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A new sparse domain approach is proposed in this paper to realize the single image super-resolution (SR) reconstruction based upon one single hybrid dictionary, which is deduced from the mixture of both the high resolution (HR) image patch samples and the low resolution (LR) ones. Moreover, a linear model is proposed to characterize the relationship between the sparse representations of both the HR image patches and the corresponding LR ones over the same hybrid dictionary. It is shown that, the requirement on the identical sparse representation of both HR and LR image patches over the corresponding HR dictionary and the LR dictionary can be relaxed. It is unveiled that, the use of one single hybrid dictionary can not only provide a more flexible framework to keep the similar sparse characteristics between the HR patches and the corresponding degenerated LR patches, but also to accommodate their differences. On this basis, the sparse domain based SR reconstruction problem is reformulated. Moreover, the proposed linear model between the sparse representations of both the HR patch and the corresponding LR patch over the same hybrid dictionary offers us a new method to interpret the image degeneration characteristics in sparse domain. Finally, practical experimental results are presented to test and verify the proposed SR approach. [ABSTRACT FROM AUTHOR]

Many problems in signal processing and statistical inference involve finding sparse solution to some underdetermined linear system of equations. This is also the application condition of compressive sensing (CS) which can find the sparse solution from the measurements far less than the original signal. In this paper, we propose l1- and l2-norm joint regularization based reconstruction framework to approach the original l0-norm based sparseness-inducing constrained sparse signal reconstruction problem. Firstly, it is shown that, by employing the simple conjugate gradient algorithm, the new formulation provides an effective framework to deduce the solution as the original sparse signal reconstruction problem with l0-norm regularization item. Secondly, the upper reconstruction error limit is presented for the proposed sparse signal reconstruction framework, and it is unveiled that a smaller reconstruction error than l1-norm relaxation approaches can be realized by using the proposed scheme in most cases. Finally, simulation results are presented to validate the proposed sparse signal reconstruction approach. [ABSTRACT FROM AUTHOR]