This paper introduces a new iterative regularization method for inverse problems, particularly focusing on image processing tasks such as denoising and deblurring. The method is based on Bregman distances and aims to improve upon the traditional Rudin-Osher-Fatemi (ROF) model, which is widely used for image restoration. The ROF model minimizes the total variation of an image to recover the true signal from noisy data, but it often suffers from the "staircasing" effect, which smooths textures and can lead to poor results. The proposed iterative regularization procedure involves updating the estimate of the true signal iteratively using the Bregman distance. Specifically, at each iteration, the estimate is updated by minimizing a modified ROF model that includes the Bregman distance term. This process continues until the residual between the estimate and the noisy image drops below a certain threshold, which is determined by the noise level. The method is shown to converge monotonically to the true noise-free image, and numerical results demonstrate significant improvements over standard models in denoising tasks. The paper also discusses the generalization of the method to other inverse problems and regularization models, such as anisotropic total variation and approximations of total variation. The analysis includes proving the well-definedness of the iterates, monotonicity properties of the residual and Bregman distance, and convergence results for both exact and noisy data. The stopping criterion, based on the discrepancy principle, ensures that the method converges to a solution that is close to the true image, even in the presence of noise.This paper introduces a new iterative regularization method for inverse problems, particularly focusing on image processing tasks such as denoising and deblurring. The method is based on Bregman distances and aims to improve upon the traditional Rudin-Osher-Fatemi (ROF) model, which is widely used for image restoration. The ROF model minimizes the total variation of an image to recover the true signal from noisy data, but it often suffers from the "staircasing" effect, which smooths textures and can lead to poor results. The proposed iterative regularization procedure involves updating the estimate of the true signal iteratively using the Bregman distance. Specifically, at each iteration, the estimate is updated by minimizing a modified ROF model that includes the Bregman distance term. This process continues until the residual between the estimate and the noisy image drops below a certain threshold, which is determined by the noise level. The method is shown to converge monotonically to the true noise-free image, and numerical results demonstrate significant improvements over standard models in denoising tasks. The paper also discusses the generalization of the method to other inverse problems and regularization models, such as anisotropic total variation and approximations of total variation. The analysis includes proving the well-definedness of the iterates, monotonicity properties of the residual and Bregman distance, and convergence results for both exact and noisy data. The stopping criterion, based on the discrepancy principle, ensures that the method converges to a solution that is close to the true image, even in the presence of noise.