研究目的
To develop a new variational model and proximal algorithm for joint image denoising and contour detection based on the Ambrosio–Tortorelli approximation of the Mumford–Shah functional, with flexibility in penalization choices and convergence guarantees.
研究成果
The proposed method effectively performs joint image denoising and contour detection, producing piecewise smooth results without staircasing effects. It offers faster convergence compared to recent discrete formulations, with proven local convergence guarantees. Future directions include extending to nonconvex penalizations and applications in textured image segmentation.
研究不足
The model is limited to convex penalizations (?1 and quadratic-?1) in this study; nonconvex penalizations like ?0 are mentioned but not extensively explored. The method may not handle textured images well, as indicated for future work. Computational cost, while lower than some methods, still increases with image size.
1：Experimental Design and Method Selection:
The methodology involves adapting the Proximal Alternating Minimization (PAM) algorithm to minimize a nonconvex functional derived from the Ambrosio–Tortorelli approximation. The functional includes terms for data fidelity, smoothness, and penalization (?1-norm or quadratic-?1). Closed-form expressions for proximal operators are derived to facilitate optimization.
2：1). Closed-form expressions for proximal operators are derived to facilitate optimization.
Sample Selection and Data Sources:
2. Sample Selection and Data Sources: Experiments are conducted on noisy images with additive white Gaussian noise (variance 0.2) of different sizes (e.g., 128x128, 256x256, 512x512 pixels).
3：2) of different sizes (e.g., 128x128, 256x256, 512x512 pixels).
List of Experimental Equipment and Materials:
3. List of Experimental Equipment and Materials: No specific hardware or software is mentioned; the work is computational, likely using standard computing environments.
4：Experimental Procedures and Operational Workflow:
The algorithm alternates between updating the image u and the contour variable v using proximal steps. Parameters are set as γk = δk = 0.99 / (β ||D||^2) for convergence, with ε fixed at 10^-5. Comparisons are made with state-of-the-art methods like TV minimization, MS relaxation, and Discrete AT.
5：99 / (β ||D||^2) for convergence, with ε fixed at 10^-Comparisons are made with state-of-the-art methods like TV minimization, MS relaxation, and Discrete AT.
Data Analysis Methods:
5. Data Analysis Methods: Performance is evaluated using Signal-to-Noise Ratio (SNR) and Structural Similarity (SSIM) metrics for denoising quality, and computational time is measured for efficiency.
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