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<p>In this paper, we focus on the problem of phase retrieval from intensity measurements of the short-time linear canonical transform (STLCT). Specifically, we show that the STLCT enables unique recovery of any square-integrable function in high-dimensional space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{2}(\mathbb {R}^{{\textbf {d}}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi mathvariant="bold">d</mi> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> through phaseless STLCT sampling on rectangular square-root lattices. When considering the uniform lattices, we construct counterexamples in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^{2}(\mathbb {R})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>L</mi> <mn>2</mn> </msup> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="double-struck">R</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> that demonstrate the limitations of STLCT phase retrieval in this setting. Nevertheless, for functions in band-limited function spaces, phase retrieval can still be achieved on uniform lattices.</p>

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Phaseless sampling with short-time linear canonical transform on square-root lattices

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Yali Dong,
  • Rui Liu,
  • Heying Wang

摘要

In this paper, we focus on the problem of phase retrieval from intensity measurements of the short-time linear canonical transform (STLCT). Specifically, we show that the STLCT enables unique recovery of any square-integrable function in high-dimensional space \(L^{2}(\mathbb {R}^{{\textbf {d}}})\) L 2 ( R d ) through phaseless STLCT sampling on rectangular square-root lattices. When considering the uniform lattices, we construct counterexamples in \(L^{2}(\mathbb {R})\) L 2 ( R ) that demonstrate the limitations of STLCT phase retrieval in this setting. Nevertheless, for functions in band-limited function spaces, phase retrieval can still be achieved on uniform lattices.