研究目的
To develop an efficient algorithm for image restoration from random sampling noisy frequency data using total variation and wavelet sparsity regularization, with rigorous error estimates and parameter choice strategies.
研究成果
The proposed algorithm effectively restores images from random sampling noisy frequency data by balancing sparsity and edge preservation through TV and wavelet regularization. Numerical results show satisfactory performance with small sampling ratios, and the method outperforms existing schemes in terms of reconstruction quality, though it requires more computation time.
研究不足
The method may not recover all image details perfectly, especially for parts with high grey values, due to the use of partial frequency data and lack of L2 penalty. The inner iteration process can be computationally intensive for large images.
1：Experimental Design and Method Selection:
The study uses an optimization model with total variation and wavelet sparsity regularization. The Bregman iteration scheme is employed for minimization, with an inner iteration process using Tikhonov regularization to solve the Euler-Lagrange equation.
2：Sample Selection and Data Sources:
The experiments use synthetic images (e.g., checkerboard and phantom brain images from MATLAB) and practical MRI brain images. Noisy frequency data are simulated with relative error δ.
3：List of Experimental Equipment and Materials:
A laptop with MATLAB R2017a, Intel Core i5 processor, 8 GB memory.
4：Experimental Procedures and Operational Workflow:
Frequency data are generated with noise, sampled using random band sampling or radial sampling. The Bregman iteration with inner conjugate gradient method is applied to minimize the cost functional.
5：Data Analysis Methods:
Performance is evaluated using improved signal-to-noise ratio (ISNR), relative error (ReErr), and computation time.
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