Compressive sampling (CS) aims at acquiring a signal at a sampling rate below the Nyquist rate by exploiting prior knowledge that a signal is sparse or correlated in some domain. Despite the remarkable progress in the theory of CS, the sampling rate on a single image required by CS is still very high in practice. In this paper, a non-local compressive sampling (NLCS) recovery method is proposed to further reduce the sampling rate by exploiting non-local patch correlation and local piecewise smoothness present in natural images. Two non-local sparsity measures, i.e., non-local wavelet sparsity and non-local joint sparsity, are proposed to exploit the patch correlation in NLCS. An efﬁcient iterative algorithm is developed to solve the NLCS recovery problem, which is shown to have stable convergence behavior in experiments. The experimental results show that our NLCS signiﬁcantly improves the state-of-the-art of image compressive sampling.
The attendant code is on Xianbiao Shu's page.
- Xianbiao Shu, Narendra Ahuja. "Imaging via Three-dimensional Compressive Sampling (3DCS) ". Proc. of International Conference on Computer Vision (ICCV), 2011,(pdf, code).
- Xianbiao Shu, Narendra Ahuja. "Hybrid Compressive Sampling via a New Total Variation TVL1". Proc. of European Conference on Computer Vision (ECCV), 2010,(pdf, code).
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