025-08-08T17:58:25Z","proceeding":"eess.IV","tasks":"[\"eess.IV\",\"cs.CV\",\"cs.LG\",\"eess.SP\"]","methods":"[]","has_code":false}