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A two-stage proximal gradient algorithm for sparse optimization problems
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DOI：10.1016/j.sigpro.2026.110600.png)
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Abstract
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Sparse signal recovery and image reconstruction represent crucial areas within sparse optimization research. This work extends the nonconvex ℓ0 minimization framework to complex-valued problems, enhancing sparsity promotion in noisy signal recovery applications and image reconstruction tasks. Drawing inspiration from the proven effectiveness of logarithmic total variation regularization and nonconvex continuous surrogate functions, we develop a novel two-stage accelerated proximal gradient algorithm. The proposed method achieves superior computational efficiency without compromising numerical precision. Notably, it significantly reduces the staircase artifacts that commonly plague continuous function approximation, as demonstrated by our numerical metric. Theoretical analysis coupled with comprehensive numerical experiments validates the algorithm’s efficiency and convergence behavior across both optimization stages in various application scenarios.
Keywords:
sparse signal recovery
image reconstruction
nonconvex ℓ0 minimization
proximal gradient algorithm
staircase artifacts
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