  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.
