Total Variation Denoising

The paper mentions the total variation denoising function: J = tv(I, iter, dt, ep, lam, I0). This implementation uses a gradient descent approach where the time step (dt) controls the update magnitude in each iteration. The epsilon parameter (ep) prevents division by zero in gradient calculations, while lambda (lam) balances between noise removal and fidelity to the original image. When lam=0, the algorithm performs pure denoising without preserving specific features.

Total variation denoising is a widely used image processing technique that progressively reduces noise through iterative smoothing. The algorithm works by minimizing the total variation of the image while preserving edges. The iter parameter determines convergence speed, with higher values providing better denoising but requiring more computation time. The time step dt affects stability - values too large may cause divergence, while very small values slow convergence. The epsilon parameter regularizes the gradient calculation to maintain numerical stability.

Before applying total variation denoising, images must first be converted to grayscale format. The algorithm then performs iterative computations using the specified parameters to gradually reduce noise. Key implementation aspects include: gradient calculation using finite differences, regularization with epsilon to avoid singularities, and weighting between denoising and fidelity terms. By default, the function uses 1 iteration, time step 0.2, epsilon 1, and lambda 0. If no input noisy image I0 is specified, the original image I serves as the default noisy input.

Overall, total variation denoising provides an effective and computationally efficient method for image noise reduction. The method is particularly valuable for preserving edge information while smoothing homogeneous regions, making it suitable for applications requiring both noise removal and feature preservation in digital image processing workflows.