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AN EFFICIENT PROXIMAL ALGORITHM FOR SQUARED L1 OVER L2 REGULARIZED SPARSE RECOVERY
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DOI：10.3934/ipi.2026028.png)
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Abstract
En 中文
Regularization plays a crucial role in addressing the fundamental inverse problem of sparse signal recovery. In this paper, we consider a squared L1/L2 regularized model for sparse recovery from noisy measurements. We first establish the existence of optimal solutions to the model under mild conditions. Next, we propose a proximal method for solving a general fractional optimization problem which has the squared L1/L2 regularized model as a special case. We prove that any accumulation point of the solution sequence generated by the proposed method is a critical point of the fractional optimization problem. Under additional KL assumptions on some potential function, we establish the sequential convergence of the proposed method. When this method is specialized to the squared L1/L2 regularized model, the proximal operator involved in each iteration admits a simple closed form solution that can be computed with very low computational cost. Furthermore, for each of the three concrete models, the solution sequence generated by this specialized algorithm converges to a critical point. Numerical experiments demonstrate the superiority of the proposed algorithm for sparse recovery based on squared L1/L2 regularization.
Keywords:
Squared L1/L2 regularization
proximal algorithm
sparse recovery
Journal
I
IF:
1.5
Papers:
59
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