Greedy regression in sparse coding space for single-image super-resolution

  • Authors:

  • Yi Tang;Yuan Yuan;Pingkun Yan;Xuelong Li

  • Affiliations:

  • Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, ...;Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, ...;Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, ...;Center for OPTical IMagery Analysis and Learning (OPTIMAL), State Key Laboratory of Transient Optics and Photonics, Xi'an Institute of Optics and Precision Mechanics, Chinese Academy of Sciences, ...

  • Venue:
  • Journal of Visual Communication and Image Representation
  • Year:
  • 2013

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Abstract

Based on the assumption about the sparse representation of natural images and the theory of compressed sensing, very promising results about single-image super-resolution were obtained by an excellent algorithm introduced by Yang et al. [45]. However, their success could not be well explained theoretically. The lack of theoretical insight has hindered the further improvement of the algorithm. In this paper, Yang's algorithm is revisited in the view of learning theory. According to this point, Yang's algorithm can be considered as a linear regression method in a special feature space which is named as sparse coding space by us. In fact, it has been shown that Yang's algorithm is a result of optimal linear estimation in sparse coding space. More importantly, our theoretical analysis suggests that Yang's algorithm can be improved by using more flexible regression methods than the linear regression method. Following the idea, a novel single-image super-resolution algorithm which is designed based on the framework of L"2-Boosting is proposed in the paper. The experimental results show the effectiveness of the proposed algorithm by comparing with other methods, which verify our theoretical analysis about Yang's algorithm.