Hybrid compressive sampling via a new total variation TVL1

Compressive sampling (CS) is aimed at acquiring a signal or image from data which is deemed insufficient by Nyquist/Shannon sampling theorem. Its main idea is to recover a signal from limited measurements by exploring the prior knowledge that the signal is sparse or compressible in some domain. In this paper, we propose a CS approach using a new total-variation measure TVL1, or equivalently TVl1, which enforces the sparsity and the directional continuity in the gradient domain. Our TVl1 based CS is characterized by the following attributes. First, by minimizing the l1-norm of partial gradients, it can achieve greater accuracy than the widely-used TVl1l2 based CS. Second, it, named hybrid CS, combines low-resolution sampling (LRS) and random sampling (RS), which is motivated by our induction that these two sampling methods are complementary. Finally, our theoretical and experimental results demonstrate that our hybrid CS using TVl1 yields sharper and more accurate images.