HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration

• URL: http://arxiv.org/abs/2407.13120v5
• Date: Fri, 04 Jul 2025 02:26:02 GMT
• Title: HPPP: Halpern-type Preconditioned Proximal Point Algorithms and Applications to Image Restoration
• Authors: Shuchang Zhang, Hui Zhang, Hongxia Wang,
• Abstract summary: We propose a Halpern-type PPP (HPPP) algorithm, which leverages the strong convergence and acceleration properties of Halpern's Hilbert method.<n>Finally, we propose a novel algorithm for image restoration by combining HP algorithm with denoiser priors such as PlugPlay (PP) prior, which can be viewed as an accelerated iteration method.
• Score: 7.614347936574962
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, the degenerate preconditioned proximal point (PPP) method provides a unified and flexible framework for designing and analyzing operator-splitting algorithms such as Douglas-Rachford (DR). However, the degenerate PPP method exhibits weak convergence in the infinite-dimensional Hilbert space and lacks accelerated variants. To address these issues, we propose a Halpern-type PPP (HPPP) algorithm, which leverages the strong convergence and acceleration properties of Halpern's iteration method. Moreover, we propose a novel algorithm for image restoration by combining HPPP with denoiser priors such as Plug-and-Play (PnP) prior, which can be viewed as an accelerated PnP method. Finally, numerical experiments including several toy examples and image restoration validate the effectiveness of our proposed algorithms.

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