Compressive Sampling

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 ? 1 -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.