{"ID":2871435,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.11397","arxiv_id":"2509.11397","title":"Solving ill-conditioned polynomial equations using score-based priors with application to multi-target detection","abstract":"Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new framework that integrates score-based diffusion priors with moment-based estimators to regularize and solve these nonlinear inverse problems. This introduces a new role for generative models: stabilizing polynomial recovery from noisy statistical features. As a concrete application, we study the multi-target detection (MTD) model in the high-noise regime. We demonstrate two main results: (i) diffusion priors substantially improve recovery from third-order moments, and (ii) they make the super-resolution MTD problem, otherwise ill-posed, feasible. Numerical experiments on MNIST data confirm consistent gains in reconstruction accuracy across SNR levels. Our results suggest a promising new direction for combining generative priors with nonlinear polynomial inverse problems.","short_abstract":"Recovering signals from low-order moments is a fundamental yet notoriously difficult task in inverse problems. This recovery process often reduces to solving ill-conditioned systems of polynomial equations. In this work, we propose a new framework that integrates score-based diffusion priors with moment-based estimator...","url_abs":"https://arxiv.org/abs/2509.11397","url_pdf":"https://arxiv.org/pdf/2509.11397v1","authors":"[\"Rafi Beinhorn\",\"Shay Kreymer\",\"Amnon Balanov\",\"Michael Cohen\",\"Alon Zabatani\",\"Tamir Bendory\"]","published":"2025-09-14T19:21:32Z","proceeding":"eess.SP","tasks":"[\"eess.SP\",\"stat.ML\"]","methods":"[\"Diffusion Model\"]","has_code":false}