研究目的
To propose and evaluate a method for image denoising that combines Dual Tree Complex Wavelet Transform (DTCWT), Singular Value Decomposition (SVD) with a Frobenius energy correcting factor, and bilateral filtering to overcome limitations of traditional wavelet-based methods, such as shift variance and poor directional selectivity, and to preserve edge details while removing noise.
研究成果
The proposed method combining DTCWT, SVD with Frobenius energy correction, and bilateral filtering effectively denoises images corrupted by white Gaussian noise while preserving edge details. Experimental results on standard images show superior performance in terms of PSNR compared to existing techniques, with average gains of up to approximately 6 dB. This indicates the method's robustness and potential for practical image denoising applications, though further research could explore its applicability to other noise models and real-world images.
研究不足
The method is specifically designed for white Gaussian noise and may not generalize well to other noise types. Computational complexity could be high due to the use of DTCWT, SVD, and bilateral filtering. The approach relies on accurate estimation of noise and signal variances, which might be challenging in practical scenarios. Edge preservation, while improved, may still have limitations in highly textured images.
1：Experimental Design and Method Selection:
The method involves decomposing a noisy image using DTCWT to handle shift invariance and directional selectivity issues. SVD is applied to the approximation sub-band for dimensionality reduction and noise separation, using a Frobenius energy correcting factor. A bilateral filter is used for edge preservation, and bivariate shrinkage function is employed for thresholding based on Bayesian estimation.
2：Sample Selection and Data Sources:
Standard grayscale test images (Lena, Boat, Barbara) of size 512x512 pixels are used, corrupted by additive white Gaussian noise at various power levels (σ = 10, 15, 20, 25, 30).
3：0).
List of Experimental Equipment and Materials:
3. List of Experimental Equipment and Materials: No specific equipment or materials are mentioned; the method is computational and implemented using algorithms, likely in software such as MATLAB (implied by the acknowledgment to Selesnick for MATLAB codes).
4：Experimental Procedures and Operational Workflow:
The image is symmetrically extended to handle boundaries. DTCWT decomposes it into real and imaginary coefficients. SVD is applied to the low-pass coefficient matrix, with singular values adjusted using the Frobenius factor. The resulting matrix is filtered with a bilateral filter. Bivariate shrinkage is applied using estimated noise and signal variances (noise variance estimated by robust median estimator, signal variance by neighbor coefficients). Inverse DTCWT reconstructs the denoised image.
5：Data Analysis Methods:
Performance is evaluated using Peak Signal-to-Noise Ratio (PSNR) in decibels. Results are compared with existing methods (three-scale dependency, bivariate shrinkage with inter-scale dependency, and bivariate shrinkage with local variance) using PSNR values from literature.
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