Scholarlink

<p>We study the inverse problem of reconstructing symmetric <i>m</i>-tensor fields in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {R}^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> from generalized Radon transforms, which arise naturally in areas such as medical imaging, seismology, and tomography. We introduce longitudinal and transversal Radon transforms, along with their momentum variants, which extend classical Radon transforms to tensor fields. We provide explicit kernel characterizations and establish invertibility modulo these kernels. Furthermore, we show that symmetric <i>m</i>-tensor fields can be uniquely recovered from suitable combinations of introduced transforms. Our results provide a mathematical foundation for imaging of tensor-valued physical quantities, going beyond scalar tomography.</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

Generalized Radon transforms over symmetric m-tensor fields in \(\mathbb {R}^n\)

  • 期刊论文

  • 发表日期：

    2026年1月3日

查看全文
  • Anuj Abhishek,
  • Rohit Kumar Mishra,
  • Chandni Thakkar

摘要

We study the inverse problem of reconstructing symmetric m-tensor fields in \(\mathbb {R}^n\) R n from generalized Radon transforms, which arise naturally in areas such as medical imaging, seismology, and tomography. We introduce longitudinal and transversal Radon transforms, along with their momentum variants, which extend classical Radon transforms to tensor fields. We provide explicit kernel characterizations and establish invertibility modulo these kernels. Furthermore, we show that symmetric m-tensor fields can be uniquely recovered from suitable combinations of introduced transforms. Our results provide a mathematical foundation for imaging of tensor-valued physical quantities, going beyond scalar tomography.