Abstract

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 TV(cid:2)1 , which enforces the sparsity and the directional continuity in the gradient domain. Our TV(cid:2)1 based CS is characterized by the following attributes. First, by minimizing the (cid:2)1 -norm of partial gradients, it can achieve greater accuracy than the widely-used TV(cid:2)1 (cid:2)2 based CS. Second, it, named hy- brid CS, combines low-resolution sampling (LRS) and random sampling (RS), which is motivated by our induction that these two sampling methods are com- plementary. Finally, our theoretical and experimental results demonstrate that our hybrid CS using TV(cid:2)1 yields sharper and more accurate images.