Solving ill-conditioned polynomial equations using score-based priors with application to multi-target detection
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914036536311808 |
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| author | Beinhorn, Rafi Kreymer, Shay Balanov, Amnon Cohen, Michael Zabatani, Alon Bendory, Tamir |
| author_facet | Beinhorn, Rafi Kreymer, Shay Balanov, Amnon Cohen, Michael Zabatani, Alon Bendory, Tamir |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Solving ill-conditioned polynomial equations using score-based priors with application to multi-target detection Beinhorn, Rafi Kreymer, Shay Balanov, Amnon Cohen, Michael Zabatani, Alon Bendory, Tamir Signal Processing Machine Learning 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. |
| title | Solving ill-conditioned polynomial equations using score-based priors with application to multi-target detection |
| topic | Signal Processing Machine Learning |
| url | https://arxiv.org/abs/2509.11397 |