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Abstract <p> In this paper, we study the recovery conditions of weighted <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\ell_{1}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\ell_{1-2}\)</EquationSource> </InlineEquation>-minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. First, we consider the recovery condition of signals with additive <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\ell_{2}\)</EquationSource> </InlineEquation> noise via <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\ell_{1}\)</EquationSource> </InlineEquation>-minimization in the framework of cumulative coherence when arbitrarily many distinct weights are permitted. We also change this condition in the framework of mutual coherence. Second, we consider the recovery condition of signals with additive <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\ell_{2}\)</EquationSource> </InlineEquation> noise via <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\ell_{1-2}\)</EquationSource> </InlineEquation>-minimization in the framework of mutual coherence when arbitrarily many distinct weights are permitted. </p>

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Theoretical Analysis of Weighted \(\ell_{1}\) and \(\ell_{1-2}\)-Minimization with Multiple Weighting Sets

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • H. Li,
  • L. Guo

摘要

Abstract

In this paper, we study the recovery conditions of weighted \(\ell_{1}\) and \(\ell_{1-2}\) -minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. First, we consider the recovery condition of signals with additive \(\ell_{2}\) noise via \(\ell_{1}\) -minimization in the framework of cumulative coherence when arbitrarily many distinct weights are permitted. We also change this condition in the framework of mutual coherence. Second, we consider the recovery condition of signals with additive \(\ell_{2}\) noise via \(\ell_{1-2}\) -minimization in the framework of mutual coherence when arbitrarily many distinct weights are permitted.