Enhanced total variation minimization for stable image reconstruction

The total variation (TV) regularization has phenomenally boosted various variational models for image processing tasks. We propose to combine the backward diffusion process in the earlier literature of image enhancement with the TV regularization, and show that the resulting enhanced TV minimization model is particularly effective for reducing the loss of contrast. The main purpose of this paper is to establish stable reconstruction guarantees for the enhanced TV model from noisy subsampled measurements with two sampling strategies, non-adaptive sampling for general linear measurements and variable-density sampling for Fourier measurements. In particular, under some weaker restricted isometry property conditions, the enhanced TV minimization model is shown to have tighter reconstruction error bounds than various TV-based models for the scenario where the level of noise is significant and the amount of measurements is limited. Advantages of the enhanced TV model are also numerically validated by preliminary experiments on the reconstruction of some synthetic, natural, and medical images.