  The total variation-based image denoising model has been generalized and
extended in numerous ways, improving its performance in different contexts. We
propose a new penalty function motivated by the recent progress in the
statistical literature on high-dimensional variable selection. Using a
particular instantiation of the majorization-minimization algorithm, the
optimization problem can be efficiently solved and the computational procedure
realized is similar to the spatially adaptive total variation model. Our
two-pixel image model shows theoretically that the new penalty function solves
the bias problem inherent in the total variation model. The superior
performance of the new penalty is demonstrated through several experiments. Our
investigation is limited to "blocky" images which have small total variation.
