Scholarlink

<p>This paper presents a novel two-stage neural network approach to approximate 2D functions with jump discontinuities from data across varying noise conditions, from noise-free to highly noisy scenarios. While traditional methods struggle particularly with discontinuity detection in high-noise environments, our methodology demonstrates consistent performance across a spectrum of noise levels in synthetic testing. Our approach combines a specialized U-Net architecture for discontinuity detection with a Dual UNet architecture for function reconstruction. The first stage uses a custom U-Net specifically designed to detect discontinuities in function data, demonstrating improved performance compared to general-purpose segmentation models on this task. The second stage introduces a Dual UNet architecture that processes probabilistic region classifications through multi-modal input fusion and detail-preserving reconstruction. Testing on synthetic data shows competitive performance compared to existing spline-based methods across the tested range of noise conditions. Our approach handles both open and closed curve discontinuities. <b>Current scope and limitations:</b> The method is designed for functions with a single jump discontinuity on gridded data. As a learning-based approach, it provides empirical performance without theoretical approximation guarantees. Within these constraints, the methodology demonstrates practical value for noisy environments and may have potential applications in domains such as medical imaging, signal processing, and computational fluid dynamics where robustness to noise is important.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Approximation of 2D function with a jump discontinuity - the high noise case

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年4月28日

查看全文
  • Qusay Muzaffar,
  • David Levin,
  • Michael Werman

摘要

This paper presents a novel two-stage neural network approach to approximate 2D functions with jump discontinuities from data across varying noise conditions, from noise-free to highly noisy scenarios. While traditional methods struggle particularly with discontinuity detection in high-noise environments, our methodology demonstrates consistent performance across a spectrum of noise levels in synthetic testing. Our approach combines a specialized U-Net architecture for discontinuity detection with a Dual UNet architecture for function reconstruction. The first stage uses a custom U-Net specifically designed to detect discontinuities in function data, demonstrating improved performance compared to general-purpose segmentation models on this task. The second stage introduces a Dual UNet architecture that processes probabilistic region classifications through multi-modal input fusion and detail-preserving reconstruction. Testing on synthetic data shows competitive performance compared to existing spline-based methods across the tested range of noise conditions. Our approach handles both open and closed curve discontinuities. Current scope and limitations: The method is designed for functions with a single jump discontinuity on gridded data. As a learning-based approach, it provides empirical performance without theoretical approximation guarantees. Within these constraints, the methodology demonstrates practical value for noisy environments and may have potential applications in domains such as medical imaging, signal processing, and computational fluid dynamics where robustness to noise is important.