| Citation: |
He Wang, Haichuan Ma, Luoyi Shi, Yasong Chen. A NOVEL RELAXATION PROJECTION METHOD FOR SOLVING SPLIT EQUALITY PROBLEMS AND ITS APPLICATION IN SIGNAL PROCESSING[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2751-2770. doi: 10.11948/20260048
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A NOVEL RELAXATION PROJECTION METHOD FOR SOLVING SPLIT EQUALITY PROBLEMS AND ITS APPLICATION IN SIGNAL PROCESSING
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Abstract
The split equality problem(SEP) finds significant applications in fields including image reconstruction, language processing, and seismic exploration, all of which often demand real-time processing. Thus, how to effectively enhance the convergence speed of algorithms has long been a core concern for researchers and engineers. To address this challenge, this paper proposes a novel relaxed projection approach for solving the split equality problem in real Hilbert spaces. Specifically, the relaxed projections introduced herein are computed via simple operations at each iteration step. On one hand, the relaxation technique accelerates the algorithm's convergence; on the other hand, it mitigates the computational difficulty associated with general metric projections. Under mild conditions, we analyze the weak convergence of the proposed algorithm. Finally, two numerical experiments, one involving an application to signal recovery and another to image deblurring are conducted to demonstrate the advantages of the proposed method over a recently developed related algorithm.
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References
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He Wang, Haichuan Ma, Luoyi Shi, Yasong Chen. A NOVEL RELAXATION PROJECTION METHOD FOR SOLVING SPLIT EQUALITY PROBLEMS AND ITS APPLICATION IN SIGNAL PROCESSING[J]. Journal of Applied Analysis & Computation, 2026, 16(5): 2751-2770. doi: 10.11948/20260048
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Figure 1.
From left to right:
$ {\text{Case}} $ -
Figure 2.
Original images.
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Figure 3.
Images that have been blurred by the matrices
$ M_{\text{Gauss}} $ $ M_{\text{Circle}} $ $ M_{\text{Motion}} $ -
Figure 4.
Images that have been restored by the Proposed Algorithm 1, Algorithm 2 and Modafi ACQA/RACQA, where the oringinal image is Car.tif and all the algorithm's iteration number k=3200.
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Figure 5.
Images that have been restored by the Proposed Algorithm 1, Algorithm 2 and Modafi ACQA/RACQA, where the oringinal image is Door.tif and all the algorithm's iteration number k=3200.