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<p>Compressed sensing (CS) relies on achieving a sufficiently small Restricted Isometry Constant (RIC) for the sensing matrix to accurately reconstruct sparse discrete signals. While the restricted isometry property (RIP) is commonly used to ensure this, additional improvements in RIC can be attained under specific conditions by introducing weights to the sensing matrix, equalizing all nonzero singular values. This work presents a novel method for reweighting the sensing matrix iteratively through the multiplication of the normal equation of the linear system. Demonstrating a consistent convergence of the condition number towards 1 with increasing iterations, our approach establishes an RIC improvement model equivalent to standard compressed sensing. Experimental validations across diverse matrices showcase the enhanced performance of reweighted sensing matrices, offering improved accuracy and efficiency in reconstructing sparse signals within compressed sensing applications.</p>

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Enhancing sparse signal recovery with an improved reweighted sensing matrix method

  • 期刊论文

  • 发表日期：

    2026年4月15日

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  • Elahe Soltani,
  • Farshid Abdollahi

摘要

Compressed sensing (CS) relies on achieving a sufficiently small Restricted Isometry Constant (RIC) for the sensing matrix to accurately reconstruct sparse discrete signals. While the restricted isometry property (RIP) is commonly used to ensure this, additional improvements in RIC can be attained under specific conditions by introducing weights to the sensing matrix, equalizing all nonzero singular values. This work presents a novel method for reweighting the sensing matrix iteratively through the multiplication of the normal equation of the linear system. Demonstrating a consistent convergence of the condition number towards 1 with increasing iterations, our approach establishes an RIC improvement model equivalent to standard compressed sensing. Experimental validations across diverse matrices showcase the enhanced performance of reweighted sensing matrices, offering improved accuracy and efficiency in reconstructing sparse signals within compressed sensing applications.