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<p>We present a novel algorithm for solving the non-negative sparse signal recovery problem. The algorithm employs the concept of interior point methods within the context of sequential quadratic programing to keep the iterations away from the boundaries of the solution space. This approach offers two main benefits that distinguish it from existing methods. First, it generates more accurate search directions by exploiting the Hessian structure of the objective function, achieving a possible superlinear rate of convergence. It has been demonstrated that computing the Hessian is cost-effective. Second, the algorithm initially starts from an all-one vector, which reduces the complexity of the method. This contrasts with many state-of-the-art methods that use the pseudo-inverse to initiate the iterations. Simulation results demonstrate that the proposed approach outperforms some existing state-of-the-art methods under various conditions (e.g., noiseless and noisy scenarios). Furthermore, the proposed method also yields significant results in practical applications such as face recognition.</p>

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Non-negative sparse signal recovery with a feasible based sequential quadratic programming

  • 期刊论文

  • 发表日期：

    2025年6月18日

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  • Mohammad Saeid Alamdari,
  • Masoud Fatemi,
  • Aboozar Ghaffari

摘要

We present a novel algorithm for solving the non-negative sparse signal recovery problem. The algorithm employs the concept of interior point methods within the context of sequential quadratic programing to keep the iterations away from the boundaries of the solution space. This approach offers two main benefits that distinguish it from existing methods. First, it generates more accurate search directions by exploiting the Hessian structure of the objective function, achieving a possible superlinear rate of convergence. It has been demonstrated that computing the Hessian is cost-effective. Second, the algorithm initially starts from an all-one vector, which reduces the complexity of the method. This contrasts with many state-of-the-art methods that use the pseudo-inverse to initiate the iterations. Simulation results demonstrate that the proposed approach outperforms some existing state-of-the-art methods under various conditions (e.g., noiseless and noisy scenarios). Furthermore, the proposed method also yields significant results in practical applications such as face recognition.