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<p>In this study, we consider the practical low-rank matrix completion problem, i.e., recovering a low-rank matrix from a sampling of its entries. In numerous fields dealing with low-rank structures, data loss and corruption are major concerns. However, this problem is not always solvable. Despite theoretical guarantees based on matrix incoherence and sampling complexity, these conditions serve primarily as foundational assumptions for analysis rather than as practical constraints. Inspired by these theoretical conditions, this paper introduces a novel approach that imposes constraints on the matrix factors. This formulation leads to a novel constrained model that serves as an alternative to the standard nuclear norm minimization problem, from which the classical SVT method is derived. Accordingly, we develop the modified singular value thresholding (MSVT) algorithm based on this reformulated model. It is important to emphasize that our primary contribution lies in redefining the underlying optimization problem rather than proposing a new solution technique; this distinction justifies our focus on comparing the MSVT algorithm with the original SVT method, as both are derived from their respective problem formulations. The proposed model is efficiently solved using a Linearized Alternating Direction Method of Multipliers (LADMM) framework. The incorporated constraint acts as a practical regularizer, guiding the optimization toward solution regions that yield improved empirical recovery. Numerical experiments on real-world datasets demonstrate that the MSVT algorithm achieves higher recovery accuracy and significantly faster convergence compared to the standard SVT method. Furthermore, comparisons with the recently proposed FLGSR approach confirm that MSVT delivers competitive or superior performance in terms of both reconstruction quality and computational efficiency. These results highlight the effectiveness of translating theoretical insights into a practical method for solving matrix completion problems.</p>

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Efficient low-rank image recovery model through a modified singular value thresholding algorithm

  • 期刊论文

  • 发表日期：

    2026年7月10日

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  • Faezeh Aghamohammadi,
  • Fatemeh Shakeri

摘要

In this study, we consider the practical low-rank matrix completion problem, i.e., recovering a low-rank matrix from a sampling of its entries. In numerous fields dealing with low-rank structures, data loss and corruption are major concerns. However, this problem is not always solvable. Despite theoretical guarantees based on matrix incoherence and sampling complexity, these conditions serve primarily as foundational assumptions for analysis rather than as practical constraints. Inspired by these theoretical conditions, this paper introduces a novel approach that imposes constraints on the matrix factors. This formulation leads to a novel constrained model that serves as an alternative to the standard nuclear norm minimization problem, from which the classical SVT method is derived. Accordingly, we develop the modified singular value thresholding (MSVT) algorithm based on this reformulated model. It is important to emphasize that our primary contribution lies in redefining the underlying optimization problem rather than proposing a new solution technique; this distinction justifies our focus on comparing the MSVT algorithm with the original SVT method, as both are derived from their respective problem formulations. The proposed model is efficiently solved using a Linearized Alternating Direction Method of Multipliers (LADMM) framework. The incorporated constraint acts as a practical regularizer, guiding the optimization toward solution regions that yield improved empirical recovery. Numerical experiments on real-world datasets demonstrate that the MSVT algorithm achieves higher recovery accuracy and significantly faster convergence compared to the standard SVT method. Furthermore, comparisons with the recently proposed FLGSR approach confirm that MSVT delivers competitive or superior performance in terms of both reconstruction quality and computational efficiency. These results highlight the effectiveness of translating theoretical insights into a practical method for solving matrix completion problems.