Standards for Total Variation Denoising

Total Variation Denoising (TV Denoising) is a classical image denoising method proposed by Rudin, Osher, and Fatemi in 1992 (ROF model). The core idea of this method is to smooth noise by minimizing the total variation (TV) of the image while preserving edge information as much as possible.

### Principles of Standard TV Denoising Standard TV denoising adopts the L2 norm as the data fidelity term while introducing a TV regularization term to control the smoothness of the image. The optimization objective can be expressed as minimizing the following energy function: Data fidelity term: Ensures that the difference between the denoised image and the original noisy image is not too large. TV regularization term: Controls the sparsity of the image gradient, making the smoothed image more "piecewise constant," thereby reducing noise while retaining edge structures.

### Texture-Preserving TV Denoising (Gilboa et al.) Although standard TV denoising effectively removes noise, it may excessively smooth details when processing images with rich textures. Guy Gilboa et al. (2003) proposed an improved method by adjusting the weight of the TV regularization term or adopting adaptive strategies to more effectively preserve texture information during denoising.

### MATLAB Implementation Approach Implementing TV denoising in MATLAB typically involves the following steps: Gradient calculation: Use finite difference methods to compute the image gradient. Optimization solving: Employ gradient descent, Split Bregman algorithm, or Alternating Direction Method of Multipliers (ADMM) to solve the TV minimization problem. Parameter adjustment: Tune the regularization parameter to balance denoising strength and detail preservation. Texture optimization: In Gilboa's method, incorporate local texture information to adjust the weight of the TV term.

### Extended Considerations Integration with deep learning: Modern approaches can combine deep neural networks, such as integrating TV with U-Net, to further enhance denoising performance. Non-local TV: Introduce non-local similarity constraints to improve protection of complex textures.

This method is not only applicable to image denoising but can also be extended to noise suppression tasks in fields such as medical imaging and remote sensing images.