研究目的
To develop a recursive evaluation of Stein’s unbiased risk estimate (SURE) for automatic parameter selection in total variation-based image denoising and deconvolution, enabling accurate estimation of the regularization parameter and optimal restoration performance.
研究成果
The proposed recursive SURE method provides an accurate and automated way to select the regularization parameter for TV-based image recovery, outperforming the discrepancy principle in terms of PSNR with negligible loss compared to the optimal MSE. It enables monitoring of MSE evolution during iterations and handles large-scale data efficiently via Monte Carlo simulation. Future work should focus on extensions to more complex regularizers and faster optimization techniques.
研究不足
The method requires known noise variance and may be computationally intensive for very large images due to iterative processes. The Monte Carlo simulation introduces stochasticity, and the global search for optimal λ can be time-consuming. Extensions to non-convex regularizers and multiple parameters are not addressed in this work.
1：Experimental Design and Method Selection:
The study uses total variation minimization for image recovery, employing Chambolle's algorithm for denoising and ADMM for deconvolution. A recursive evaluation of SURE is developed to estimate the mean squared error during iterations, with Monte Carlo simulation for practical computation without explicit matrix operations.
2：Sample Selection and Data Sources:
Four test images (Cameraman, Coco, House, Bridge) of sizes 256x256 or 512x512 are used, covering a range of natural images. Images are degraded with additive white Gaussian noise at various variance levels (σ2 = 1, 10, 100, 1000) and blurred with different kernels (rational, separable, uniform, Gaussian) for deconvolution experiments.
3：List of Experimental Equipment and Materials:
Computational resources (e.g., RAM for handling large matrices) are implied but not specified. Software for numerical computations (e.g., for Fourier transforms) is used but not detailed.
4：Experimental Procedures and Operational Workflow:
For denoising, Chambolle's algorithm is iterated with fixed λ, and SURE is computed recursively using Jacobian matrices and Monte Carlo simulation. For deconvolution, ADMM is used with Chambolle's algorithm for inner iterations, and SURE is evaluated similarly. The process involves initializing parameters, performing iterations until convergence (relative error below 10^-5), and computing PSNR for performance measurement.
5：Data Analysis Methods:
Performance is measured using peak signal-to-noise ratio (PSNR). SURE values are compared to true MSE (where accessible) and discrepancy principle results. Statistical analysis involves averaging over noise realizations and parameter searches.
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